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Fenestration devices for energy conservation—III. The influence of angle-dependent shading coefficients on energy savings
FENESTRATION DEVICES FOR ENERGY CONSERVATION-III. THE INFLUENCE OF ANGLE-DEPENDENT SHADING COEFFICIENTS ON ENERGY SAVINGS-rM. R. BRAMBLEY and S. S. PENNER Energy
Center and Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, La Jolla. CA 92093. U.S.A. (Recrirvd
15 April
1980)
Abstract --~The results of measured, angle-dependent, solar-optical properties are presented for a window film and a sunscreen. These properties are used to determine shading coefficients as functions of the angle of incidence of the direct solar radiation. Energy savings for the coohng season (in the transition climatic region of San Diego County) have been estimated and are compared with results for constant values of the shading coefficients. Constant values of the shading coefficients. derived from solar-optical properties for normally incident direct solar radiation, lead to high estimates (errors of < 10 cents/m’-yr) of energy savings for window films and low estimates (errors of < $1.00/m2-yr) for sunscreens.
NOTATION r % %I> 0 I’ o\(R 4 2x1
integrated absorptance integrated absorptance of glass integrated absorptance of the shading device angle of incidence of the direct (circumsolar) radiation average integrated reflectance monochromatic directional-hemispherical reflectance frequency lower cut-off frequency of the pyranometer window upper cut-off frequency of the pyranometer window average integrated transmittance monochromatic directional transmittance average integrated transmittance of glass average integrated transmittance of the shading device vector specifying the direction of incident solar radiation relative to the fenestration (or pyranometer) solid angle viewed by the pyranometer vector specifying the position of the solar disk relative to the fenestration (or pyranometer) Inside surface combined (radiation and convection) heat-transfer coefficient outside surface combined (radiation and convection) heat-transfer coefficient effective surface to surface heat-transfer coefficient across the air space in the fenestration monochromatic intensity of solar radiation incident from a unit solid angle about the direction R’ solar heat gam heat transfer across a fenestration attributable to temperature differences between the inside and outside shading coefficient; the ratio of the instantaneous solar heat gain through a fenestratlon to the solar heat gain through 3.2 mm (l/8 in.). double-strength. single (DSS) glass solar heat gain factor: the instantaneous solar heat gain through 3.2 mm DSS glass time Inside temperature outside temperature overall coefficient of heat-transfer from outside to inside air
I.
INTRODUCTION
In two previous papers.‘q2 we have given relations for estimating energy savings attributable to the use of fenestration devices and have estimated savings (for the transition tSupported
by the San Diego Gas and Electric
Company
through
a grant
to the UCSD
Energy
Center.
M. R. BRAMBLEYand S. S. PENNER
62
climatic region of San Diego County) using constant values for the shading coefficients (SC). In this paper, we summarize the results of a detailed study3 on the determination of the influence of constant values of SC on estimates of energy savings. We have performed tests on commercially available laminated films with low emissivity in the infrared applied to the inside surface of 3.2 mm (l/8 in.) thick, double-strength, single glass (DSS), and perforated and woven plastic or fiberglass sunscreens.
2. SOLAR-OPTICAL
PROPERTIES
AND
SHADING
COEFFICIENTS
The integrated solar transmittances (5) and reflectances (p) of the samples were measured by using3 procedures that are similar to the ASTM method for determining solar transmittance4 and the ASHRAE method for determining solar-optical properties.” The measured quantities are P” 52
s )‘=I’,s R’=P )(I‘
r,.(Q’)l,..i(Q’) dR’ (1)
s ?=I’,s fl’-fl’
!,.,;(a’) dR’
and
sf VU
\“\‘,
Pl
n,=fl*
VU
’ ~ 2rc)r,..i(n’) py(R
s \‘=v,s Ij’=lP
dR’
r,..i(n') dR’
where rI and r, represent, respectively, the lower and upper frequency cut-offs of the pyranometer, R* is the solid angle viewed by the detector, r,,,i(n’) is the monochromatic intensity of the radiation incident from a unit solid angle about the direction R’, s,,(W) is the monochromatic transmittance of the sample for radiation incident from a unit solid angle about 51’. and p,.@‘-+ 2n) is the monochromatic, directional-hemispherical reflectance of the sample. The numerators in Eqs. (1) and (2) are the total integrated transmitted and reflected intensities, respectively; the denominators represent the total integrated incident intensities. Since the distribution of incident intensity I,,,i(Q’) varies with the position of the sun Sr, (i.e. approximately with the angle of incidence of the direct solar radiation 8), we determine r(0) and p(O). The integrated solar absorptance is defined by the relation $0) =
1 -
[p(e)
+
T(e)].
(3)
Experimental results for a window film and a sunscreen are shown in Figs. l-6. The discontinuity in the slope of r(0) for the sunscreen is attributable to the assumption that T = 0 after 0 reaches a cut-off angle.? The measured properties of 3.2 mm DSS glass are shown in Figs. 7 and 8. Shading coefficients SC are obtained by using relations from Ref. 1. For a window with a film at the glass temperature and applied to the inside surface, the fenestration may be treated as a single pane of glass, i.e.
CT+ (Ur’~~,,)rlri,.,““yla.h
SC= CT+ (~~~~,,)~13.2rnrn~ss~,n,. ’
(4)
where U 1 hi/J,/(hi + II,,). For summer conditions,“’ hi = 12.1, h, = 33.1, and U = 8.86 w/m’-“C (1.46, 4.00, and 1.07 Btu/ft’-hr-“F. respectively). For films with low tThis postulated behavior is not precisely correct. Above the cut-off angle. only diffuse sunlight is transmitted. For clear days, when the diffuse radiant flux contributes _ 20”;, of which less than _ 20’3~~is transmitted. the solar transmittance T is less than _ 4”i.
Fenestration
0.20
devices for energy
63
conservation-111
_.
. .
G ;:
.
‘.
O.lO-
0.00.
I 20
0
I
I 40
I
I 60
I 00
dtdegrees) Fig. I. The observed (.) solar transmittance r(B) is shown for an insulating to the inside surface of I/S in. DSS glass. The line represents a least-squares data points (T = 0.0527 + 0.136 cos0 - 0.0272 cos’0).
window film applied fi to the measured
0.60-
0.50_
040,
0.00
I
0
20
40
60
60
e(degrees) Fig. 2. The observed (‘) integrated solar reflectance ~(0) is shown for an insulating wmdow film applied to the inside surface of l/8 in. DSS glass. The solid curve represents the least-squares fit to the measured data points (p = 0.585 - 0.391 co& + 0.297 cos’0).
o.40 L-----
0.30
c
0.001 0 Fig. 3. The integrated
20
40 f?(degrees)
60
00
solar absorptance of an insulating window film applied surface of I/S in. DSS glass is shown as a function of 0.
to the inside
M. R.
64
BRAMBLEY and
S. S.
PENNER
8(degrees) Fig. 4. The observed (. ) solar transmittance r(6) is shown for a sunscreen. The line represents the least-squares fit to the measured data points (T = - 0.111 + 0.607 cost? - 0.246 co&I).
emittance in the i.r. (i.e. E z 0.24), hi = 6.46 w/m*-“C iJ = 5.39 w/m*-“C (0.65 Btu/ft*-hr-“F); thus, sc
=
CT+ 0.164low cmittancc b
+
o.27
(0.78 Btu/ft*-hr-“F)
and
filmonglass
43.2rnmDSSglass
’
The experimental data have been used in Eq. (5) to obtain SC(e) for a film applied to the inside surface of 3.2 mm DSS glass (see Fig. 9).
°rees
1
Fig. 5. The observed (.) integrated solar reflectance p(B) is shown for a sunscreen. The line represents the least-squares fit to the measured data points (p = 0.474 - 0.522 cos0 + 0.214 co&).
Fenestration
devices for energy
65
conservation-III
060
0.50
_
0.40
UJ a 0.30
0.20
0.10
8 (degrees) Fig. 6. The integrated
solar absorptance
a of a sunscreen
is shown
as a function
of 0.
Sunscreens mounted externally to single glass and separated by an enclosed air-space represent the most effective configuration studied by us. For these,’
1
SC=
3.2mmDSSpla~
0.60s 9
0.500.40
-
0.30
-
0.20
-
0. I 0 0.00
. . I
0
.
20
I
I
I 40
60
80
6 (degrees) Fig. 7. The observed ( .) solar reflectance p(B) of l/8 in. DSS glass is shown. The line represents the relation p = 0.606 - 1.23 cos0 + 0.710cos2B and was obtained by using a least-squares regression on the data.
(6)
66
M. R. BRAMBLEY and S. S. PENNER
*. . “\’
0.30 0.20 0.1 0
0.001 0 20
60
60 40 8 (degrees)
1
Fig. 8. The observed (‘) solar transmittance r(0) of I/S in. DSS glass is shown. The line represents the relation r = 0.378 + 0.949 cos0 - 0.473 co& obtained by using a least-squares regression on the data.
0.205 ” v)o.lo -
0.00
I 20
0
I 40 8 (degrees)
I 00
I 60
Fig. 9. The shading coefficient (SC) for an insulating window film applied to the inside surface of l/8 in. DSS glass is plotted against the angle of incidence 0 of the direct solar radiation.
0.30 -
o^ 0.20 ; 0.10 -
000
I 0
I 20
I 40 8 (degrees)
I 60
80
Fig. 10. The shading coefficient (SC) for a sunscreen mounted externally to l/8 in. DSS glass and separated by an enclosed air-space is shown as a function of the angle of incidence 0 of the direct solar radiation.
Fenestratlon
devices for energy
conservation
61
III
where
hi and /I, have been defined previously, h, is the effective heat-transfer
coefficient between the glass and the screen, and the subscripts SD and y indicate properties of the shading device (screen) and glass, respectively. Using ASHRAE summer conditions at the inside and outside surfaces and h, = 6.63 w/m”-‘C (0.80 Btu/ft’-hr-“F), Eq. (6) becomes (7) The values of SC(@) derived from Eq. (7) are shown in Fig. 10 for a sunscreen. The discontinuity in SC(e) is attributable to the assumption that r(0) = 0 for 8 greater than the cut-off angle. The shading coefficient for sunscreens is strongly dependent on rsr, [set Eq. (7)] and decreases with increasing 8 up to the cut-off angle. Therefore, the applicable average shading coefficient is less than the value measured at normal incidence.
3.
ENERGY
SAVINGS
DURING
THE
COOLING
SEASON
The energy savings attributable to selected fenestration devices compared to single glazing have been evaluated (for the transition climatic region in San Diego County) according to the methodology described in Ref. 1. The heat gains were evaluated using appropriate daily solar heat-gain factors (SHGF) and temperature profiles for each month of the cooling season. The daily heat gains were determined from the relations’ QAT. =
u I”
(T, - TW
(8)
and
Qs -J
(SC) (SHGF) dr
.
(9)
dailycoolinypcr~otl
where QATand Qs are, respectively, the heat gain associated with temperature differences across the fenestration per unit area and the daily solar heat gain; Ti and 7;, are the instantaneous inside and outside temperatures, respectively. Monthly heat gains are obtained by multiplying Qs and Qar by the number of days of the month; seasonal values are obtained by summing over the months of the cooling season. The results obtained using the SC(e) are shown in Table 1, whereas Table 2 shows the corresponding estimates for the constant value of SC at normal incidence for direct solar radiation (0 = 0”). Energy savings compared to 3.2 mm DSS glass are also listed. Since all heat gains through the window during the daily cooling period have been assumed to contribute to the air-conditioning load, the calculated energy savings represent upper limits. The savings for cooling per year, in current dollars, are given for electricity prices of 4.3 and 5.0 cents per kWh. For the film, variations in SC with 0 are so small that use of the constant value of SC at B = 0” results in less than a IO centsim’ increase in the yearly savings for cooling at an electricity price of 4.3 cents,‘kWh (see Tables I and 3).t The largest differences are found for north-facing windows for which sunlight is rarely incident directly. A value of SC for north-facing windows at 6 = 90’ would be more appropriate than the value at 8 = 0”. For screens, the solar heat gains are greater for constant values of the SC (Table 2) than for SC = SC(e) (Table 1). In Ref. 3, we have shown this difference to vary by factors of 1.2 (for a dark sunscreen facing West) to 8.8 (for a white sunscreen facing North). E%timates of monetary savings were shown to increase by up to about 20”/: (compare Tables 1 and 2). tFor
other films tested by us, the greatest
difference
was 27&m’
DSS glass
A representative Bunscreen mounted externall) to 3. 2 mm DSS glass and separate by an enclosed air %pace.
insulating window film adhering to the inside surface of l/8 inch DSS glass.
A re pre tentative
l/8”
Fenestration
see Fig. 1 0
rig. 9
5ee
. 00
SC
3.79
511 125
125
125
602 189
125
I
AT
(kwhth /m2-Yr)
Q
445
tkwhth /m2-yr)
QS
savings=
636
0
0
0
7 27 314
0
(kwhth /m2-yr)
- QT
T l/+3” DSS glass
570
(kwhth /m2-yr)
%=Q~+Q~~
Q
Energy
@4.
NA
NA
NA
NA
NA NA
NA
@5. Ob/bh NA
3d/kwh
wm2-yr)
Value of cooling savings
Table 1. Fenestration performance characteristics of 3.2 mm (l/S in.) DSS glass, a window film applied to a single glass, and a sunscreen mounted externally and separated by an enclosed air space during the cooling season (May through October) in the transition climatic region of San Diego County. The data refer to SC(B) (see Figs. 9 and 10) and were determined from experimentally measured solar-optical properties, solar heat gain factors applicable for a clear day on the 21st of each month, an indoor temperature of 18.3”C (65”F), representative outdoor daily temperature profiles for each month based on monthly mean daily maximum and minimum temperatures, and a COP = 3.0 for an electric air-conditioner.
A representative sunscreen mounted externally to 3. 2mm DSS glass and separated by an enclosed airs pace.
A re pre sentative insulating window film adhering to the inside surface of l/8 inch DSS glass.
Fenestration
0.330
0. 249
SC
3.79
5. 39
(w/m2-“C)
u
1
I
63 170
North
East
199
west
127
47
150
111
th /m2-yr)
148
I
1
1
I
(hh
South
East
North
West
South
Orientation
QS
I
I
I
I
AT
117 224
54 54
368
253
54
412
197
47 4
202
190
54
I
432
124 204
77
77
77
77
(kwhth /m2-yr)
Q
($/m2-yr)
Value of cooling savings
Table 2. Fenestration performance characteristics of an insulating window film applied to 3.2 mm (I ;8 in.) DSS glass. and a Sunscreen mounted externally and separated by an enclosed air space during the cooling Season (May through October) in the transition climatic region of San Diego County. The data refer to constant values of the SC corresponding to solar-optical propertics for normally incident, direct solar radiation (0 = O), solar heat gain factors applicable for a clear day on the 21st of each month. an Indoor temperature of 18.3 C (65 F). representative outdoor daily temperature profiles for each month based on monthly mean daily maximum and minimum temperatures. and a COP = 3.0 for an electric air-conditioner
M. R. BRAMBLEY and S. S. PENKER
70 Table
3. The particular
constant values of the SC which yield calculated values of solar heat gains (Q.) that are equal to the values obtained by using SC(O); also shown are the constant values of the SC at B = 0
seasonal
Orientation
A
South
East
West
0. 286
0. 247
0. 252
0. 249
0. 249
0. 148
0.193
0. 237
0. 252
0
representative
insulating film
window
adhering
the of
North
inside
to
surface
3.2mmDSS
glass. A representative sunscreen mounted to
3.2
glass by
externally mm and
DSS
330
separated
an enclosed
air-
space.
In Table 3, we list the particular constant values of the SC which correspond to actual energy savings estimated by using variable SC(e), together with the values corresponding to 8 = 0”. These results again indicate that the performance of insulating window films is only minimally affected by the use of variable shading coefficients. On the other hand, sunscreens perform more effectively during the cooling season than would be expected for shading coefficients at H = 0”. in general, the values of the SC for north-facing windows should correspond to larger angles of incidence (i.e. H = 90’) than 8 = 0’. 4. CONCLUSIONS
The transmitted solar radiation comprises approx. 76% of the solar heat gain through a single pane of glass with an insulating film and 98% without the film. The shading coefficient varies with 8 approximately in the same manner as the ratio of the transmittances (5, ow emittance film on gl~s/~3.2 mm DSS glass ). This ratio is nearly constant for 0 2 60”. At larger values of 8, the transmittance of the glass decreases somewhat faster with increasing 8 than the transmittance of the glass-film combination, thus leading to a small increase in SC with increasing 8 (see Fig. 9) between 60 and 90”. Since the film is in intimate contact with the glass, this fenestration behaves essentially like a single pane of glass and the shading coefficient is therefore nearly constant. The use of SC(e) instead of a constant value at normal incidence (0 = 0’) affects estimates of energy and monetary savings neglibly. Thus, the use of a constant value for the SC of films on glass constitutes a good approximation. For a sunscreen mounted externally to single glazing, about 72% of the solar heat gain is attributable to transmitted solar radiation at 0 = 0”. The value of SC(e) is roughly proportional to the transmittance of the shading device, T&8), for 0 less than the cut-off angle [see Eq. (7)]. For 8 greater than the cut-off angle, T&e) = 0 and SC(e) becomes [see Eq. (7)] approximately proportional to the ratio %D/T~. The transmittance of the glass T,(o) decreases faster than the absorptance of the shading device [%n(8)] with increasing 8 (compare Figs. 6 and 8). As the result, d(SC)/dB > 0 for 8 greater than the cut-off angle. The sunscreen and glass are separated by an air space in this fenestration device. The screen shields the glass from progressively more of the incident solar radiation as 8 is increased, while the solar radiation incident on unshaded glass varies as CO& The solar radiation on the screened glass varies as T&o) cd where T&e) is a decreasing function of 8 up to the cut-off angle. For screened windows, constant values of the SC (at 0 = 0’) yield solar heat gains that are too large3 by up to 880% and corresponding estimates of energy and monetary savings that are too small by up to 20%.
Fenestration
devices for energy
conservatton
111
71
These results indicate that variable SC(e) must be used to estimate solar heat gains properly for screened. externally shaded windows and that the introduction of a constant value for the shading coefficient at 0 = 0” does not lead to a satisfactory simplified procedure for estimating solar heat gains.
REFERENCES and S. S. Penner. Eurry,r 4. I (1979). M. R. Brambley and S. S. Penner, /37rryy 4. 27 (1979). M. R. Brambley and S. S. Penner, Fenestration devices for energy conservation -III. Experimental results for selected fenestrations. Energy Center and Department of Applied Mechanics and Engineering Sciences. liniversity of California. San Diego, La Jolla. CA 92093. 129 pp. (March 1980). Copies of this report are available from the authors on request. ASTM Standard E 424-71. “Standard Methods of Test for Solar Energy Transmittance and ReHectance (Terrestrial) of Sheet Materials”, American Society for Testing and Materrals. 1971. ASHRAE Standard 74.~73, “Method of Measuring Solar-Optical Properties of Materials”, The Amertcan Society of Heating. Refrigerating. and Air-Conditioning Engineers. 1973. .ASHRAE Htuldhook of Fuudurnrnrtrls, American Society of Heatrng. Refrigeratrng. and Atr-Condrtionrng f ngrnecrs. New York ( 1977).
I. M. R. Brambley
2. 3.
4. 5. 6.
APPENDIX
Using measured properties, we find that window (fly) screens produce from - 554<, (for west-facing windows) to - loo”, for north-facing windows of the solar-energy reduction achieved by specially designed sunscreens and insulating window films. Payback periods have been computed as functions of installation costs (C), with the electricity price as a parameter. for window (fly) screens replaced by sunscreens during the cooling season in the transition region of San Diego County. Acceptable payback periods of less than _ 6 years are achieved only for installation costs 2 $2.60/ft2 ($27.99/m’), even for west-facing windows at an electricity price of I.Oc/kWh. Payback periods for north-facing windows, for C 5 $l/ft’, exceed the IO-year life of the devices. These results indicate that undamaged window screens should generally not be replaced with sunscreens unless the installation costs for the sunscreens are very low.
Center and Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, La Jolla. CA 92093. U.S.A. (Recrirvd
15 April
1980)
Abstract --~The results of measured, angle-dependent, solar-optical properties are presented for a window film and a sunscreen. These properties are used to determine shading coefficients as functions of the angle of incidence of the direct solar radiation. Energy savings for the coohng season (in the transition climatic region of San Diego County) have been estimated and are compared with results for constant values of the shading coefficients. Constant values of the shading coefficients. derived from solar-optical properties for normally incident direct solar radiation, lead to high estimates (errors of < 10 cents/m’-yr) of energy savings for window films and low estimates (errors of < $1.00/m2-yr) for sunscreens.
NOTATION r % %I> 0 I’ o\(R 4 2x1
integrated absorptance integrated absorptance of glass integrated absorptance of the shading device angle of incidence of the direct (circumsolar) radiation average integrated reflectance monochromatic directional-hemispherical reflectance frequency lower cut-off frequency of the pyranometer window upper cut-off frequency of the pyranometer window average integrated transmittance monochromatic directional transmittance average integrated transmittance of glass average integrated transmittance of the shading device vector specifying the direction of incident solar radiation relative to the fenestration (or pyranometer) solid angle viewed by the pyranometer vector specifying the position of the solar disk relative to the fenestration (or pyranometer) Inside surface combined (radiation and convection) heat-transfer coefficient outside surface combined (radiation and convection) heat-transfer coefficient effective surface to surface heat-transfer coefficient across the air space in the fenestration monochromatic intensity of solar radiation incident from a unit solid angle about the direction R’ solar heat gam heat transfer across a fenestration attributable to temperature differences between the inside and outside shading coefficient; the ratio of the instantaneous solar heat gain through a fenestratlon to the solar heat gain through 3.2 mm (l/8 in.). double-strength. single (DSS) glass solar heat gain factor: the instantaneous solar heat gain through 3.2 mm DSS glass time Inside temperature outside temperature overall coefficient of heat-transfer from outside to inside air
I.
INTRODUCTION
In two previous papers.‘q2 we have given relations for estimating energy savings attributable to the use of fenestration devices and have estimated savings (for the transition tSupported
by the San Diego Gas and Electric
Company
through
a grant
to the UCSD
Energy
Center.
M. R. BRAMBLEYand S. S. PENNER
62
climatic region of San Diego County) using constant values for the shading coefficients (SC). In this paper, we summarize the results of a detailed study3 on the determination of the influence of constant values of SC on estimates of energy savings. We have performed tests on commercially available laminated films with low emissivity in the infrared applied to the inside surface of 3.2 mm (l/8 in.) thick, double-strength, single glass (DSS), and perforated and woven plastic or fiberglass sunscreens.
2. SOLAR-OPTICAL
PROPERTIES
AND
SHADING
COEFFICIENTS
The integrated solar transmittances (5) and reflectances (p) of the samples were measured by using3 procedures that are similar to the ASTM method for determining solar transmittance4 and the ASHRAE method for determining solar-optical properties.” The measured quantities are P” 52
s )‘=I’,s R’=P )(I‘
r,.(Q’)l,..i(Q’) dR’ (1)
s ?=I’,s fl’-fl’
!,.,;(a’) dR’
and
sf VU
\“\‘,
Pl
n,=fl*
VU
’ ~ 2rc)r,..i(n’) py(R
s \‘=v,s Ij’=lP
dR’
r,..i(n') dR’
where rI and r, represent, respectively, the lower and upper frequency cut-offs of the pyranometer, R* is the solid angle viewed by the detector, r,,,i(n’) is the monochromatic intensity of the radiation incident from a unit solid angle about the direction R’, s,,(W) is the monochromatic transmittance of the sample for radiation incident from a unit solid angle about 51’. and p,.@‘-+ 2n) is the monochromatic, directional-hemispherical reflectance of the sample. The numerators in Eqs. (1) and (2) are the total integrated transmitted and reflected intensities, respectively; the denominators represent the total integrated incident intensities. Since the distribution of incident intensity I,,,i(Q’) varies with the position of the sun Sr, (i.e. approximately with the angle of incidence of the direct solar radiation 8), we determine r(0) and p(O). The integrated solar absorptance is defined by the relation $0) =
1 -
[p(e)
+
T(e)].
(3)
Experimental results for a window film and a sunscreen are shown in Figs. l-6. The discontinuity in the slope of r(0) for the sunscreen is attributable to the assumption that T = 0 after 0 reaches a cut-off angle.? The measured properties of 3.2 mm DSS glass are shown in Figs. 7 and 8. Shading coefficients SC are obtained by using relations from Ref. 1. For a window with a film at the glass temperature and applied to the inside surface, the fenestration may be treated as a single pane of glass, i.e.
CT+ (Ur’~~,,)rlri,.,““yla.h
SC= CT+ (~~~~,,)~13.2rnrn~ss~,n,. ’
(4)
where U 1 hi/J,/(hi + II,,). For summer conditions,“’ hi = 12.1, h, = 33.1, and U = 8.86 w/m’-“C (1.46, 4.00, and 1.07 Btu/ft’-hr-“F. respectively). For films with low tThis postulated behavior is not precisely correct. Above the cut-off angle. only diffuse sunlight is transmitted. For clear days, when the diffuse radiant flux contributes _ 20”;, of which less than _ 20’3~~is transmitted. the solar transmittance T is less than _ 4”i.
Fenestration
0.20
devices for energy
63
conservation-111
_.
. .
G ;:
.
‘.
O.lO-
0.00.
I 20
0
I
I 40
I
I 60
I 00
dtdegrees) Fig. I. The observed (.) solar transmittance r(B) is shown for an insulating to the inside surface of I/S in. DSS glass. The line represents a least-squares data points (T = 0.0527 + 0.136 cos0 - 0.0272 cos’0).
window film applied fi to the measured
0.60-
0.50_
040,
0.00
I
0
20
40
60
60
e(degrees) Fig. 2. The observed (‘) integrated solar reflectance ~(0) is shown for an insulating wmdow film applied to the inside surface of l/8 in. DSS glass. The solid curve represents the least-squares fit to the measured data points (p = 0.585 - 0.391 co& + 0.297 cos’0).
o.40 L-----
0.30
c
0.001 0 Fig. 3. The integrated
20
40 f?(degrees)
60
00
solar absorptance of an insulating window film applied surface of I/S in. DSS glass is shown as a function of 0.
to the inside
M. R.
64
BRAMBLEY and
S. S.
PENNER
8(degrees) Fig. 4. The observed (. ) solar transmittance r(6) is shown for a sunscreen. The line represents the least-squares fit to the measured data points (T = - 0.111 + 0.607 cost? - 0.246 co&I).
emittance in the i.r. (i.e. E z 0.24), hi = 6.46 w/m*-“C iJ = 5.39 w/m*-“C (0.65 Btu/ft*-hr-“F); thus, sc
=
CT+ 0.164low cmittancc b
+
o.27
(0.78 Btu/ft*-hr-“F)
and
filmonglass
43.2rnmDSSglass
’
The experimental data have been used in Eq. (5) to obtain SC(e) for a film applied to the inside surface of 3.2 mm DSS glass (see Fig. 9).
°rees
1
Fig. 5. The observed (.) integrated solar reflectance p(B) is shown for a sunscreen. The line represents the least-squares fit to the measured data points (p = 0.474 - 0.522 cos0 + 0.214 co&).
Fenestration
devices for energy
65
conservation-III
060
0.50
_
0.40
UJ a 0.30
0.20
0.10
8 (degrees) Fig. 6. The integrated
solar absorptance
a of a sunscreen
is shown
as a function
of 0.
Sunscreens mounted externally to single glass and separated by an enclosed air-space represent the most effective configuration studied by us. For these,’
1
SC=
3.2mmDSSpla~
0.60s 9
0.500.40
-
0.30
-
0.20
-
0. I 0 0.00
. . I
0
.
20
I
I
I 40
60
80
6 (degrees) Fig. 7. The observed ( .) solar reflectance p(B) of l/8 in. DSS glass is shown. The line represents the relation p = 0.606 - 1.23 cos0 + 0.710cos2B and was obtained by using a least-squares regression on the data.
(6)
66
M. R. BRAMBLEY and S. S. PENNER
*. . “\’
0.30 0.20 0.1 0
0.001 0 20
60
60 40 8 (degrees)
1
Fig. 8. The observed (‘) solar transmittance r(0) of I/S in. DSS glass is shown. The line represents the relation r = 0.378 + 0.949 cos0 - 0.473 co& obtained by using a least-squares regression on the data.
0.205 ” v)o.lo -
0.00
I 20
0
I 40 8 (degrees)
I 00
I 60
Fig. 9. The shading coefficient (SC) for an insulating window film applied to the inside surface of l/8 in. DSS glass is plotted against the angle of incidence 0 of the direct solar radiation.
0.30 -
o^ 0.20 ; 0.10 -
000
I 0
I 20
I 40 8 (degrees)
I 60
80
Fig. 10. The shading coefficient (SC) for a sunscreen mounted externally to l/8 in. DSS glass and separated by an enclosed air-space is shown as a function of the angle of incidence 0 of the direct solar radiation.
Fenestratlon
devices for energy
conservation
61
III
where
hi and /I, have been defined previously, h, is the effective heat-transfer
coefficient between the glass and the screen, and the subscripts SD and y indicate properties of the shading device (screen) and glass, respectively. Using ASHRAE summer conditions at the inside and outside surfaces and h, = 6.63 w/m”-‘C (0.80 Btu/ft’-hr-“F), Eq. (6) becomes (7) The values of SC(@) derived from Eq. (7) are shown in Fig. 10 for a sunscreen. The discontinuity in SC(e) is attributable to the assumption that r(0) = 0 for 8 greater than the cut-off angle. The shading coefficient for sunscreens is strongly dependent on rsr, [set Eq. (7)] and decreases with increasing 8 up to the cut-off angle. Therefore, the applicable average shading coefficient is less than the value measured at normal incidence.
3.
ENERGY
SAVINGS
DURING
THE
COOLING
SEASON
The energy savings attributable to selected fenestration devices compared to single glazing have been evaluated (for the transition climatic region in San Diego County) according to the methodology described in Ref. 1. The heat gains were evaluated using appropriate daily solar heat-gain factors (SHGF) and temperature profiles for each month of the cooling season. The daily heat gains were determined from the relations’ QAT. =
u I”
(T, - TW
(8)
and
Qs -J
(SC) (SHGF) dr
.
(9)
dailycoolinypcr~otl
where QATand Qs are, respectively, the heat gain associated with temperature differences across the fenestration per unit area and the daily solar heat gain; Ti and 7;, are the instantaneous inside and outside temperatures, respectively. Monthly heat gains are obtained by multiplying Qs and Qar by the number of days of the month; seasonal values are obtained by summing over the months of the cooling season. The results obtained using the SC(e) are shown in Table 1, whereas Table 2 shows the corresponding estimates for the constant value of SC at normal incidence for direct solar radiation (0 = 0”). Energy savings compared to 3.2 mm DSS glass are also listed. Since all heat gains through the window during the daily cooling period have been assumed to contribute to the air-conditioning load, the calculated energy savings represent upper limits. The savings for cooling per year, in current dollars, are given for electricity prices of 4.3 and 5.0 cents per kWh. For the film, variations in SC with 0 are so small that use of the constant value of SC at B = 0” results in less than a IO centsim’ increase in the yearly savings for cooling at an electricity price of 4.3 cents,‘kWh (see Tables I and 3).t The largest differences are found for north-facing windows for which sunlight is rarely incident directly. A value of SC for north-facing windows at 6 = 90’ would be more appropriate than the value at 8 = 0”. For screens, the solar heat gains are greater for constant values of the SC (Table 2) than for SC = SC(e) (Table 1). In Ref. 3, we have shown this difference to vary by factors of 1.2 (for a dark sunscreen facing West) to 8.8 (for a white sunscreen facing North). E%timates of monetary savings were shown to increase by up to about 20”/: (compare Tables 1 and 2). tFor
other films tested by us, the greatest
difference
was 27&m’
DSS glass
A representative Bunscreen mounted externall) to 3. 2 mm DSS glass and separate by an enclosed air %pace.
insulating window film adhering to the inside surface of l/8 inch DSS glass.
A re pre tentative
l/8”
Fenestration
see Fig. 1 0
rig. 9
5ee
. 00
SC
3.79
511 125
125
125
602 189
125
I
AT
(kwhth /m2-Yr)
Q
445
tkwhth /m2-yr)
QS
savings=
636
0
0
0
7 27 314
0
(kwhth /m2-yr)
- QT
T l/+3” DSS glass
570
(kwhth /m2-yr)
%=Q~+Q~~
Q
Energy
@4.
NA
NA
NA
NA
NA NA
NA
@5. Ob/bh NA
3d/kwh
wm2-yr)
Value of cooling savings
Table 1. Fenestration performance characteristics of 3.2 mm (l/S in.) DSS glass, a window film applied to a single glass, and a sunscreen mounted externally and separated by an enclosed air space during the cooling season (May through October) in the transition climatic region of San Diego County. The data refer to SC(B) (see Figs. 9 and 10) and were determined from experimentally measured solar-optical properties, solar heat gain factors applicable for a clear day on the 21st of each month, an indoor temperature of 18.3”C (65”F), representative outdoor daily temperature profiles for each month based on monthly mean daily maximum and minimum temperatures, and a COP = 3.0 for an electric air-conditioner.
A representative sunscreen mounted externally to 3. 2mm DSS glass and separated by an enclosed airs pace.
A re pre sentative insulating window film adhering to the inside surface of l/8 inch DSS glass.
Fenestration
0.330
0. 249
SC
3.79
5. 39
(w/m2-“C)
u
1
I
63 170
North
East
199
west
127
47
150
111
th /m2-yr)
148
I
1
1
I
(hh
South
East
North
West
South
Orientation
QS
I
I
I
I
AT
117 224
54 54
368
253
54
412
197
47 4
202
190
54
I
432
124 204
77
77
77
77
(kwhth /m2-yr)
Q
($/m2-yr)
Value of cooling savings
Table 2. Fenestration performance characteristics of an insulating window film applied to 3.2 mm (I ;8 in.) DSS glass. and a Sunscreen mounted externally and separated by an enclosed air space during the cooling Season (May through October) in the transition climatic region of San Diego County. The data refer to constant values of the SC corresponding to solar-optical propertics for normally incident, direct solar radiation (0 = O), solar heat gain factors applicable for a clear day on the 21st of each month. an Indoor temperature of 18.3 C (65 F). representative outdoor daily temperature profiles for each month based on monthly mean daily maximum and minimum temperatures. and a COP = 3.0 for an electric air-conditioner
M. R. BRAMBLEY and S. S. PENKER
70 Table
3. The particular
constant values of the SC which yield calculated values of solar heat gains (Q.) that are equal to the values obtained by using SC(O); also shown are the constant values of the SC at B = 0
seasonal
Orientation
A
South
East
West
0. 286
0. 247
0. 252
0. 249
0. 249
0. 148
0.193
0. 237
0. 252
0
representative
insulating film
window
adhering
the of
North
inside
to
surface
3.2mmDSS
glass. A representative sunscreen mounted to
3.2
glass by
externally mm and
DSS
330
separated
an enclosed
air-
space.
In Table 3, we list the particular constant values of the SC which correspond to actual energy savings estimated by using variable SC(e), together with the values corresponding to 8 = 0”. These results again indicate that the performance of insulating window films is only minimally affected by the use of variable shading coefficients. On the other hand, sunscreens perform more effectively during the cooling season than would be expected for shading coefficients at H = 0”. in general, the values of the SC for north-facing windows should correspond to larger angles of incidence (i.e. H = 90’) than 8 = 0’. 4. CONCLUSIONS
The transmitted solar radiation comprises approx. 76% of the solar heat gain through a single pane of glass with an insulating film and 98% without the film. The shading coefficient varies with 8 approximately in the same manner as the ratio of the transmittances (5, ow emittance film on gl~s/~3.2 mm DSS glass ). This ratio is nearly constant for 0 2 60”. At larger values of 8, the transmittance of the glass decreases somewhat faster with increasing 8 than the transmittance of the glass-film combination, thus leading to a small increase in SC with increasing 8 (see Fig. 9) between 60 and 90”. Since the film is in intimate contact with the glass, this fenestration behaves essentially like a single pane of glass and the shading coefficient is therefore nearly constant. The use of SC(e) instead of a constant value at normal incidence (0 = 0’) affects estimates of energy and monetary savings neglibly. Thus, the use of a constant value for the SC of films on glass constitutes a good approximation. For a sunscreen mounted externally to single glazing, about 72% of the solar heat gain is attributable to transmitted solar radiation at 0 = 0”. The value of SC(e) is roughly proportional to the transmittance of the shading device, T&8), for 0 less than the cut-off angle [see Eq. (7)]. For 8 greater than the cut-off angle, T&e) = 0 and SC(e) becomes [see Eq. (7)] approximately proportional to the ratio %D/T~. The transmittance of the glass T,(o) decreases faster than the absorptance of the shading device [%n(8)] with increasing 8 (compare Figs. 6 and 8). As the result, d(SC)/dB > 0 for 8 greater than the cut-off angle. The sunscreen and glass are separated by an air space in this fenestration device. The screen shields the glass from progressively more of the incident solar radiation as 8 is increased, while the solar radiation incident on unshaded glass varies as CO& The solar radiation on the screened glass varies as T&o) cd where T&e) is a decreasing function of 8 up to the cut-off angle. For screened windows, constant values of the SC (at 0 = 0’) yield solar heat gains that are too large3 by up to 880% and corresponding estimates of energy and monetary savings that are too small by up to 20%.
Fenestration
devices for energy
conservatton
111
71
These results indicate that variable SC(e) must be used to estimate solar heat gains properly for screened. externally shaded windows and that the introduction of a constant value for the shading coefficient at 0 = 0” does not lead to a satisfactory simplified procedure for estimating solar heat gains.
REFERENCES and S. S. Penner. Eurry,r 4. I (1979). M. R. Brambley and S. S. Penner, /37rryy 4. 27 (1979). M. R. Brambley and S. S. Penner, Fenestration devices for energy conservation -III. Experimental results for selected fenestrations. Energy Center and Department of Applied Mechanics and Engineering Sciences. liniversity of California. San Diego, La Jolla. CA 92093. 129 pp. (March 1980). Copies of this report are available from the authors on request. ASTM Standard E 424-71. “Standard Methods of Test for Solar Energy Transmittance and ReHectance (Terrestrial) of Sheet Materials”, American Society for Testing and Materrals. 1971. ASHRAE Standard 74.~73, “Method of Measuring Solar-Optical Properties of Materials”, The Amertcan Society of Heating. Refrigerating. and Air-Conditioning Engineers. 1973. .ASHRAE Htuldhook of Fuudurnrnrtrls, American Society of Heatrng. Refrigeratrng. and Atr-Condrtionrng f ngrnecrs. New York ( 1977).
I. M. R. Brambley
2. 3.
4. 5. 6.
APPENDIX
Using measured properties, we find that window (fly) screens produce from - 554<, (for west-facing windows) to - loo”, for north-facing windows of the solar-energy reduction achieved by specially designed sunscreens and insulating window films. Payback periods have been computed as functions of installation costs (C), with the electricity price as a parameter. for window (fly) screens replaced by sunscreens during the cooling season in the transition region of San Diego County. Acceptable payback periods of less than _ 6 years are achieved only for installation costs 2 $2.60/ft2 ($27.99/m’), even for west-facing windows at an electricity price of I.Oc/kWh. Payback periods for north-facing windows, for C 5 $l/ft’, exceed the IO-year life of the devices. These results indicate that undamaged window screens should generally not be replaced with sunscreens unless the installation costs for the sunscreens are very low.