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Analysis of solar radiation transfer: A method to estimate the porosity of a plastic shading net
Energy Conversion and Management 52 (2011) 1755–1762
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Analysis of solar radiation transfer: A method to estimate the porosity of a plastic shading net A.M. Abdel-Ghany ⇑, I.M. Al-Helal Department of Agricultural Engineering, College of Food and Agriculture Sciences, King Saud University, P O Box 2460, Riyadh 11451, Saudi Arabia
a r t i c l e
i n f o
Article history: Received 3 March 2010 Accepted 7 November 2010
Keywords: Plastic net Porosity Solar radiation Transmittance Forward scattering
a b s t r a c t Plastic nets with opaque threads are frequently used for shading agricultural structures under high solar radiation conditions. A parameter that is often used to define a net is the net porosity (P). Value of P is usually estimated by one of three methods: image processing, direct beam transmittance, or solar radiation balance (hereafter radiation balance). Image processing is a rather slow process because it requires scanning the net sample at high resolution. The direct beam transmittance and radiation balance methods greatly overestimate P because some of the solar radiation incident on the thread surfaces is forward scattered and add a considerable amount of radiation to that transmitted from the net pores directly. In this study, the radiation balance method was modified to estimate P precisely. The amount of solar radiation scattered forward on the thread surfaces was estimated separately. Thus, the un-scattered solar radiation transmitted from the net pores directly, which describes the net porosity, P could be estimated. This method, in addition to the image processing and the direct beam transmittance methods were used to estimate P for different types of nets that are commonly used for shading structures in summer. Values of P estimated by using the proposed method were in good accordance with those measured by the image processing method at a resolution of 4800 dpi. The direct beam transmittance and the radiation balance methods resulted in overestimation errors in the values of P. This error strongly depends on the color of the net. The estimated errors were +14% for a green net and +37% for a white net when using the radiation balance method, and were +16% and +38%, respectively, when using the direct beam transmittance method. In the image processing method, a resolution of 2400 dpi is sufficient to estimate P precisely and the higher resolutions showed no significant effect on the value of P. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Plastic nets made from high-density polyethylene (HDPE) are widely used in various agricultural applications to protect crops and nurseries from hail, strong wind, snow, strong rainfall, insects, animals and birds. Shading is the most important application of the plastic nets in hot and sunny regions to reduce the solar radiation levels and improve the environment. Shade netting is also used for covering animals, swimming pools, playground and car parks. During the last decade, the uses of plastic nets for covering agricultural structures have steadily expanded because they offer many advantages and environmental and economical benefits [1–3]. Many types of plastic nets with different colors and textures are available in the markets and used by customers. However, the choices of nets have been mostly empirically determined so far. This is because technical information such as the physical ⇑ Corresponding author. Tel./fax: +966 (01) 4678352. E-mail addresses: [email protected], [email protected] (A.M. AbdelGhany). 0196-8904/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2010.11.002
properties of these nets still unclear. In addition, appropriate methodologies to measure the physical properties of plastic nets have not been established yet. Net porosity P is the most important physical property describing a net because it has a considerable effect on the radiation transfer through the net as well as the shading power. Moreover, the net porosity is an essential parameter needed to estimate the ventilation rate of a structure covered with this net. Porosity is simply defined as the dimensionless ratio of the open area divided by the total area of the net surface; and is the complementary value of the net solidity, (solidity = 1–P). Based on a survey of previous studies performed in this area, three methods have been used to estimate the net porosity [1]. These methods are: (i) image processing method based on a microscopic analysis of the image of the net sample, (ii) direct beam transmittance method based on measuring the net transmittance to direct beam solar radiation at normal incidence and (iii) radiation balance method based on applying solar energy balance below and above the net surface to estimate the total transmittance of the net to global solar radiation. Description and problems associated with each method can be summarized as follows:
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Nomenclature total surface area of the net [m2] total empty area of the net surface [m2] area of surface-1 and -2 which reflect radiation downward [m2] A3 area of the net pore that receive the scattered radiation downward [m2] a, b, c, D, Dm, d construction dimensions in Fig. 1a–c [mm] dt time interval [sec] Ep un-scattered solar energy transmitted from the net pores directly [W m2] solar energy transmitted from the net pores due to the Esc forward scattering on the thread surfaces [W m2] F1-2 view factor from surface-1 to surface-2 [-] Fsc ratio of the forward scattered radiation to the total radiation transmitted [-] G downward incident solar radiation flux over the net surface [W m2]
A Aa A1, A2
1.1. Image processing method Consider a sample of a plastic net material having a volume V. This sample is composed of a solid matrix (i.e. threads material) with some amount of air inside. The volume fraction of air phase is given by [4] as:
P ¼ V a =V
ð1Þ
in which P is the porosity and Va is the volume of air in the solid matrix. Since plastic nets are always made of thin and uniform threads, their porosity can be approximated as:
P ¼ Aa =A
ð2Þ
where Aa represents the empty area filled with air and A is the total surface area of the net. Porosity described by Eq. (1) can be determined only by weighing the net sample in vacuum conditions and in atmospheric air condition. Such procedure is quite difficult to apply for evaluating the net porosity. Porosity described by Eq. (2) can be determined by magnifying the sample with the help of a microscope and measuring the representative areas Aa and A. A simple technique is usually used by tacking the net sample to a thin frame and scanning it in a flatbed scanner. Image is analyzed for measuring the representative areas of Aa and A. This method is widely used to estimate P. For example, it was used at scanning resolutions of 2400 dpi in [5], 600 dpi in [6]; and with unspecified resolutions in [4,7,8]. Even though scanning resolution is expected to affect the value of P, the effect of scanning resolution on the precision of the value for P has not yet been examined. 1.2. Direct beam transmittance method In this method, the net sample is tacked on a frame; global solar radiation is measured below and above the net surface at an incidence angle of solar beam radiation, h equal to zero. This procedure is repeated with shading the frame with an opaque plate to measure the diffuse solar radiation below and above the net sample. The direct beam radiation is determined as the difference between the global and diffuse radiations. In this case, net transmittance to direct beam is estimated as the ratio between direct beam below and above the net. Value of P is considered as the net transmittance to direct beam radiation at normal incidence. This method has been used by several investigators, for example, [6,8–10]. However, values of P estimated by this method were much higher than
R S t T U V Va
a P / h
q
reflected radiation upward from the net surface [W m2] texture dimension in Fig. 1 (b) [mm] time [sec] downward radiation below the net surface [W m2] upward radiation below the net surface [W m2] total volume of a porous material [m3] volume of pores filled with air [m3] absorptance of the net material [-] the net porosity [-] the total transmittance of the net to global solar radiation [-] incidence angle of solar beam radiation [°] reflectance of the net material [-]
those estimated by the image processing method. Reported differences were around +12% in [6] for metallic screens; +8% in [8] for net with black threads; and from +13% to +25% in [10] for nets with white and amber threads. Investigators attributed these differences to the transparency of the thread materials. However, these differences were found even when the nets were made of black threads which are opaque to solar radiation. In fact this difference is mainly due to the nature of the radiation transmitted through the net. In nets, a portion of the incident radiation scatters forward on the thread surface and is transmitted through the net and the other portion is un-scattered radiation that is transmitted directly through the net pores without striking any part of the thread surfaces [see Fig. 1a–c]. Only the un-scattered radiation is related to the net porosity. Thus, the net total transmittance is the sum of the two portions and is usually higher than the net porosity. 1.3. Radiation balance method In this method, the net sample is tacked on a horizontal frame (as shown in Fig. 2). Downward and upward global solar radiation fluxes are measured beneath (i.e., T and U) and above (i.e., G and R) the net surface. Radiation balance below and above the net surface is applied to express the values of T and R as:
T ¼ G/ þ ð1 /ÞqU
ð3Þ
R ¼ U/ þ ð1 /ÞqG
ð4Þ
By solving Eqs. (3) and (4) simultaneously, values of the net transmittance to global solar radiation / and the thread reflectance q could be determined. Previous studies assumed that / is equal to the net porosity [6,8]. However, / was always found to be much higher than the net porosity obtained by using the image processing method because / is equivalent to the net porosity plus a fraction equal to the ratio of the radiation scattered downward through the net pores to the total radiation transmitted through the net. Based on the previous discussion, an appropriate method to estimate the porosity of a plastic net precisely is urgently needed. The objectives of this study are to: (i) modify the radiation balance method to be used for determining the value of P precisely, (ii) examine the effect of scanning resolution used in the image processing method on the value of P and (iii) check the precession of the proposed method by comparing its results with the results of the image processing and direct beam transmittance methods.
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Fig. 1. Schematic diagrams of the structures approximated the tested nets and mechanisms of solar radiation transfer showing the forward scattering.
Fig. 2. Schematic diagram of the experimental set up and locations of the solarimeters used to measure the global solar radiation components below and above the net sample. Dimensions are in cm, not to scale.
2. The Proposed method Solving Eqs. (3) and (4) for / gives:
/ ¼ ðTG RUÞ=ðG2 U 2 Þ
ð5Þ
Net absorptance a as a radiative property needed for any thermal analysis can be expressed as:
ð1 /Þa ¼ ½ðG RÞ ðT UÞ=ðG þ UÞ
ð6Þ
where q and a are the reflectance and absorptance of the net mate^ reprerial (i.e., opaque plastic threads, q + a = 1). The parameter u sents the apparent porosity of the net, i.e., the true porosity plus the fraction of solar radiation scattered downward and then transmitted through the net pores. In other words, / represents the total transmittance of the net to global solar radiation. Values of q and a are deduced from direct substitution of / into Eqs. (3) and (6).
The common shapes of the textures of the commercial plastic net are either parallel strips held by interlaced strips/wires (e.g., beige-80, orange-80 and blue-80 nets in Fig. 3); or parallel interlaced threads, like robs, held by wires (e.g., green-50, white-50 nets in Fig. 3); or knitted wires in random shape (e.g., dark green-80 nets in Fig. 3). Schematic diagrams, not to scale, of the radiation transfer through these structures were approximated and illustrated in Fig. 1a–c. This figure shows the mechanism of radiation transfer through the net structure as two parts (i.e., the forward scattered and un-scattered radiation). The sum of the two parts is equal to / G in W m2. For estimating the net porosity, the two parts of radiation need to be determined separately. The transmitted radiation due to the forward scattering through the thread surfaces is determined under the following assumptions: (i) Due to the three dimensional shape and roughness of the net texture, the incident radiation on the thread surface reflects forward and backward diffusively. Therefore the view factor concept can be applied to evaluate the forward scattering. In addition, the effect of solar azimuth angle on the reflected and transmitted radiation was neglected. (ii) Due to the random orientation of the thread surfaces with respect to the incident beam radiation, one surface only [i.e., surface-1 or surface-2 in Fig. 1a–c] is consider for reflection depends on the incident angle of the beam radiation h before and after noon. (iii) The downward scattered radiation due to the radiation incident on surface-1 or surface-2 reaches the empty area-3 either directly or after one, two or multiple reflections between surfaces 1 and 2 [Fig. 1a and b]. Thus, the transmitted solar energy due to the forward scattering Esc after the multiple reflections of the incident radiation between surfaces 1 and 2 is given by [11] as:
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Fig. 3. Magnified scanner images of the different nets tested in this study.
Esc ¼
GA1 qF 13 1 1 qF 12 A3
ð7Þ
where F12 and F13 are the shape factors between surface-1 and surface-2 and between surface-1 and the empty area-3, respectively. And A1 and A3 are the area of surface-1 and the empty area-3 per unit length of the net. Relations used to estimate the values of F12, F13, A1, A2 and A3 are explained in the Appendix A.
Table 1 Geometrical description and the structural dimensions of threads for the tested nets. Net type
Texture description
Dimensions (mm)
White-50
Parallel interlaced threads, like woven robs, held by wires Parallel interlaced threads, like straight robs, held by wires Parallel strips held by interlaced strips Parallel strips held by interlaced strips Parallel strips held by interlaced strips Knitted wires, irregular openings
D = 2, S = 1, d = 1
Green-50 Orange-80 Beige-80
In the case of the knitted wire net (e.g., dark green-80 net), the radiation transmission was approximated as in Fig. 1c and the reflection between surfaces 1 and 2 was neglected. The value of Esc was estimated from Eq. (7) by making F12 equal to zero and F13 equal to 0.5. According to ASTM standard D1003 [12], the ratio of solar radiation scattered during transmission to the total radiation transmitted Fsc is defined as ‘haze’ which is equivalent to the scattering coefficient for solar beam radiation [12]. Thus, in the present analysis the scattering coefficient Fsc is given by:
F sc ¼ Esc =/G
ð8Þ
The amount of un-scattered solar radiation Ep that is transmitted through the net pores directly is given by:
Ep ¼ /G Esc
ð9Þ
Each net pore is surrounded by three dimensional surfaces; therefore the value of Ep changes with the time of the day. Accordingly, the net porosity P is estimated as:
P¼
Z
t2
t1
Ep dt=
Z
t2
Gdt
ð10Þ
t1
where t1 and t2 are the sunrise and sunset times, respectively. 3. Materials and methods 3.1. Shading net materials Six different plastic shading nets that are commonly used for shading structures in hot and long summer seasons were selected for testing. These nets were locally produced by Saudi Yarn and Knitted Technology Factory (SYNTECH-ISO 9001). The nets were classified based on the producer definition into two groups: nets-80 and nets-50, which means the nominal shading rates are 80% and 50%, respectively. Net material (colored HDPE) was
Blue-80 Dark green-80
D = 1.75, S = 2.5, d = 1 a = 1.2, b = 12, c = 4 a = 1, b = 13, c = 2.1 a = 2, b = 10, c = 5 Dm = 3.5, d = 1
assumed opaque to transmit radiation. Textures of nets were either interlaced threads or interlaced strips. Threads made of plastic yarns knitted together and look as robe or wire. Threads or flat plastic strips are arranged in parallel and held by interlaced strips or wires to perform the texture. Net texture is multidirectional surfaces and multidimensional spaces. Nets in each group have different colors (i.e., white and green for nets-50; blue, beige, orange and dark green for nets-80). Samples of the tested nets were tacked to a thin frame (5 cm 5 cm), scanned with a flatbed scanner (HP5590) and the photos were magnified several times to make the analysis easier. Photos of the nets were magnified and illustrated in Fig. 3. Geometrical descriptions and dimensions of the net texture were measured and are illustrated in Table 1. 3.2. Experimental measurements Two experiments were conducted on the roof of the building of the Agricultural Research and Experiment Station, Agriculture Engineering Department, King Saud University (Riyadh, Saudi Arabia, 46° 470 E, longitude and 24° 390 N, latitude). The building was higher than nearby buildings and trees. The two experiments are for the proposed method (i.e., modified radiation balance method) and for the direct beam transmittance method. In addition, other experiment was conducted for the image processing method. Detailed of these experiments are as follows: 3.2.1. Image processing experiment A simple technique was applied by tacking the net sample to a thin frame (5 cm 5 cm) and scanning it at resolutions of 600,
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Fig. 4. Schematic diagram of the experimental set up used to measure the transmittances of the tested nets to direct beam solar radiation at normal incidence. Dimensions are in cm, not to scale.
1200, 2400, 3600 and 4800 dpi with a flatbed scanner (HP-5590). Photos of the scanned nets were magnified and converted to high contrast black and white colors to represent the threads projection area and the empty area using ADOBE Photoshop software. Gray color generated by shadows of some threads was carefully removed from the images. The resulting images were only black and white and represent the projected area of threads and pores filled with air in the net. A program was designed based on software package that support the image processing (C++-Evision and Labview-NIvision) for measuring the representative area of threads projection and the empty area. The value of P was estimated corresponding to each scanning resolution as the ratio between the empty area to the total area of the net sample. 3.2.2. Direct beam transmittance experiment Each net sample was tacked on a black-painted wooden box (60 cm 60 cm 20 cm), Fig. 4. The box was oriented toward the sun disc and adjusted to make the incident angle h, of solar beam equal to zero. Global solar radiation was measured in the box before and after tacking the net sample by using a solarimeter fixed horizontally at the base center of the box. The net sample was removed as quickly as possible and the change of incident radiation within this time was minor and could be neglected. This procedure was repeated with shading the box with an opaque plate to measure the diffuse solar radiation in the box with and without the net. The direct beam radiation was determined as the difference between the global and diffuse radiation. In this case, the transmittance of the net to direct beam radiation was estimated as the ratio of the direct beam measured in the box with the net to the direct beam measured in the box without the net. As in the previous studies that used this method, the value of P was considered to be equal to the transmittance of the net to direct beam radiation at normal incidence. 3.2.3. The proposed method experiment Each net sample was tacked on a black-painted wooden frame (200 cm 150 cm 150 cm). Layout dimensions and locations of
solarimeters used to measure the solar radiation components (i.e., G, R, T and U) are illustrated, not to scale, in Fig. 2. The frame was oriented longitudinally in the E–W direction. Horizontal bars mounted 20 cm below and above the center of the frame in Fig. 2 supported the solarimeters used to measure the global radiation components. The arrangement in Fig. 2 allows the specular components of the reflected solar radiation from the net surface to reach the inverted solarimeters at incidence angles h from 0° up to 80°. At times when h was higher than 80°, the incident and reflected radiations were usually diffuse and the reflected portion could be detected by the inverted solarimeters. This experiment in addition to the direct beam experiment was conducted from 6 am to 6 pm on clear sunny days during the period from April 29, 2009 to May 7, 2009. One net sample was tested on a given day. Solarimeters used in the experiments were CMP3 (Kipp & Zonen B.V. Inc., USA), having a time response of 18 s, a maximum error of ±2%, a sensitivity of 5–20 lV/Wm2, a working temperature range of 40 °C to +80 °C, and a wavelength range of 310–2800 nm. The solarimeters used in the two experiments were calibrated before use by means of the supplier. The measured parameters were recorded every 5 min in a data logger (Li-1400, 9 channels, Li-COR, Inc.). 4. Results and discussion For all the net types, a scanning resolution of 2400 dpi was sufficient to obtain a precise value of P (Fig. 5). Increasing the resolution higher than 2400 dpi did not affect the value of P significantly. In addition, the time required to process the image of the net sample increased with increasing scanning resolution. The value of P at a resolution of 4800 dpi was considered as the most accurate value and was used as a reference for comparison to validate the results of the proposed method. The forward scattering of the incident radiation on the thread surfaces (Esc) mainly depended on the net color, increased with increasing net brightness and decreased with the net darkness [Fig. 6a]. Therefore, Esc was higher for white-50, beige-80 and or-
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55
0.8
50
Porosity, Π (%)
40 35 30 25 20 15 10
Total transmittance φ, (-)
0.7 White-50 Beige-80 Green-50 Orange-80 Blue-80 Dark green-80
45
5
0.6 0.5 0.4 0.3 White-50 Green-50 Beige-80 Orange-80 Blue-80 Dark green-80
0.2 0.1 0.0
0 0
600
10
1200 1800 2400 3000 3600 4200 4800 5400
20
Fig. 5. Effect of scanning resolution on the value of the net porosity, P estimated by using the image processing method.
(a) 600
40
50
60
70
80
90
Fig. 7. The total transmittances to global solar radiation, / for the tested nets as affected by the incidence angle of beam radiation, h.
1.0 Green-50 White-50 Blue-80 Beige-80 Orange-80 Dark green-80
500 400
0.9 0.8 0.7
Fsc, (-)
Esc, (Wm-2)
30
Incidence angle θ, (degree)
Scanning resolution (dpi)
300 200
0.6
White-50 Green-50 Beige-80 Orange-80 Blue-80 Dark green-80
0.5 0.4 0.3 0.2
100
0.1 0
0.0 6
7
8
9
10
11
12 13 14
15
16 17 18
(b)
600 White-50 Green-50 Beige-80 Orange-80 Blue-80 Dark green-80
Ep, (Wm-2)
500 400 300 200 100 0 6
7
8
9
10
11
12 13 14
10
20
30
40
50
60
70
80
90
Incidence angle θ, (degree)
Time of the day, (hr)
15 16
17 18
Time of the day, (hr) Fig. 6. Time courses of solar energy transmitted from the nets: (a) due to forward scattering of the incident radiation on the threads surfaces Esc, (b) un-scattered radiation transmitted directly from the net pores, Ep.
ange-80 nets than for green-50, blue-80 and dark green-80 nets. The un-scattered radiation (Ep) mainly depended on the net structure and the percent of the area that was pores in the net texture [Fig. 6b]. The total transmittances of global solar radiation through the nets / [defined in Eq. (5)] decreased with increasing incidence angle h (Fig. 7) in a manner similar to the transmittance through the translucent homogeneous materials (e.g., plastic films and glass). However, / slightly decreased with increasing h because
Fig. 8. Ratio of the transmitted radiation due to the forward scattering to the total transmitted radiation (scattering coefficient Fsc) as affected by the incidence angle h for the tested nets.
of the increase of the forward scattering coefficient (Fsc) with increasing h. Also because of the increase of the diffuse radiation percent, allocated with a relatively high value of /, at high values of h around the times of sunrise and the sunset. / is a function of the scattering coefficient Fsc [Eq. (8)], which depends mainly on the net color, and the fraction of radiation that is transmitted directly from the net pores (i.e., un-scattered transmittance). To correctly estimate net porosityP when using the radiation methods, it is necessary to separating the scattering coefficient Fsc from the total net transmittance /. Fsc increased with increasing h, with increasing brightness of the net color, and with increasing surface area of the threads that reflect the incident radiation downward (Fig. 8). Fsc decreased with increasing darkness of the color and with decreasing surface area of the threads that scatter the radiation. For all the tested net, except green-50, Fsc reached unity at high values of h around the times of sunrise and sunset. This means that all the transmitted radiation at high values of h is mainly due to scattering. In other words, the contribution of the scattered radiation to the total transmittance of the net is greatest at high incidence angles in the early morning and late afternoon. To validate the proposed method, values of P obtained from the proposed method (Eq. (10)) were compared with those obtained from: (i) the image processing method at a resolution of 4800 dpi, which gives the most accurate values of P, (ii) the radiation balance method
A.M. Abdel-Ghany, I.M. Al-Helal / Energy Conversion and Management 52 (2011) 1755–1762
1.0 Direct beam transmittance method Radiation balance method Image processing method Proposed method
0.9
Net porosity Π (-)
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
White-50 Green-50 Beige-80 Orange-80 Blue-80 Dark green-80
Net types Fig. 9. Porosities, P of the tested nets estimated by using: the proposed method, direct beam transmittance method, radiation balance method and image processing method at scanning resolution of 4800 dpi.
1.0 White-50 Green-50 Beige-80
Thread reflectance ρ, (-)
0.9
Orange-80 Blue-80 Dark green-80
0.8 0.7 0.6
range from 0.8% for dark green-80 net to 2% for white-50 net. This indicates that the proposed method is accurate and can be used to predict the value of P precisely for any type of plastic net. Referring to the image processing method as a reference, the radiation balance and the direct beam transmittance methods gave high overestimation errors on the values of P for the different nets (Fig. 9). The direct beam method resulted in errors in the range from +16% for the green-50 net to +38% for the white-50 and beige-80 nets. The radiation balance method resulted in errors in the range from +14% for the green-50 net to +37% for the white-50 and beige-80 nets. These results show that the direct beam and the radiation balance methods do not give accurate estimates for the value of P for a plastic net. Radiative properties of the thread material are essential physical properties used to characterize a net and are required for any energy transfer analysis of a net-covered structure. The thread reflectance q [calculated from Eqs. (3) and (4)], mainly depends on the thread color, increasing with increasing brightness (Fig. 10). White, beige, and orange nets in this order showed higher values of q than blue, green and dark green nets. q slightly increased with increasing h because the specular component of the reflected radiation is small and most of the incident radiation reflects diffusively. The absorptance of the net threads a was not significantly affected by h but was significantly affected by the net color (Fig. 11). Thus, the dark green, blue, and green nets showed higher values of a than the white, beige, and orange nets.
0.5 0.4
5. Conclusions
0.3 0.2 0.1 0.0 10
20
30
40
50
60
70
80
90
Incidence angle θ, (degree) Fig. 10. Threads reflectance, q as affected by the incidence angle of solar beam radiation h for the tested nets.
1.0 0.9
Thread absorptance α, (−)
1761
0.8 0.7 0.6 0.5 0.4
A methodology was presented, validated and used to estimate the porosities of different types of plastic nets. The method is a modified version of the radiation balance method that takes into account the forward scattering of the incident radiation on the thread surfaces. Un-scattered radiation transmitted from the net pores directly could be estimated separately and used to calculate the net porosity. Results of the proposed method were in good accordance with results of the image processing method at significantly high scanning resolution. Forward scattering adds a considerable amount of radiation to that transmitted through the net pores. Therefore, the currently used radiation balance and direct beam transmittance methods result in large overestimation errors in the value of P. These errors strongly depended on the color of the net. For the white net, the estimated errors were +38% for the direct beam transmittance method and +37% for the radiation balance method, whereas for the green net, these errors were reduced to +14% and +16%, respectively. In the image processing method, the scanning resolution should be higher than or equal to 2400 dpi for accurate estimation of the porosity.
0.3
Acknowledgements
0.2
White-50 Green-50
0.1
Orange-80 Blue-80 Dark green-80
Beige-80
0.0 10
20
30
40
50
60
70
80
90
Incidence angle θ, (degree) Fig. 11. Threads absorptance, a as affected by the incidence angle of solar beam radiation h for the tested nets.
[the integrated value of / from Eq. (5)] and (iii) the direct beam transmittance method. The values of P obtained from the proposed method were in good agreement with those obtained from the image processing method at high resolution (Fig. 9). The difference between the results of the two methods was in the
This work has been supported by the National Plan for Sciences and Technology (NPST) program by King Saud University, project number 09-ENE912-02. Authors express thank to Mr. M. R. Shady for his technical assistance during the experiments. Appendix A A.1. Relations to estimate the view factors and the related surface areas The Beige-80, orange-80 and blue-80 nets, were approximated as identical, parallel, directly opposed rectangles in Fig. 1a. The view factor is given by [13] as:
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2
!1=2 2 4 ð1 þ X 2 Þð1 þ Y 2 Þ ln pXY 1 þ X2 þ Y 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffi X þ X 1 þ Y 2 tan1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ Y2 # qffiffiffiffiffiffiffiffiffiffiffiffiffiffi Y þ Y 1 þ X 2 tan1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi X tan1 X Y tan1 Y 1 þ X2
The surface areas A1, A2 and A3 were approximated as:
F 12 ¼
X ¼ a=c; Y ¼ b=c
A1 ¼ A2 ¼ p2 Dm d=4; A3 ¼ pD2m =4
where d is the wire diameter and Dm is the mean diameter of the empty area.
ðA1Þ ðA2Þ
where a, b and c are the strip thickness, length of the empty area and width of the empty area, respectively. The view factor relations are as follows:
F 12 þ 2F 13 ¼ 1; F 12 ¼ F 21
ðA3Þ
The surface areas A1, A2 and A3 were estimated per unit length of the net as:
A1 ¼ A2 ¼ b a; A3 ¼ b c
ðA4Þ
White-50 and green-50 nets were approximated as infinitely long parallel cylinders of the same diameter in Fig. 1b. The view factor is given by [13] as:
F 12 ¼
1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 X ; X ¼ 1 þ S=D X 2 1 þ sin X p
ðA5Þ
The view factor relations were considered as in Eq. (A3). The surface areas A1, A2 and A3 per unit length of the net were estimated as:
A1 ¼ A2 ¼ pD=4; A3 ¼ S þ D
ðA6Þ
The dark green-80 net was approximated as in Fig. 1c and the view factor is given by:
F 12 ¼ 0; F 13 ¼ 0:5
ðA8Þ
ðA7Þ
References [1] Castellano S, Scarascia GM, Russo G, Briassoulis D, Mistriotis A, Hemming S, et al. Plastic nets in agriculture: a general review of types and applications. Appl Eng Agric 2008;24:799–808. [2] Briassoulis D, Mistriotis A, Eleftherakis D. Mechanical behavior and properties of agricultural nets. Part II: analysis of the performance of the main categories of agricultural nets. Polymer Test 2007;20:970–84. [3] Briassoulis D, Mistriotis A, Eleftherakis D. Mechanical behavior and properties of agricultural nets. Part I: testing methods for agricultural nets. Polymr Test 2007;26:822–32. [4] Miguel AF. Airflow through porous screens: from theory to practical considerations. Energy Build 1998;28:63–9. [5] Castellano S, Russo G, Scarascia GM. The influence of construction parameters on radiometric performances of agricultural nets. Acta Hort 2006;718:283–90. [6] Cohen S, Fuchs M. Measuring and predicting radiometric properties of refractive shade nets and thermal screens. J Agric Eng Res 1999;73:245–55. [7] Soni P, Salokhe VM, Tantau HJ. Effect of screen mesh size on vertical temperature distribution in naturally ventilated tropical greenhouses. Biosyst Eng 2005;92:469–82. [8] Castellano S, Candura A, Scarascia GM. Relationship between solidity ratio, colour and shading effect of agricultural nets. Acta Hort 2008;801:253–8. [9] Teitel M, Segal I. Net thermal radiation under shading screens. J Agric Eng Res 1995;61:19–26. [10] Desmarais G, Ratti C, Raghavan GSV. Heat transfer modeling of screenhouses. Solar Energy 1999;65:271–84. [11] Siegel R, Howell JR. Thermal radiation heat transfer. 3rd ed. Washington: Taylor & Francis Inc.; 1992. [12] Burek SAM, Norton B, Probert SD. Transmission and forward scattering of insolation through plastic (transparent and semi-transparent) materials. Solar Energy 1989;42:457–75. [13] Howell J R. A catalog of radiation heat transfer, 2nd ed. at:.
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Analysis of solar radiation transfer: A method to estimate the porosity of a plastic shading net A.M. Abdel-Ghany ⇑, I.M. Al-Helal Department of Agricultural Engineering, College of Food and Agriculture Sciences, King Saud University, P O Box 2460, Riyadh 11451, Saudi Arabia
a r t i c l e
i n f o
Article history: Received 3 March 2010 Accepted 7 November 2010
Keywords: Plastic net Porosity Solar radiation Transmittance Forward scattering
a b s t r a c t Plastic nets with opaque threads are frequently used for shading agricultural structures under high solar radiation conditions. A parameter that is often used to define a net is the net porosity (P). Value of P is usually estimated by one of three methods: image processing, direct beam transmittance, or solar radiation balance (hereafter radiation balance). Image processing is a rather slow process because it requires scanning the net sample at high resolution. The direct beam transmittance and radiation balance methods greatly overestimate P because some of the solar radiation incident on the thread surfaces is forward scattered and add a considerable amount of radiation to that transmitted from the net pores directly. In this study, the radiation balance method was modified to estimate P precisely. The amount of solar radiation scattered forward on the thread surfaces was estimated separately. Thus, the un-scattered solar radiation transmitted from the net pores directly, which describes the net porosity, P could be estimated. This method, in addition to the image processing and the direct beam transmittance methods were used to estimate P for different types of nets that are commonly used for shading structures in summer. Values of P estimated by using the proposed method were in good accordance with those measured by the image processing method at a resolution of 4800 dpi. The direct beam transmittance and the radiation balance methods resulted in overestimation errors in the values of P. This error strongly depends on the color of the net. The estimated errors were +14% for a green net and +37% for a white net when using the radiation balance method, and were +16% and +38%, respectively, when using the direct beam transmittance method. In the image processing method, a resolution of 2400 dpi is sufficient to estimate P precisely and the higher resolutions showed no significant effect on the value of P. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Plastic nets made from high-density polyethylene (HDPE) are widely used in various agricultural applications to protect crops and nurseries from hail, strong wind, snow, strong rainfall, insects, animals and birds. Shading is the most important application of the plastic nets in hot and sunny regions to reduce the solar radiation levels and improve the environment. Shade netting is also used for covering animals, swimming pools, playground and car parks. During the last decade, the uses of plastic nets for covering agricultural structures have steadily expanded because they offer many advantages and environmental and economical benefits [1–3]. Many types of plastic nets with different colors and textures are available in the markets and used by customers. However, the choices of nets have been mostly empirically determined so far. This is because technical information such as the physical ⇑ Corresponding author. Tel./fax: +966 (01) 4678352. E-mail addresses: [email protected], [email protected] (A.M. AbdelGhany). 0196-8904/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2010.11.002
properties of these nets still unclear. In addition, appropriate methodologies to measure the physical properties of plastic nets have not been established yet. Net porosity P is the most important physical property describing a net because it has a considerable effect on the radiation transfer through the net as well as the shading power. Moreover, the net porosity is an essential parameter needed to estimate the ventilation rate of a structure covered with this net. Porosity is simply defined as the dimensionless ratio of the open area divided by the total area of the net surface; and is the complementary value of the net solidity, (solidity = 1–P). Based on a survey of previous studies performed in this area, three methods have been used to estimate the net porosity [1]. These methods are: (i) image processing method based on a microscopic analysis of the image of the net sample, (ii) direct beam transmittance method based on measuring the net transmittance to direct beam solar radiation at normal incidence and (iii) radiation balance method based on applying solar energy balance below and above the net surface to estimate the total transmittance of the net to global solar radiation. Description and problems associated with each method can be summarized as follows:
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Nomenclature total surface area of the net [m2] total empty area of the net surface [m2] area of surface-1 and -2 which reflect radiation downward [m2] A3 area of the net pore that receive the scattered radiation downward [m2] a, b, c, D, Dm, d construction dimensions in Fig. 1a–c [mm] dt time interval [sec] Ep un-scattered solar energy transmitted from the net pores directly [W m2] solar energy transmitted from the net pores due to the Esc forward scattering on the thread surfaces [W m2] F1-2 view factor from surface-1 to surface-2 [-] Fsc ratio of the forward scattered radiation to the total radiation transmitted [-] G downward incident solar radiation flux over the net surface [W m2]
A Aa A1, A2
1.1. Image processing method Consider a sample of a plastic net material having a volume V. This sample is composed of a solid matrix (i.e. threads material) with some amount of air inside. The volume fraction of air phase is given by [4] as:
P ¼ V a =V
ð1Þ
in which P is the porosity and Va is the volume of air in the solid matrix. Since plastic nets are always made of thin and uniform threads, their porosity can be approximated as:
P ¼ Aa =A
ð2Þ
where Aa represents the empty area filled with air and A is the total surface area of the net. Porosity described by Eq. (1) can be determined only by weighing the net sample in vacuum conditions and in atmospheric air condition. Such procedure is quite difficult to apply for evaluating the net porosity. Porosity described by Eq. (2) can be determined by magnifying the sample with the help of a microscope and measuring the representative areas Aa and A. A simple technique is usually used by tacking the net sample to a thin frame and scanning it in a flatbed scanner. Image is analyzed for measuring the representative areas of Aa and A. This method is widely used to estimate P. For example, it was used at scanning resolutions of 2400 dpi in [5], 600 dpi in [6]; and with unspecified resolutions in [4,7,8]. Even though scanning resolution is expected to affect the value of P, the effect of scanning resolution on the precision of the value for P has not yet been examined. 1.2. Direct beam transmittance method In this method, the net sample is tacked on a frame; global solar radiation is measured below and above the net surface at an incidence angle of solar beam radiation, h equal to zero. This procedure is repeated with shading the frame with an opaque plate to measure the diffuse solar radiation below and above the net sample. The direct beam radiation is determined as the difference between the global and diffuse radiations. In this case, net transmittance to direct beam is estimated as the ratio between direct beam below and above the net. Value of P is considered as the net transmittance to direct beam radiation at normal incidence. This method has been used by several investigators, for example, [6,8–10]. However, values of P estimated by this method were much higher than
R S t T U V Va
a P / h
q
reflected radiation upward from the net surface [W m2] texture dimension in Fig. 1 (b) [mm] time [sec] downward radiation below the net surface [W m2] upward radiation below the net surface [W m2] total volume of a porous material [m3] volume of pores filled with air [m3] absorptance of the net material [-] the net porosity [-] the total transmittance of the net to global solar radiation [-] incidence angle of solar beam radiation [°] reflectance of the net material [-]
those estimated by the image processing method. Reported differences were around +12% in [6] for metallic screens; +8% in [8] for net with black threads; and from +13% to +25% in [10] for nets with white and amber threads. Investigators attributed these differences to the transparency of the thread materials. However, these differences were found even when the nets were made of black threads which are opaque to solar radiation. In fact this difference is mainly due to the nature of the radiation transmitted through the net. In nets, a portion of the incident radiation scatters forward on the thread surface and is transmitted through the net and the other portion is un-scattered radiation that is transmitted directly through the net pores without striking any part of the thread surfaces [see Fig. 1a–c]. Only the un-scattered radiation is related to the net porosity. Thus, the net total transmittance is the sum of the two portions and is usually higher than the net porosity. 1.3. Radiation balance method In this method, the net sample is tacked on a horizontal frame (as shown in Fig. 2). Downward and upward global solar radiation fluxes are measured beneath (i.e., T and U) and above (i.e., G and R) the net surface. Radiation balance below and above the net surface is applied to express the values of T and R as:
T ¼ G/ þ ð1 /ÞqU
ð3Þ
R ¼ U/ þ ð1 /ÞqG
ð4Þ
By solving Eqs. (3) and (4) simultaneously, values of the net transmittance to global solar radiation / and the thread reflectance q could be determined. Previous studies assumed that / is equal to the net porosity [6,8]. However, / was always found to be much higher than the net porosity obtained by using the image processing method because / is equivalent to the net porosity plus a fraction equal to the ratio of the radiation scattered downward through the net pores to the total radiation transmitted through the net. Based on the previous discussion, an appropriate method to estimate the porosity of a plastic net precisely is urgently needed. The objectives of this study are to: (i) modify the radiation balance method to be used for determining the value of P precisely, (ii) examine the effect of scanning resolution used in the image processing method on the value of P and (iii) check the precession of the proposed method by comparing its results with the results of the image processing and direct beam transmittance methods.
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Fig. 1. Schematic diagrams of the structures approximated the tested nets and mechanisms of solar radiation transfer showing the forward scattering.
Fig. 2. Schematic diagram of the experimental set up and locations of the solarimeters used to measure the global solar radiation components below and above the net sample. Dimensions are in cm, not to scale.
2. The Proposed method Solving Eqs. (3) and (4) for / gives:
/ ¼ ðTG RUÞ=ðG2 U 2 Þ
ð5Þ
Net absorptance a as a radiative property needed for any thermal analysis can be expressed as:
ð1 /Þa ¼ ½ðG RÞ ðT UÞ=ðG þ UÞ
ð6Þ
where q and a are the reflectance and absorptance of the net mate^ reprerial (i.e., opaque plastic threads, q + a = 1). The parameter u sents the apparent porosity of the net, i.e., the true porosity plus the fraction of solar radiation scattered downward and then transmitted through the net pores. In other words, / represents the total transmittance of the net to global solar radiation. Values of q and a are deduced from direct substitution of / into Eqs. (3) and (6).
The common shapes of the textures of the commercial plastic net are either parallel strips held by interlaced strips/wires (e.g., beige-80, orange-80 and blue-80 nets in Fig. 3); or parallel interlaced threads, like robs, held by wires (e.g., green-50, white-50 nets in Fig. 3); or knitted wires in random shape (e.g., dark green-80 nets in Fig. 3). Schematic diagrams, not to scale, of the radiation transfer through these structures were approximated and illustrated in Fig. 1a–c. This figure shows the mechanism of radiation transfer through the net structure as two parts (i.e., the forward scattered and un-scattered radiation). The sum of the two parts is equal to / G in W m2. For estimating the net porosity, the two parts of radiation need to be determined separately. The transmitted radiation due to the forward scattering through the thread surfaces is determined under the following assumptions: (i) Due to the three dimensional shape and roughness of the net texture, the incident radiation on the thread surface reflects forward and backward diffusively. Therefore the view factor concept can be applied to evaluate the forward scattering. In addition, the effect of solar azimuth angle on the reflected and transmitted radiation was neglected. (ii) Due to the random orientation of the thread surfaces with respect to the incident beam radiation, one surface only [i.e., surface-1 or surface-2 in Fig. 1a–c] is consider for reflection depends on the incident angle of the beam radiation h before and after noon. (iii) The downward scattered radiation due to the radiation incident on surface-1 or surface-2 reaches the empty area-3 either directly or after one, two or multiple reflections between surfaces 1 and 2 [Fig. 1a and b]. Thus, the transmitted solar energy due to the forward scattering Esc after the multiple reflections of the incident radiation between surfaces 1 and 2 is given by [11] as:
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Fig. 3. Magnified scanner images of the different nets tested in this study.
Esc ¼
GA1 qF 13 1 1 qF 12 A3
ð7Þ
where F12 and F13 are the shape factors between surface-1 and surface-2 and between surface-1 and the empty area-3, respectively. And A1 and A3 are the area of surface-1 and the empty area-3 per unit length of the net. Relations used to estimate the values of F12, F13, A1, A2 and A3 are explained in the Appendix A.
Table 1 Geometrical description and the structural dimensions of threads for the tested nets. Net type
Texture description
Dimensions (mm)
White-50
Parallel interlaced threads, like woven robs, held by wires Parallel interlaced threads, like straight robs, held by wires Parallel strips held by interlaced strips Parallel strips held by interlaced strips Parallel strips held by interlaced strips Knitted wires, irregular openings
D = 2, S = 1, d = 1
Green-50 Orange-80 Beige-80
In the case of the knitted wire net (e.g., dark green-80 net), the radiation transmission was approximated as in Fig. 1c and the reflection between surfaces 1 and 2 was neglected. The value of Esc was estimated from Eq. (7) by making F12 equal to zero and F13 equal to 0.5. According to ASTM standard D1003 [12], the ratio of solar radiation scattered during transmission to the total radiation transmitted Fsc is defined as ‘haze’ which is equivalent to the scattering coefficient for solar beam radiation [12]. Thus, in the present analysis the scattering coefficient Fsc is given by:
F sc ¼ Esc =/G
ð8Þ
The amount of un-scattered solar radiation Ep that is transmitted through the net pores directly is given by:
Ep ¼ /G Esc
ð9Þ
Each net pore is surrounded by three dimensional surfaces; therefore the value of Ep changes with the time of the day. Accordingly, the net porosity P is estimated as:
P¼
Z
t2
t1
Ep dt=
Z
t2
Gdt
ð10Þ
t1
where t1 and t2 are the sunrise and sunset times, respectively. 3. Materials and methods 3.1. Shading net materials Six different plastic shading nets that are commonly used for shading structures in hot and long summer seasons were selected for testing. These nets were locally produced by Saudi Yarn and Knitted Technology Factory (SYNTECH-ISO 9001). The nets were classified based on the producer definition into two groups: nets-80 and nets-50, which means the nominal shading rates are 80% and 50%, respectively. Net material (colored HDPE) was
Blue-80 Dark green-80
D = 1.75, S = 2.5, d = 1 a = 1.2, b = 12, c = 4 a = 1, b = 13, c = 2.1 a = 2, b = 10, c = 5 Dm = 3.5, d = 1
assumed opaque to transmit radiation. Textures of nets were either interlaced threads or interlaced strips. Threads made of plastic yarns knitted together and look as robe or wire. Threads or flat plastic strips are arranged in parallel and held by interlaced strips or wires to perform the texture. Net texture is multidirectional surfaces and multidimensional spaces. Nets in each group have different colors (i.e., white and green for nets-50; blue, beige, orange and dark green for nets-80). Samples of the tested nets were tacked to a thin frame (5 cm 5 cm), scanned with a flatbed scanner (HP5590) and the photos were magnified several times to make the analysis easier. Photos of the nets were magnified and illustrated in Fig. 3. Geometrical descriptions and dimensions of the net texture were measured and are illustrated in Table 1. 3.2. Experimental measurements Two experiments were conducted on the roof of the building of the Agricultural Research and Experiment Station, Agriculture Engineering Department, King Saud University (Riyadh, Saudi Arabia, 46° 470 E, longitude and 24° 390 N, latitude). The building was higher than nearby buildings and trees. The two experiments are for the proposed method (i.e., modified radiation balance method) and for the direct beam transmittance method. In addition, other experiment was conducted for the image processing method. Detailed of these experiments are as follows: 3.2.1. Image processing experiment A simple technique was applied by tacking the net sample to a thin frame (5 cm 5 cm) and scanning it at resolutions of 600,
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Fig. 4. Schematic diagram of the experimental set up used to measure the transmittances of the tested nets to direct beam solar radiation at normal incidence. Dimensions are in cm, not to scale.
1200, 2400, 3600 and 4800 dpi with a flatbed scanner (HP-5590). Photos of the scanned nets were magnified and converted to high contrast black and white colors to represent the threads projection area and the empty area using ADOBE Photoshop software. Gray color generated by shadows of some threads was carefully removed from the images. The resulting images were only black and white and represent the projected area of threads and pores filled with air in the net. A program was designed based on software package that support the image processing (C++-Evision and Labview-NIvision) for measuring the representative area of threads projection and the empty area. The value of P was estimated corresponding to each scanning resolution as the ratio between the empty area to the total area of the net sample. 3.2.2. Direct beam transmittance experiment Each net sample was tacked on a black-painted wooden box (60 cm 60 cm 20 cm), Fig. 4. The box was oriented toward the sun disc and adjusted to make the incident angle h, of solar beam equal to zero. Global solar radiation was measured in the box before and after tacking the net sample by using a solarimeter fixed horizontally at the base center of the box. The net sample was removed as quickly as possible and the change of incident radiation within this time was minor and could be neglected. This procedure was repeated with shading the box with an opaque plate to measure the diffuse solar radiation in the box with and without the net. The direct beam radiation was determined as the difference between the global and diffuse radiation. In this case, the transmittance of the net to direct beam radiation was estimated as the ratio of the direct beam measured in the box with the net to the direct beam measured in the box without the net. As in the previous studies that used this method, the value of P was considered to be equal to the transmittance of the net to direct beam radiation at normal incidence. 3.2.3. The proposed method experiment Each net sample was tacked on a black-painted wooden frame (200 cm 150 cm 150 cm). Layout dimensions and locations of
solarimeters used to measure the solar radiation components (i.e., G, R, T and U) are illustrated, not to scale, in Fig. 2. The frame was oriented longitudinally in the E–W direction. Horizontal bars mounted 20 cm below and above the center of the frame in Fig. 2 supported the solarimeters used to measure the global radiation components. The arrangement in Fig. 2 allows the specular components of the reflected solar radiation from the net surface to reach the inverted solarimeters at incidence angles h from 0° up to 80°. At times when h was higher than 80°, the incident and reflected radiations were usually diffuse and the reflected portion could be detected by the inverted solarimeters. This experiment in addition to the direct beam experiment was conducted from 6 am to 6 pm on clear sunny days during the period from April 29, 2009 to May 7, 2009. One net sample was tested on a given day. Solarimeters used in the experiments were CMP3 (Kipp & Zonen B.V. Inc., USA), having a time response of 18 s, a maximum error of ±2%, a sensitivity of 5–20 lV/Wm2, a working temperature range of 40 °C to +80 °C, and a wavelength range of 310–2800 nm. The solarimeters used in the two experiments were calibrated before use by means of the supplier. The measured parameters were recorded every 5 min in a data logger (Li-1400, 9 channels, Li-COR, Inc.). 4. Results and discussion For all the net types, a scanning resolution of 2400 dpi was sufficient to obtain a precise value of P (Fig. 5). Increasing the resolution higher than 2400 dpi did not affect the value of P significantly. In addition, the time required to process the image of the net sample increased with increasing scanning resolution. The value of P at a resolution of 4800 dpi was considered as the most accurate value and was used as a reference for comparison to validate the results of the proposed method. The forward scattering of the incident radiation on the thread surfaces (Esc) mainly depended on the net color, increased with increasing net brightness and decreased with the net darkness [Fig. 6a]. Therefore, Esc was higher for white-50, beige-80 and or-
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55
0.8
50
Porosity, Π (%)
40 35 30 25 20 15 10
Total transmittance φ, (-)
0.7 White-50 Beige-80 Green-50 Orange-80 Blue-80 Dark green-80
45
5
0.6 0.5 0.4 0.3 White-50 Green-50 Beige-80 Orange-80 Blue-80 Dark green-80
0.2 0.1 0.0
0 0
600
10
1200 1800 2400 3000 3600 4200 4800 5400
20
Fig. 5. Effect of scanning resolution on the value of the net porosity, P estimated by using the image processing method.
(a) 600
40
50
60
70
80
90
Fig. 7. The total transmittances to global solar radiation, / for the tested nets as affected by the incidence angle of beam radiation, h.
1.0 Green-50 White-50 Blue-80 Beige-80 Orange-80 Dark green-80
500 400
0.9 0.8 0.7
Fsc, (-)
Esc, (Wm-2)
30
Incidence angle θ, (degree)
Scanning resolution (dpi)
300 200
0.6
White-50 Green-50 Beige-80 Orange-80 Blue-80 Dark green-80
0.5 0.4 0.3 0.2
100
0.1 0
0.0 6
7
8
9
10
11
12 13 14
15
16 17 18
(b)
600 White-50 Green-50 Beige-80 Orange-80 Blue-80 Dark green-80
Ep, (Wm-2)
500 400 300 200 100 0 6
7
8
9
10
11
12 13 14
10
20
30
40
50
60
70
80
90
Incidence angle θ, (degree)
Time of the day, (hr)
15 16
17 18
Time of the day, (hr) Fig. 6. Time courses of solar energy transmitted from the nets: (a) due to forward scattering of the incident radiation on the threads surfaces Esc, (b) un-scattered radiation transmitted directly from the net pores, Ep.
ange-80 nets than for green-50, blue-80 and dark green-80 nets. The un-scattered radiation (Ep) mainly depended on the net structure and the percent of the area that was pores in the net texture [Fig. 6b]. The total transmittances of global solar radiation through the nets / [defined in Eq. (5)] decreased with increasing incidence angle h (Fig. 7) in a manner similar to the transmittance through the translucent homogeneous materials (e.g., plastic films and glass). However, / slightly decreased with increasing h because
Fig. 8. Ratio of the transmitted radiation due to the forward scattering to the total transmitted radiation (scattering coefficient Fsc) as affected by the incidence angle h for the tested nets.
of the increase of the forward scattering coefficient (Fsc) with increasing h. Also because of the increase of the diffuse radiation percent, allocated with a relatively high value of /, at high values of h around the times of sunrise and the sunset. / is a function of the scattering coefficient Fsc [Eq. (8)], which depends mainly on the net color, and the fraction of radiation that is transmitted directly from the net pores (i.e., un-scattered transmittance). To correctly estimate net porosityP when using the radiation methods, it is necessary to separating the scattering coefficient Fsc from the total net transmittance /. Fsc increased with increasing h, with increasing brightness of the net color, and with increasing surface area of the threads that reflect the incident radiation downward (Fig. 8). Fsc decreased with increasing darkness of the color and with decreasing surface area of the threads that scatter the radiation. For all the tested net, except green-50, Fsc reached unity at high values of h around the times of sunrise and sunset. This means that all the transmitted radiation at high values of h is mainly due to scattering. In other words, the contribution of the scattered radiation to the total transmittance of the net is greatest at high incidence angles in the early morning and late afternoon. To validate the proposed method, values of P obtained from the proposed method (Eq. (10)) were compared with those obtained from: (i) the image processing method at a resolution of 4800 dpi, which gives the most accurate values of P, (ii) the radiation balance method
A.M. Abdel-Ghany, I.M. Al-Helal / Energy Conversion and Management 52 (2011) 1755–1762
1.0 Direct beam transmittance method Radiation balance method Image processing method Proposed method
0.9
Net porosity Π (-)
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
White-50 Green-50 Beige-80 Orange-80 Blue-80 Dark green-80
Net types Fig. 9. Porosities, P of the tested nets estimated by using: the proposed method, direct beam transmittance method, radiation balance method and image processing method at scanning resolution of 4800 dpi.
1.0 White-50 Green-50 Beige-80
Thread reflectance ρ, (-)
0.9
Orange-80 Blue-80 Dark green-80
0.8 0.7 0.6
range from 0.8% for dark green-80 net to 2% for white-50 net. This indicates that the proposed method is accurate and can be used to predict the value of P precisely for any type of plastic net. Referring to the image processing method as a reference, the radiation balance and the direct beam transmittance methods gave high overestimation errors on the values of P for the different nets (Fig. 9). The direct beam method resulted in errors in the range from +16% for the green-50 net to +38% for the white-50 and beige-80 nets. The radiation balance method resulted in errors in the range from +14% for the green-50 net to +37% for the white-50 and beige-80 nets. These results show that the direct beam and the radiation balance methods do not give accurate estimates for the value of P for a plastic net. Radiative properties of the thread material are essential physical properties used to characterize a net and are required for any energy transfer analysis of a net-covered structure. The thread reflectance q [calculated from Eqs. (3) and (4)], mainly depends on the thread color, increasing with increasing brightness (Fig. 10). White, beige, and orange nets in this order showed higher values of q than blue, green and dark green nets. q slightly increased with increasing h because the specular component of the reflected radiation is small and most of the incident radiation reflects diffusively. The absorptance of the net threads a was not significantly affected by h but was significantly affected by the net color (Fig. 11). Thus, the dark green, blue, and green nets showed higher values of a than the white, beige, and orange nets.
0.5 0.4
5. Conclusions
0.3 0.2 0.1 0.0 10
20
30
40
50
60
70
80
90
Incidence angle θ, (degree) Fig. 10. Threads reflectance, q as affected by the incidence angle of solar beam radiation h for the tested nets.
1.0 0.9
Thread absorptance α, (−)
1761
0.8 0.7 0.6 0.5 0.4
A methodology was presented, validated and used to estimate the porosities of different types of plastic nets. The method is a modified version of the radiation balance method that takes into account the forward scattering of the incident radiation on the thread surfaces. Un-scattered radiation transmitted from the net pores directly could be estimated separately and used to calculate the net porosity. Results of the proposed method were in good accordance with results of the image processing method at significantly high scanning resolution. Forward scattering adds a considerable amount of radiation to that transmitted through the net pores. Therefore, the currently used radiation balance and direct beam transmittance methods result in large overestimation errors in the value of P. These errors strongly depended on the color of the net. For the white net, the estimated errors were +38% for the direct beam transmittance method and +37% for the radiation balance method, whereas for the green net, these errors were reduced to +14% and +16%, respectively. In the image processing method, the scanning resolution should be higher than or equal to 2400 dpi for accurate estimation of the porosity.
0.3
Acknowledgements
0.2
White-50 Green-50
0.1
Orange-80 Blue-80 Dark green-80
Beige-80
0.0 10
20
30
40
50
60
70
80
90
Incidence angle θ, (degree) Fig. 11. Threads absorptance, a as affected by the incidence angle of solar beam radiation h for the tested nets.
[the integrated value of / from Eq. (5)] and (iii) the direct beam transmittance method. The values of P obtained from the proposed method were in good agreement with those obtained from the image processing method at high resolution (Fig. 9). The difference between the results of the two methods was in the
This work has been supported by the National Plan for Sciences and Technology (NPST) program by King Saud University, project number 09-ENE912-02. Authors express thank to Mr. M. R. Shady for his technical assistance during the experiments. Appendix A A.1. Relations to estimate the view factors and the related surface areas The Beige-80, orange-80 and blue-80 nets, were approximated as identical, parallel, directly opposed rectangles in Fig. 1a. The view factor is given by [13] as:
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A.M. Abdel-Ghany, I.M. Al-Helal / Energy Conversion and Management 52 (2011) 1755–1762
2
!1=2 2 4 ð1 þ X 2 Þð1 þ Y 2 Þ ln pXY 1 þ X2 þ Y 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffi X þ X 1 þ Y 2 tan1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ Y2 # qffiffiffiffiffiffiffiffiffiffiffiffiffiffi Y þ Y 1 þ X 2 tan1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi X tan1 X Y tan1 Y 1 þ X2
The surface areas A1, A2 and A3 were approximated as:
F 12 ¼
X ¼ a=c; Y ¼ b=c
A1 ¼ A2 ¼ p2 Dm d=4; A3 ¼ pD2m =4
where d is the wire diameter and Dm is the mean diameter of the empty area.
ðA1Þ ðA2Þ
where a, b and c are the strip thickness, length of the empty area and width of the empty area, respectively. The view factor relations are as follows:
F 12 þ 2F 13 ¼ 1; F 12 ¼ F 21
ðA3Þ
The surface areas A1, A2 and A3 were estimated per unit length of the net as:
A1 ¼ A2 ¼ b a; A3 ¼ b c
ðA4Þ
White-50 and green-50 nets were approximated as infinitely long parallel cylinders of the same diameter in Fig. 1b. The view factor is given by [13] as:
F 12 ¼
1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 X ; X ¼ 1 þ S=D X 2 1 þ sin X p
ðA5Þ
The view factor relations were considered as in Eq. (A3). The surface areas A1, A2 and A3 per unit length of the net were estimated as:
A1 ¼ A2 ¼ pD=4; A3 ¼ S þ D
ðA6Þ
The dark green-80 net was approximated as in Fig. 1c and the view factor is given by:
F 12 ¼ 0; F 13 ¼ 0:5
ðA8Þ
ðA7Þ
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