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Measurements of the total transmittance of the solar radiation through an absorbing black liquid water
IN HEAT AND MASS TRANSFER 0094-4548/79/0101-0057502.00/0 Vol. 6, pp. 57-60, 1979 © Pergamon Press Ltd. Printed in Great Britain
MEASUREMENTS OF THE TOTAL TRANSM1TI'ANCE OF THE SOLAR RADIATION THROUGH AN ABSORBING BLACK LIQUID WATER
R J. Huang and S. Nieh Department of Mechanical Engineering National Taiwan University, Taipei, Taiwan, R.O.C.
(C~t~,Lhnicated by J.P. Hartnett and W.J. ~ c z )
INTRODUCTION Recently, black liquid is frequently used as a working fluid to directly absorb the solar radiation in many solar energy applications. A typical example is done by Minardi and Chuang [1] who develop a black liquid solar collector which uses a highly absorbing black liquid circulating in a transparent plain channel to directly absorb solar radiation. In this collector, a small fraction of the incident solar radiation energy is first reflected and absorbed by the transparent channel wall, and the remaining fraction is then transmitted across the black liquid at which the radiation energy is absorbed. It is obvious that the magnitude of the radiation energy absorbed is dominated by the overall absorptance or transmittance of the black liquid which depends on the black ingredient concentration and the depth of the liquid. Little knowledge has been known about the radiation properties of the black liquid up to date. To study the problems of water quality and thermal pollution in lakes, reservoirs, and rivers, Viskanta and Toor [2,3] and Snider and Viskanta [4] carried out some analytical and experimental investigations on the radiative energy transfer in layer of pure water in which water is considered as an absorbing, emitting, and scattering body, and a rather complex analytical model is developed to predict the heat transfer behavior. However, literatures on the behavior of radiant energy transfer in a black liquid are still lacking. An experiment is therefore carried out in the present paper to directly study the total transmittance of the solar radiation through layer of black liquid water. EXPERIMENT AND RESULTS The blackbox-pyranometer method using sunlight as the radiation source is employed here to measure the total transmittance of the black liquid. The apparatus, as shown in Fig. 1, consists of a blackbox which is sealed and curtained at the inner wall by two layers of heavy black silk
57
58
B.J. Huang and S. Nieh
Vol. 6, No. 1
\MIRROR \
r-GRADUATED
SOLAR RADIATION
,
,
~
BLAC KBOX
Fig. 1 Schematic Diagram of Apparatus curtains, and an 12.5 cm-diameter hole is left at the top of the blackbox to allow the sunlight to pass through. A flat-bottom acrylic square container which is transparent to the solar spectrum and with 3 mm thick, 12 cm deep, 15 x 15 cm dimension, is horizontally placed right on the opening hole. The black liquid water made from Direct Black EX dye which is made in Holland is poured into the container from a 1000 c.c. plastic metering bottle. The depth of the black liquid water then can be accurately controlled with negligible errors. A large mercury reflecting mirror is mounted on an adjustable frame to reflect sunlight toward the blackbox through the light guider and incident on the liquid normally. A R413 STAR PYRANOMETER connected to a chart recorder is placed right below the hole with a distance of 18 cm to measure the radiation intensity of the transmitted solar radiation. The pyranometer consists of a 7 cm-diameter hemispherical glass dome and a sensing element made of 72 CrNi-Constantan junctions in contact with 12 alternately black and white painted Cu-segments with diameter of 3.8 era, and the spectral response of the pyranometer ranges from 0.3 to 3.0 gm which is the solar spectrum. Therefore, only the transmittance in solar spectrum will be measured in the present experiment. After the apparatus is set, the measurement is first made to determine the total transmitted radiation intensity without black liquid water in the container, i.e. zero depth. The black liquid water is then poured into the container to a certain depth, and the total transmitted radiation intensity is measured again. The ratio of the above two results thus gives the total transmittance
Vol. 6, NO. 1
TRANSMI'ITANCEC~THESOLARRADIATION
59
of the solar radiation through the black liquid water. This measuring procedure is repeated over and over again for different depths up to 10 cm and different concentrations up to 0.1 (measured in weight). To minimize the error due to the variation of the solar incidence during the experiment, this procedure is get done within ten minutes. The experimental results are plotted in Fig. 2. And, it is found that an empirical equation, eq. (1), can be determined to accurately fit the experimental data to within an average error of 4%: (C,X) = exp{-(0.246 + 10C°'~) X°'34* [log(1+5.5C)] °~slt
LOt 'r
.
.
.
.
.
.
(1)
.
1.0
P.E. 0.8 I~
~
-
"1 0.8
I'J
d o.6
eli o 0.000
U
z <
0.001
I--
D 0.010 + 0.020 o o.o 50 A 0 . t 00 Eq.(1)
z 0.4 I-.J
~o~
0L ~ T 0
04
02
O. 1
2
3
~
4
DEPTH, X cm
Fig. 2 Total Transmittance of Black Liquid Water
DISCUSSIONS One of the systematic errors which are possibly encountered in the experiment would result from the thermal emission of the black liquid water due to the temperature rise during'the experiment when the liquid exposes to the solar radiation for a period of time. However, this error is
60
B.J. Huang and S. Nieh
%7ol. 6, No. i
minimized since the transmittance measurements are taken so quickly that the maximum temperature rise is only about 2°C and the resulting thermal radiation is negligible. It should be noted that the total transmittance of the black liquid water measured in the present experiment is not exactly the real transmittance of the absorbing body as defined in Bouger's law, but includes the interracial reflection effects. Since it is very difficult to correct the effects due to the interracial reflection in the absorbing black liquid water, being obviously not a transparent body, either from experiment or from classical electromagnetic theory, the empirical equation, eq. (1), only represents the overall transmittance. However, it can be seen from eq. (1) that, even the interfacial reflections being corrected, Bouger's law for absorbing gasseous media seems still doesn't hold for the present black liquid water in solar spectrum. The physical significance for this phenomenon is not clear at the present time, and further investigations are required. NOMENCLATURES
C X
Total transmittance of the black liquid water, dimensionless. Weight concentration of the black liquid water, dimensionless. Depth of the black liquid water, era. REFERENCES
1. J. E. Minardi and H. N. Chuang, Performance of a Black-Liquid Flat-Plate Solar Collector, Solar Energy, 17, 179-183(1975). 2. R. Viskanta and J. S. Toor, Radiant Energy Transfer in Waters, Water Resour. Res., 6(3), 595-608(1972). 3. R. Viskanta and J. S. Toor, Effect of Multiple Scattering on Radiant Energy Transfer, J. Geophysical Research, 78(18), 3538-3551(1973). 4. D. M. Snider and R. Viskanta, Radiation Induced Thermal Stratification in Surface Layers of Stagnant Water, J. Heat Transfer, ASME, 35-40(Feb. 1975).
MEASUREMENTS OF THE TOTAL TRANSM1TI'ANCE OF THE SOLAR RADIATION THROUGH AN ABSORBING BLACK LIQUID WATER
R J. Huang and S. Nieh Department of Mechanical Engineering National Taiwan University, Taipei, Taiwan, R.O.C.
(C~t~,Lhnicated by J.P. Hartnett and W.J. ~ c z )
INTRODUCTION Recently, black liquid is frequently used as a working fluid to directly absorb the solar radiation in many solar energy applications. A typical example is done by Minardi and Chuang [1] who develop a black liquid solar collector which uses a highly absorbing black liquid circulating in a transparent plain channel to directly absorb solar radiation. In this collector, a small fraction of the incident solar radiation energy is first reflected and absorbed by the transparent channel wall, and the remaining fraction is then transmitted across the black liquid at which the radiation energy is absorbed. It is obvious that the magnitude of the radiation energy absorbed is dominated by the overall absorptance or transmittance of the black liquid which depends on the black ingredient concentration and the depth of the liquid. Little knowledge has been known about the radiation properties of the black liquid up to date. To study the problems of water quality and thermal pollution in lakes, reservoirs, and rivers, Viskanta and Toor [2,3] and Snider and Viskanta [4] carried out some analytical and experimental investigations on the radiative energy transfer in layer of pure water in which water is considered as an absorbing, emitting, and scattering body, and a rather complex analytical model is developed to predict the heat transfer behavior. However, literatures on the behavior of radiant energy transfer in a black liquid are still lacking. An experiment is therefore carried out in the present paper to directly study the total transmittance of the solar radiation through layer of black liquid water. EXPERIMENT AND RESULTS The blackbox-pyranometer method using sunlight as the radiation source is employed here to measure the total transmittance of the black liquid. The apparatus, as shown in Fig. 1, consists of a blackbox which is sealed and curtained at the inner wall by two layers of heavy black silk
57
58
B.J. Huang and S. Nieh
Vol. 6, No. 1
\MIRROR \
r-GRADUATED
SOLAR RADIATION
,
,
~
BLAC KBOX
Fig. 1 Schematic Diagram of Apparatus curtains, and an 12.5 cm-diameter hole is left at the top of the blackbox to allow the sunlight to pass through. A flat-bottom acrylic square container which is transparent to the solar spectrum and with 3 mm thick, 12 cm deep, 15 x 15 cm dimension, is horizontally placed right on the opening hole. The black liquid water made from Direct Black EX dye which is made in Holland is poured into the container from a 1000 c.c. plastic metering bottle. The depth of the black liquid water then can be accurately controlled with negligible errors. A large mercury reflecting mirror is mounted on an adjustable frame to reflect sunlight toward the blackbox through the light guider and incident on the liquid normally. A R413 STAR PYRANOMETER connected to a chart recorder is placed right below the hole with a distance of 18 cm to measure the radiation intensity of the transmitted solar radiation. The pyranometer consists of a 7 cm-diameter hemispherical glass dome and a sensing element made of 72 CrNi-Constantan junctions in contact with 12 alternately black and white painted Cu-segments with diameter of 3.8 era, and the spectral response of the pyranometer ranges from 0.3 to 3.0 gm which is the solar spectrum. Therefore, only the transmittance in solar spectrum will be measured in the present experiment. After the apparatus is set, the measurement is first made to determine the total transmitted radiation intensity without black liquid water in the container, i.e. zero depth. The black liquid water is then poured into the container to a certain depth, and the total transmitted radiation intensity is measured again. The ratio of the above two results thus gives the total transmittance
Vol. 6, NO. 1
TRANSMI'ITANCEC~THESOLARRADIATION
59
of the solar radiation through the black liquid water. This measuring procedure is repeated over and over again for different depths up to 10 cm and different concentrations up to 0.1 (measured in weight). To minimize the error due to the variation of the solar incidence during the experiment, this procedure is get done within ten minutes. The experimental results are plotted in Fig. 2. And, it is found that an empirical equation, eq. (1), can be determined to accurately fit the experimental data to within an average error of 4%: (C,X) = exp{-(0.246 + 10C°'~) X°'34* [log(1+5.5C)] °~slt
LOt 'r
.
.
.
.
.
.
(1)
.
1.0
P.E. 0.8 I~
~
-
"1 0.8
I'J
d o.6
eli o 0.000
U
z <
0.001
I--
D 0.010 + 0.020 o o.o 50 A 0 . t 00 Eq.(1)
z 0.4 I-.J
~o~
0L ~ T 0
04
02
O. 1
2
3
~
4
DEPTH, X cm
Fig. 2 Total Transmittance of Black Liquid Water
DISCUSSIONS One of the systematic errors which are possibly encountered in the experiment would result from the thermal emission of the black liquid water due to the temperature rise during'the experiment when the liquid exposes to the solar radiation for a period of time. However, this error is
60
B.J. Huang and S. Nieh
%7ol. 6, No. i
minimized since the transmittance measurements are taken so quickly that the maximum temperature rise is only about 2°C and the resulting thermal radiation is negligible. It should be noted that the total transmittance of the black liquid water measured in the present experiment is not exactly the real transmittance of the absorbing body as defined in Bouger's law, but includes the interracial reflection effects. Since it is very difficult to correct the effects due to the interracial reflection in the absorbing black liquid water, being obviously not a transparent body, either from experiment or from classical electromagnetic theory, the empirical equation, eq. (1), only represents the overall transmittance. However, it can be seen from eq. (1) that, even the interfacial reflections being corrected, Bouger's law for absorbing gasseous media seems still doesn't hold for the present black liquid water in solar spectrum. The physical significance for this phenomenon is not clear at the present time, and further investigations are required. NOMENCLATURES
C X
Total transmittance of the black liquid water, dimensionless. Weight concentration of the black liquid water, dimensionless. Depth of the black liquid water, era. REFERENCES
1. J. E. Minardi and H. N. Chuang, Performance of a Black-Liquid Flat-Plate Solar Collector, Solar Energy, 17, 179-183(1975). 2. R. Viskanta and J. S. Toor, Radiant Energy Transfer in Waters, Water Resour. Res., 6(3), 595-608(1972). 3. R. Viskanta and J. S. Toor, Effect of Multiple Scattering on Radiant Energy Transfer, J. Geophysical Research, 78(18), 3538-3551(1973). 4. D. M. Snider and R. Viskanta, Radiation Induced Thermal Stratification in Surface Layers of Stagnant Water, J. Heat Transfer, ASME, 35-40(Feb. 1975).