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Accurate outdoor glass thermographic thermometry applied to solar energy devices
Solar Energy 81 (2007) 1025–1034 www.elsevier.com/locate/solener
Accurate outdoor glass thermographic thermometry applied to solar energy devices A. Krenzinger b
a,*
, A.C. de Andrade
b
a Solar Energy Laboratory, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil Faculdade de Fı´sica, Pontifı´cia Universidade Cato´lica do Rio Grande do Sul (PUCRS), Porto Alegre, Brazil
Received 18 November 2005; received in revised form 18 November 2006; accepted 28 November 2006 Available online 17 January 2007 ´ lvarez Garcı´a Communicated by: Associate Editor Gabriela A
Abstract The measurement of the temperature of the glass that covers solar collectors or photovoltaic modules is very important for the characterization of the performance of these converters. Thermography is a non-contact thermometry technique that is capable to quickly scan and record surface temperature fields, but its accuracy depends on knowing the limitations and possible errors involved with the use of this technique. This paper identifies glass infrared reflection errors and their consequences when performing outdoor thermographs. The work also proposes and experimentally validates a correction method for correcting these errors. Finally is also presented a method for estimating a thermographic equivalent sky temperature that can be used in correction procedures for the own outdoor thermographic measurements. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Thermography; Glass thermometry; Solar devices thermal analysis
1. Introduction Heat transfer in solar energy conversion devices is one of the most important parameters to be experimentally determined. The main experimental magnitude in order to know the amount of heat transfer is the temperature. Temperature measuring allows to determine thermal gradients and to evaluate thermal flux through surfaces in the interfaces of materials. A part of the thermal energy interchange is due to the radiation phenomenon, which emitted energy is proportional to the forth power of the body’s surface temperature. Then, by determining the emissive power emitted from a surface and its physical properties (basically the emittance) is quite simple to estimate the surface temperature.
*
Corresponding author. Tel./fax: +55 51 33086841. E-mail address: [email protected] (A. Krenzinger).
0038-092X/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2006.11.014
Infrared radiation can be measured using several radiometric techniques which have in common the presence of an element able to sense thermal radiation. Depending on the purposes of the instrument, the radiometer measures the incoming radiation from all the hemisphere directions, the incoming radiation from a well defined emitter region or it makes use of an array of sensors and a suitable lens system in order to register not only an incident radiation value but the radiosity field leaving a target surface. This last kind of infrared radiometry can produce infrared images and its techniques are sometimes called ‘‘infrared imagery’’ or ‘‘thermal imagery’’. Photographic infrared films was used in the first infrared imagery applications, but with the development of digital CCD sensors and associated technologies allowed the currently available possibilities. Infrared thermographic cameras are powerful apparatus capable to detect and to accurately measure thermal radiosity and surface temperature fields, which is especially useful when the technical study requires a
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differential thermal analysis. Bazilian et al. (2002) use thermographic techniques to study thermal effects of a photovoltaic roofing technology. Al-Kassir et al. (2005) illustrate infrared thermography showing energetic applications. Infrared images often are colored through software processes that pigment original gray levels with an electronic palette. The effect of this coloring process is very impressive and the resultant visual analyses seem much more accurate. The confidence provided by the camera images can blur some error possibilities and conduce to misunderstanding on their thermal analyses. This paper presents some of the outdoor glass surface thermographic thermometry errors and how to proceed in order to avoid them.
1x1011 1x1010 Temperature
Spectral Emissive Power (W/m².μm)
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300K 600K 6,000K
1x109 1x108 1x107 1x106 1x105 4
1x10
3
1x10
2
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1x101
2. Thermal radiation
0
1x10
Eb ðk; T Þ ¼
2phc2 k5 ½expðhc=kkT Þ 1
ð1Þ
where h is the Planck’s constant, k is the Boltzmann’s constant, c is the speed of light, T is the absolute temperature and k is the wavelength. Fig. 1 shows Eb(k) for different temperatures in a bilogarithmic scale and it shows that an important part (73%) of the radiation emitted by bodies which temperature are near 300 K lies in the band between 4 lm and 30 lm. The area below the curves represents the total emissive power and it is given by the Stefan–Boltzmann equation: Z 1 Eb ¼ Eb ðk; T Þ dk ¼ rT 4 ð2Þ 0
where r is the Stefan–Boltzmann constant. Fig. 2 shows a different graphic view of the same function. Now the emissive power is normalized to unit, by dividing each point by the maximum of its respective curve. This graphic is particularly elucidative to show that bodies
-1
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Wavelength (μm) Fig. 1. Blackbody spectral emissive power.
1 Temperature
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Normalized Emissive Power
The thermal energy in materials corresponds to the movement of molecules, atoms and subatomic particles which form the material. The intensity of the movement of the particles in the material depends on the temperature of the body. The electric charge displacement associated to the particle movement produce radiation emission through the body surface. The spectral range of the radiated energy constitutes the thermal radiation band from the electromagnetic spectrum, which is subdivided in three main smaller bands: ultraviolet, visible and infrared. Only bodies with very high temperatures emit ultraviolet and visible radiation with enough intensity to be detected, e.g. incandescent objects (more than 600 °C), but any body with temperature above absolute zero emits infrared radiation. The ideal emitter is called blackbody and the spectra distribution of its emission determines the maximum radiation flux that can be emitted per area unit in the surface of any body. The spectral emissive power of the blackbody is given by the Planck’s law:
0.8
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0 0.1
1
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100
Wavelength (μm) Fig. 2. Normalized blackbody spectral emissive power.
with very different surface temperature (like 300 K and 6000 K) do not share the same emitting band. A real body has an emissive power smaller than the blackbody. The ratio between the body’s surface monochromatic emissive power and the blackbody’s monochromatic emissive power at the same temperature is called monochromatic emittance e(k) and the ratio between the body’s surface total emissive power and the blackbody’s total emissive power at the same temperature is called hemispheric emittance or simply emittance e:
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R1
eðkÞEb ðk; T Þ dk rT 4
1027
ð6Þ
absorption correction factor. Fig. 3 shows the spectral transmittance of a 10-m atmospheric air layer constructed from data extracted from graphics presented by Gruner (2003) and by Dereniak and Boreman (1996). Note that exist several transmitting bands, specially from 2 lm to 2.5 lm, from 3 lm to 5 lm and from 8 lm to 13 lm. All of these bands are suitable for IR radiance transmission, but dependent on the interest temperature a band can be more affordable than the other. In particular the longer range between 8 lm and 13 lm is very appropriated for measuring radiance emitted by surfaces at near ambient temperature. Moreover, there is a lot of watching applications, mainly for surveillance and military applications, which promoted the developing of this kind of equipments. Now, if the response band is limited to a range between k1 and k2, the useful emissive power fraction is given by: R k2 eðkÞEb ðk; T Þ dk EU k ¼ R 11 ð7Þ M¼ E eðkÞEb ðk; T Þ dk 0
By sensing infrared radiation emitted by a body is possible to determine its surface temperature through noncontact measurements and there are several advantages in this kind of thermometry. The ideal sensitivity wavelength band of the radiometric sensor depends on the temperature range to be measured. If the detector is able to capture the radiant energy between 4 lm and 30 lm it is suitable to measure temperatures around 300 K. This band is not susceptible to the solar radiation and this is good for outdoor experiments, because on the contrary the sunlight could interfere in the measurements. By the other hand, is very convenient to use a sensor that responds in a band where the air is transparent. In the same way that one is familiarized to see through a long distance in the air, if the IR sensor is limited to a very high transmittance band there is not necessary to apply an air
and this ratio depends on target temperature. Fig. 4 shows M as function of temperature for k1 = 7 lm and k2 = 14 lm. Note that for temperatures around 300 K, M has a small variation, in relative terms, about 0.25%/K, which is minimum at about 380 K. This implies that, for a graybody, is almost the same to measure within these limits than to measure the total emissive power. A general schema for infrared radiant energy transfer from a target plane body to the detector can be seen in Fig. 5. There are two external sources and the target is also an infrared source itself. One of the external sources (S1) is behind the target and its infrared contribution to the sensor of the detector occurs only if the target is not opaque to the radiations within the sensitivity band of the detector. The other external source (S2) produces an increase in the radiation power received by the detector because part of its emissive power is reflected by the target to the radiometer. The radiosity is the total radiation power, per unit area, outgoing from the target body by combined emission,
e¼
0
ð3Þ
Kirchhoff’s law attests that, for each wavelength, the fraction of the incoming radiation that is absorbed by a surface (the absorptance a) is equal to the emittance, i.e., aðkÞ ¼ eðkÞ
ð4Þ
By the other hand, the incoming radiation in a body can have only three possibilities: to be reflected, to be absorbed or to be transmitted, so: qðkÞ þ aðkÞ þ sðkÞ ¼ 1
ð5Þ
where q(k) is the monochromatic reflectance and s(k) is the monochromatic transmittance. Opaque materials are those which the transmittance is null. Combining Eqs. (4) and (5) for opaque bodies results in qðkÞ ¼ 1 eðkÞ 3. Infrared radiometric thermometry and imagery
1 0.9
Air Transmittance
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Wavelength (μm) Fig. 3. Air spectral transmittance for a 10 m atmosphere layer.
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Useful Emissive Power Fraction
0.55
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0.45
LENS 0.40
HOT OBJECT
Fig. 6. Array sensor receiving image from the specular reflecting target with intervention of a hot object reflection, beyond the expected surrounding thermal radiation.
0.35
0.30
0.25
0.20 280
320
360
400
440
Temperature (K) Fig. 4. Useful emissive power fraction between 7 lm and 14 lm for different blackbody temperatures.
SOURCE 1
SOURCE 2
S2
S1
TARGET S3
τS1
ρS2 DETECTOR
εS3
Fig. 5. General scheme for infrared radiant energy transfer showing that the detector receives transmitted, reflected and emitted radiation from the target.
reflection and transmission. Dependent on the optics of the detector, the radiosity is the value that IR sensors are able to measure, not the temperature directly. If the target were a blackbody, only the emitted energy (S3) would strike the sensor, because the transmittance and reflectance would be null. For any other body, reflected or transmitted radiant energy can contribute to the infrared radiation leaving the surface. Because of this, it is very important to know the body’s surface properties. Considering Eq. (6), an opaque material with high emittance in the sensor sensibility spectral band reflects very little in the same band. However a material with a smaller emittance e will have a reflectance (1 e) and its radiosity will be strongly influenced by the radiance of the surfaces that constitute its neighborhood. In the case of the detector is a thermal imager system, these surround reflections can interfere in the image formation
and in the temperature measurements. If the target surface is a diffuse reflector or else if the surrounding source is a uniformly extended source, the image can stay without deformations, being sufficient to correct the temperature values with a mathematic algorithm that takes into account the background radiance. Fig. 6 shows the path of the radiation beam striking the sensor pixels in the case of a specular reflecting target. The pixel in the sensor sees the directional radiosity of determinate area in the target, including just the emissive power of the target and the specular direction reflected image. The resulting image in the detector’s focal plane array is a superposition of the target thermal image and the surroundings reflected image. If one pixel receives the reflection of a hot object it sees only the target emissive power and the hot object reflected radiation, i.e., the surrounding for it is that hot object. The intensity of the radiant power arriving on the sensor can be estimated using the useful emissive power fraction M and the transfer constant factor KT to modulate the target radiosity. The transfer constant factor is the fraction of the total target radiosity that strikes the sensor. It comprises the view factor, the lens transmittance and all the other practical restrictions but M. I p ¼ M K T ½eT rT 4T þ ð1 eT ÞeS rT 4S
ð8Þ
where Ip is the intensity in detector pixel, eT is the target emittance, eS is the surrounding source emittance, TT is the target temperature and TS is the surrounding temperature. 4. Optical properties and thermographic thermometry on glass Glass is one of the few solid materials that are transparent to visible radiation. Because of this, glass is manufactured in smooth flat sheets and is used mainly in building windows. Glass is very transparent in whole solar energy band and is used as cover in solar thermal collectors and photovoltaic modules. The glass sheets are specular reflectors and the reflection intensity depends directly on the glass refractive index. Eq. (9) gives the Snell’s law of refrac-
A. Krenzinger, A.C. de Andrade / Solar Energy 81 (2007) 1025–1034
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tion, where h1 and h2 are, respectively, the incident angle and the refracted angle and n1 and n2 are the refractive indexes of the incident mean (air, n1 = 1) and the refracted mean (glass). Eq. (10) gives the reflectance, for non-polarized light, at the interface air–glass as derived from the Fresnell equations (Lorrain and Corson, 1970). n1 sinðh1 Þ ¼ n2 sinðh2 Þ ð9Þ 2 2 1 n1 cosðh1 Þ n2 cosðh2 Þ 1 n1 cosðh2 Þ n2 cosðh1 Þ q¼ þ 2 n1 cosðh1 Þ þ n2 cosðh2 Þ 2 n1 cosðh2 Þ þ n2 cosðh1 Þ
ð10Þ
Ordinary glass is opaque to the infrared radiation with wavelength larger than 4 lm. This fact assures that glass transmittance is null and the incident radiation must be either absorbed or reflected. After Kirchhoff’s Law, Eq. (6) can be used to determine the emittance from the reflectance. Typical values for float glass refractive index in function of wavelength are given in Fig. 7, where the one-interface reflectance obtained from Eq. (10) is also plotted for normal incidence (dash line). Note that a glass sheet reflects more in the sensitivity band of the most of IR cameras than in visible band. In the visible band, because the light absorptance is very low, the effective reflectance is a combination of two-interfaces reflection coefficients (in the case of air–glass–air interfaces), resulting in values about 8%. For wavelengths longer than 4 lm the reflectance is produced in only one interface, so the results shown in Fig. 7 are valid for a single thin sheet as well as for glass covering applications. The effect of the specular reflection on glass can produce two kinds of errors that can induce to wrong judgment in the values of measured temperature. The first concerns to the formation of the image itself. In spite of the IR glass 4
0.4
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2
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1
0.1
0
Normal Reflectance
Refractive Index
Typical values for Float Glass Refractive Index n Normal Reflectance
0 0
5
10
15
20
25
Wavelength (μm) Fig. 7. Typical spectral values for reflectance and refractive index of float glass.
Fig. 8. Thermography of a uniform temperature glass, showing the heat reflection of the operator of the equipment.
reflectance is not very strong, its specular characteristics can alter significantly the image. Fig. 8 shows a thermographic image of a uniform temperature glass sheet where is possible not only to perceive the reflection of the thermograph operator in the glass, but also that he is wearing glasses. The glass actual temperature in this image is 21.5 °C while the effect of the reflection of the operator skin (35 °C) produces the temperature reading 24.0 °C. In cases like this is easy to perceive the occurrence of the effect, because is evident that there is not a thermal picture printed in the glass surface, but the reflected image can be more confused and then more difficult to detect. The second kind of error occurs only in outdoor conditions measurements and is caused by the fact of the sensibility wavelength band of the thermographic cameras corresponds to an atmospheric transmitting band. Under clear sky conditions there is no significant radiation emitted by the atmosphere in this band. This means that the sky equivalent blackbody temperature for the camera is drastically low. In this condition, even if the sky reflection effect do not modify the image (clouds form images in their reflection), the error exists because several camera software do not support so low background temperature or because the user is not informed about this reflection consequences. The interest in use of thermography for determining temperature fields in solar collectors or photovoltaic modules and other system components in operational conditions is quite obvious. There are innumerable applications in system thermal analyses and scientific development applied to solar engineering. However, solar collectors are glass covered and normally are tilted towards the sky. The thermographic thermometry of the glass that covers a solar collector or a PV module is subjected to both mentioned kinds of error. There are three completely different situations to be analyzed: (a) overcast sky condition, when the surrounding equivalent temperature is easy to determine and the thermal image have fidelity to the temperature field of the glass
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target; (b) partially cloudy sky condition, when the thermal image of the glass is very deformed by the reflection of the cloud boundaries; and (c) clear sky condition, when the thermal image is no influenced by the sky reflection but the difficulties on the calibration of the camera can yield errors up to 15 K in the glass temperature determination. For overcast sky condition the resultant IR images, generally, have quality enough to consider that the error is depreciable and the cares in the procedures are the same than in indoors experiments. In this case, as well as in all the cases here described, is very important to observe other than sky infrared sources, because depending on the angle of view, specular reflected radiation from other sources is expected. In the case of partially cloudy skies, if the analysis is performed during the day time, is recommendable to take a visual picture at the same time and from the same angle than the IR image. This way is possible to compare the two images and to eliminate wrong conclusions during the analysis. Fig. 9 shows a thermographic image of a PV module few minutes after to be exposed to the sun at horizontal. Both images show the cloud boundaries, but because of very different causes. Visual image contrasts the blue of the sky with the light gray of the clouds while IR image contrasts the cloud temperature with the clear sky temperature. Fig. 9 shows a thermographic image of a PV module reflecting the sky with the presence of a cloud. The glass is at 20 °C, although the regions corresponding to the reflection of clear sky are reported by the camera as 11 °C, but in the region where the reflection corresponds to the cloud image the temperature reported is near the true value. The module was recently exposed to the sun and it is warming when the thermography was taken. The lighter region in the center of the bottom of the module surface image is caused by the back connection box, which introduces a better thermal insulation so that area is warmed up. Note that there are dark points marking the vertices
Fig. 9. Thermographic image of a PV module reflecting the sky with the presence of a cloud.
of the photovoltaic cells, which are caused by colder points in the small areas not covered by the silicon. The darker region at the top of the thermal image is consequence of the effect of the sky reflection angle. At larger incident angles the glass reflectivity is stronger and the effect of the sky effective temperature is more accentuated. In the case of clear sky condition, depending on the view angle, there is no care to be taken, except about other IR sources, in order to obtain a relative image dependent only on the target temperature distribution. In spite of the image bright is proportional to the temperature, the value presented by the camera software can be very far from the actual temperature. Fig. 10a presents thermographic images of a PV module in short circuit during a thermal analysis under clear sky condition. Fig. 10b shows the IR image taken from the back side of the same module few seconds after the first image has been taken. The module was under thermal steady state condition. The front side is glass covered and the emittance was set to 0.85. The backside of the PV module is covered by Tedlar, a polymeric material, diffuse reflector with emittance assumed to be 0.9. In both cases the background temperature setting
Fig. 10. Differences between front side (a) and backside (b) thermographic thermometry of a cell in a photovoltaic module, in a clear sky day. The back measurement is more accurate.
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was kept in 25 °C, because the objective was to observe the sky reflection error anterior to possible intern algorithm correction. The difference in the registered temperatures for both sides in the same region was about 8 °C, as can be seen in the pictures. Of course the same temperature is not expected, because of different thermal resistances for heat transfer to the ambient, but a theoretical analyses show that the difference between front and back temperature in this experimental particular condition is not larger than 2 °C. Moreover, this difference can be easily confirmed by using a cheap non-contact thermometer, which can use the same measuring principles but, because it can be positioned very near the glass cover, do not allow the sky reflection interference. To set the background temperature parameter to the inferior limit (T = 20 °C for the used equipment) was not enough to plenty correct this error, but this produce the rise in measured front temperature from 41 °C to 45 °C. Depending on the relative position of the camera operator respect to the target, the effect of the reflection angle has to be corrected. This effect was already shown in Fig. 9 where a darkening is noted along the PV module surface. 5. Correction of the thermal image reflection effect To obtain the temperature from the value of the radiosity given in Eq. (8), it is necessary first understand that for the element sensor that are receiving reflected image from a hotter (or colder) object, the external source is the only surrounding source, because the pixel is unable to see anything beyond the external source by reflection on the target, so eS and TS are substituted, respectively, by eE and TE and: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Rp ð1 eT ÞeE rT 4E 4 KT TT ¼ ð11Þ eT r However, because there are others pixels in the image, whose reflected image is not the external but the surrounding source, the camera algorithm produce a temperature correction based on TS. Then it is necessary to revert the temperature information to radiosity again in order to introduce a suitable correction. This last can be implemented directly through the addiction of the correct reflected part of radiosity and the subtraction of the surrounding reflected term: Rp ¼ K T r eT T 4T ð1 eT ÞT 4Se þ ð1 eT ÞeE T 4E ð12Þ and sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 4 4 4 eT T M ð1 eT ÞeE T E þ ð1 eT ÞT Se TT ¼ eT
ð13Þ
where TM is the absolute temperature measured with the camera, inside the external source reflection image area. Note that eS no longer appears in Eqs. (12) and (13). Most infrared camera software make use of the equivalent black-
1031
body temperature TSe for the background radiation, as given by Eq. (14), because this quantity is easily obtained directly from the own camera. sffiffiffiffiffiffi 4 4 T S T Se ¼ ð14Þ eS Eq. (13) gives the corrected target temperature inside the external source reflected image. In order to apply it, the external source temperature or its radiosity must be known, as well as the settings of the camera, including eT and TSe. Nevertheless, if the real target temperature and emittance are known, it is possible to determine the external source equivalent blackbody temperature through the same camera that is being calibrated. 6. Experimental Before performing experimental tests to confirm these proposed corrections, the effective infrared reflectance was determined trough a simple experimental mounting. The camera was set to emittance e = 1 and background temperature TS = 22 °C. A blackened thick aluminum disk, with an electrical heater resistor installed in its back side, was used as blackbody source. It was warmed to about 38 °C while the ambient and surroundings temperature was 22 °C. The disk was set over a table inside the laboratory, in front of a photovoltaic module at ambient temperature which acted as the reflector target. The reflection angle was determined using trigonometric relations from measured distances in the setting. Fig. 11a and b shows examples of thermographic images obtained during this experimental setting, respectively for incident angles of 10° and 74° respect the normal. This setting was repeated for nine different incident angles, and the reflectance was obtained from Eq. (15), where TR is the absolute temperature reading inside the reflected image of the disk and TD is the absolute temperature reading directly from the disk, TT is the absolute temperature reading from the target (PV module) and TS is the temperature of ambient and surroundings (TS = 294 K). During these experimental procedures the PV module was kept at ambient temperature, so TT = TS. q¼
T 4R T 4T T 4D T 4S
ð15Þ
Fig. 12 shows the reflectance as measured and calculated from Eq. (15) and as calculated from Eq. (10) considering a mean refractive index n2 = 2.25. Error bars was inserted in order to show the effect of uncertainties of ±0.2 K in temperature measurements. Surely there are angular errors too, which are not shown in the picture and were estimated to be about ±3° (see Fig. 13). In order to validate the proposed correction method, it was assembled an experiment using a 20 l glass beaker filled with water with adjustable temperature as external source and a plane wall of an aquarium, also filled with adjustable
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Glass Reflectance
0.4
Glass Infrared Reflectance 8 -14 μm band Experimental Theoretical for n=2.25
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20
30
40
50
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70
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Incident Angle (°) Fig. 12. Results of glass infrared reflectance in function of incident angle obtained from thermographic thermometry in a photovoltaic module illuminated with a warmed blackbody surface, and comparison with theoretical prediction.
aquarium IR-camera Fig. 11. Infrared images from a blackbody surface disk and its reflected image through the glass of a PV module for: (a) 10° incident angle and (b) 74° incident angle, with temperatures indicated in Kelvin.
temperature water as the glass reflector target. The objects are arranged to set a 30° angle from the camera objective and the target normal. The mounting is presented in Fig. 13. The procedure adopted was to slowly change the temperatures in the beaker from ambient temperature (25 °C) to warm water (50 °C) keeping initially the target temperature constant and posteriorly warming the target as well. The camera was mounted on a tripod support and thermographic images were taken at different beaker and target temperatures, reaching 30 images at the end. For each target image, the camera was rotated to the beaker in order to register its external temperature under the same conditions. In this camera position, the image of the external source is not affected by the reflection of the target, only by the background surrounding temperature. From each IR image the temperatures were read inside and outside the reflected image of the beaker and the difference, which is the reflection error, plotted against the IR measured beaker temperature. Fig. 14 shows the comparison between the true target temperature and the temperature measured inside the beaker reflected image. Fig. 14 shows also the
Fig. 13. Schema of the experimental mounting, showing a warmed beaker as external source and a smooth glass aquarium wall as target.
values of the temperature corrected with Eq. (13). Fig. 15 shows the errors before and after the correction. Errors as large as 4 °C were recorded in this experiment and the results show that the errors are clearly correlated with the difference of the beaker temperature and the surrounding temperature, as it was expected. 7. Measuring effective sky temperature One of the requisites for the accurate temperature measurement using thermograph techniques is to inform the surrounding temperature in order to allow the software of the equipment to correct its effects. The surrounding temperature can be estimated either by scanning around the target with the own camera or, as it is recommended in the user’s manual (Thermoteknix, 2001) and as proposed
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mittance window. In this case is possible to measure the effective sky temperature using the previously presented relations. The methodology consists in to expose a sheet of glass, which temperature is known, to the incident sky light in order to reflect the sky image to the camera. The glass sheet should be installed in the shadow avoiding direct solar radiation absorption and so keeping the glass near ambient temperature. The emittance parameter in the camera is set to e = 1. The error in the glass temperature reading depends on the sky effective temperature and on the incident angle for the image. Considering TM the measured absolute glass temperature and TG the actual absolute glass temperature, the effective sky temperature, TSKY, is given by Eq. (16): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 4 4 T M ½1 qðhÞ T G ð16Þ T SKY ¼ qðhÞ
60
Target Temperature (°C)
50
40
Measured temperature True Target Temperature Corrected Temperature
30
20 0
5
10
15
1033
20
25
Beaker Temperature - Surrounding Temperature (°C) Fig. 14. Temperature of the aquarium wall measured with a thermographic camera, showing the effect of the reflection error. True target temperature is determined outside the reflection area.
5
Measured Raw Difference Difference After Correction
As an example of using this technique, the effective sky temperature in the conditions of the thermography presented in Fig. 10 was determined to be TSKY = 204.7 K. This value was then used as external source temperature TE, assuming emittance eE = 1, in Eq. (13). The result is the correction from 39.6 °C to 47.4 °C, which agree with the actual glass temperature. 8. Conclusion
Reflection Error (°C)
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1
0
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Beaker Temperature - Surrounding Temperature (°C) Fig. 15. Reflection error as function of the difference between the external source temperature and surrounding temperature, before and after to apply the proposed correction.
by Datcu et al. (2005), by using an aluminum diffuse mirror beside the target to represent the averaged surrounding source radiation. For outdoor applications in clear sky conditions, depending on the incident angle, both methods can be ineffective because the camera can present underload saturation as consequence of the atmospheric trans-
Thermographic thermometry is a very important technique for performing evaluation of solar energy conversion equipments, but its utilization has to be carried out with care and attention in order to obtain accurate results. When performing outdoor thermographies, two kinds of errors can arise: one of them concerns to anomalous image formation due to the reflections of surrounding objects and the other concerns to the bad estimation of the equivalent sky temperature. Both are related to the glass infrared specular reflectance which importance is often neglected. This paper propose a correction method for reflection errors which is based in preliminarily to revert temperature to radiosity information, and then subtracts the external object emissive power reflected in the target as part of the whole considered radiosity, tuning it temperature again. The method was validated for a number of experimental situations, always using glass as the reflector target. As a subsequence of this method it was shown that a thermographic equivalent sky temperature can be determined for use in correction procedures for the own thermographic measurements. Acknowledgements The authors acknowledge the financial support granted by the Brazilian Scientific and Technologic Development Council (CNPq).
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References Al-Kassir, A.R., Fernandes, J., Tinaut, F.V., Castro, F., 2005. Thermographic study of energetic installations. Applied Thermal Engineering. 25, 183–190. Bazilian, M.D., Kamalanathan, H., Prasad, D.K., 2002. Thermographic analysis of a building integrated photovoltaic system. Renewable Energy 26, 449–461. Datcu, S., Ibos, L., Candau, Y., Mateı¨, S., 2005. Improvement of building wall surface temperature measurements by infrared thermography. Infrared Physics & Technology 46, 451–467.
Dereniak, E.L., Boreman, G.D., 1996. Infrared Detectors and Systems. John Wiley & Sons, New York, p.34. Gruner, K.D. 2003. Principles of non-contact temperature measurements. pdf brochure www.raytek-europe.com. Lorrain, P., Corson, D.R., 1970. Electromagnetic Fields and Waves, second ed. W.H. Freeman and Company, San Francisco, pp. 508–519. Thermoteknix Systems, 2001, TherMonitor Infrared Reporter User manual, Appendix B: determining the background and emissivity.
Accurate outdoor glass thermographic thermometry applied to solar energy devices A. Krenzinger b
a,*
, A.C. de Andrade
b
a Solar Energy Laboratory, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil Faculdade de Fı´sica, Pontifı´cia Universidade Cato´lica do Rio Grande do Sul (PUCRS), Porto Alegre, Brazil
Received 18 November 2005; received in revised form 18 November 2006; accepted 28 November 2006 Available online 17 January 2007 ´ lvarez Garcı´a Communicated by: Associate Editor Gabriela A
Abstract The measurement of the temperature of the glass that covers solar collectors or photovoltaic modules is very important for the characterization of the performance of these converters. Thermography is a non-contact thermometry technique that is capable to quickly scan and record surface temperature fields, but its accuracy depends on knowing the limitations and possible errors involved with the use of this technique. This paper identifies glass infrared reflection errors and their consequences when performing outdoor thermographs. The work also proposes and experimentally validates a correction method for correcting these errors. Finally is also presented a method for estimating a thermographic equivalent sky temperature that can be used in correction procedures for the own outdoor thermographic measurements. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Thermography; Glass thermometry; Solar devices thermal analysis
1. Introduction Heat transfer in solar energy conversion devices is one of the most important parameters to be experimentally determined. The main experimental magnitude in order to know the amount of heat transfer is the temperature. Temperature measuring allows to determine thermal gradients and to evaluate thermal flux through surfaces in the interfaces of materials. A part of the thermal energy interchange is due to the radiation phenomenon, which emitted energy is proportional to the forth power of the body’s surface temperature. Then, by determining the emissive power emitted from a surface and its physical properties (basically the emittance) is quite simple to estimate the surface temperature.
*
Corresponding author. Tel./fax: +55 51 33086841. E-mail address: [email protected] (A. Krenzinger).
0038-092X/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2006.11.014
Infrared radiation can be measured using several radiometric techniques which have in common the presence of an element able to sense thermal radiation. Depending on the purposes of the instrument, the radiometer measures the incoming radiation from all the hemisphere directions, the incoming radiation from a well defined emitter region or it makes use of an array of sensors and a suitable lens system in order to register not only an incident radiation value but the radiosity field leaving a target surface. This last kind of infrared radiometry can produce infrared images and its techniques are sometimes called ‘‘infrared imagery’’ or ‘‘thermal imagery’’. Photographic infrared films was used in the first infrared imagery applications, but with the development of digital CCD sensors and associated technologies allowed the currently available possibilities. Infrared thermographic cameras are powerful apparatus capable to detect and to accurately measure thermal radiosity and surface temperature fields, which is especially useful when the technical study requires a
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differential thermal analysis. Bazilian et al. (2002) use thermographic techniques to study thermal effects of a photovoltaic roofing technology. Al-Kassir et al. (2005) illustrate infrared thermography showing energetic applications. Infrared images often are colored through software processes that pigment original gray levels with an electronic palette. The effect of this coloring process is very impressive and the resultant visual analyses seem much more accurate. The confidence provided by the camera images can blur some error possibilities and conduce to misunderstanding on their thermal analyses. This paper presents some of the outdoor glass surface thermographic thermometry errors and how to proceed in order to avoid them.
1x1011 1x1010 Temperature
Spectral Emissive Power (W/m².μm)
1026
300K 600K 6,000K
1x109 1x108 1x107 1x106 1x105 4
1x10
3
1x10
2
1x10
1x101
2. Thermal radiation
0
1x10
Eb ðk; T Þ ¼
2phc2 k5 ½expðhc=kkT Þ 1
ð1Þ
where h is the Planck’s constant, k is the Boltzmann’s constant, c is the speed of light, T is the absolute temperature and k is the wavelength. Fig. 1 shows Eb(k) for different temperatures in a bilogarithmic scale and it shows that an important part (73%) of the radiation emitted by bodies which temperature are near 300 K lies in the band between 4 lm and 30 lm. The area below the curves represents the total emissive power and it is given by the Stefan–Boltzmann equation: Z 1 Eb ¼ Eb ðk; T Þ dk ¼ rT 4 ð2Þ 0
where r is the Stefan–Boltzmann constant. Fig. 2 shows a different graphic view of the same function. Now the emissive power is normalized to unit, by dividing each point by the maximum of its respective curve. This graphic is particularly elucidative to show that bodies
-1
1x10
1x10
0
1
2
1x10
3
1x10
1x10
4
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Wavelength (μm) Fig. 1. Blackbody spectral emissive power.
1 Temperature
300K 6000K
Normalized Emissive Power
The thermal energy in materials corresponds to the movement of molecules, atoms and subatomic particles which form the material. The intensity of the movement of the particles in the material depends on the temperature of the body. The electric charge displacement associated to the particle movement produce radiation emission through the body surface. The spectral range of the radiated energy constitutes the thermal radiation band from the electromagnetic spectrum, which is subdivided in three main smaller bands: ultraviolet, visible and infrared. Only bodies with very high temperatures emit ultraviolet and visible radiation with enough intensity to be detected, e.g. incandescent objects (more than 600 °C), but any body with temperature above absolute zero emits infrared radiation. The ideal emitter is called blackbody and the spectra distribution of its emission determines the maximum radiation flux that can be emitted per area unit in the surface of any body. The spectral emissive power of the blackbody is given by the Planck’s law:
0.8
0.6
0.4
0.2
0 0.1
1
10
100
Wavelength (μm) Fig. 2. Normalized blackbody spectral emissive power.
with very different surface temperature (like 300 K and 6000 K) do not share the same emitting band. A real body has an emissive power smaller than the blackbody. The ratio between the body’s surface monochromatic emissive power and the blackbody’s monochromatic emissive power at the same temperature is called monochromatic emittance e(k) and the ratio between the body’s surface total emissive power and the blackbody’s total emissive power at the same temperature is called hemispheric emittance or simply emittance e:
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R1
eðkÞEb ðk; T Þ dk rT 4
1027
ð6Þ
absorption correction factor. Fig. 3 shows the spectral transmittance of a 10-m atmospheric air layer constructed from data extracted from graphics presented by Gruner (2003) and by Dereniak and Boreman (1996). Note that exist several transmitting bands, specially from 2 lm to 2.5 lm, from 3 lm to 5 lm and from 8 lm to 13 lm. All of these bands are suitable for IR radiance transmission, but dependent on the interest temperature a band can be more affordable than the other. In particular the longer range between 8 lm and 13 lm is very appropriated for measuring radiance emitted by surfaces at near ambient temperature. Moreover, there is a lot of watching applications, mainly for surveillance and military applications, which promoted the developing of this kind of equipments. Now, if the response band is limited to a range between k1 and k2, the useful emissive power fraction is given by: R k2 eðkÞEb ðk; T Þ dk EU k ¼ R 11 ð7Þ M¼ E eðkÞEb ðk; T Þ dk 0
By sensing infrared radiation emitted by a body is possible to determine its surface temperature through noncontact measurements and there are several advantages in this kind of thermometry. The ideal sensitivity wavelength band of the radiometric sensor depends on the temperature range to be measured. If the detector is able to capture the radiant energy between 4 lm and 30 lm it is suitable to measure temperatures around 300 K. This band is not susceptible to the solar radiation and this is good for outdoor experiments, because on the contrary the sunlight could interfere in the measurements. By the other hand, is very convenient to use a sensor that responds in a band where the air is transparent. In the same way that one is familiarized to see through a long distance in the air, if the IR sensor is limited to a very high transmittance band there is not necessary to apply an air
and this ratio depends on target temperature. Fig. 4 shows M as function of temperature for k1 = 7 lm and k2 = 14 lm. Note that for temperatures around 300 K, M has a small variation, in relative terms, about 0.25%/K, which is minimum at about 380 K. This implies that, for a graybody, is almost the same to measure within these limits than to measure the total emissive power. A general schema for infrared radiant energy transfer from a target plane body to the detector can be seen in Fig. 5. There are two external sources and the target is also an infrared source itself. One of the external sources (S1) is behind the target and its infrared contribution to the sensor of the detector occurs only if the target is not opaque to the radiations within the sensitivity band of the detector. The other external source (S2) produces an increase in the radiation power received by the detector because part of its emissive power is reflected by the target to the radiometer. The radiosity is the total radiation power, per unit area, outgoing from the target body by combined emission,
e¼
0
ð3Þ
Kirchhoff’s law attests that, for each wavelength, the fraction of the incoming radiation that is absorbed by a surface (the absorptance a) is equal to the emittance, i.e., aðkÞ ¼ eðkÞ
ð4Þ
By the other hand, the incoming radiation in a body can have only three possibilities: to be reflected, to be absorbed or to be transmitted, so: qðkÞ þ aðkÞ þ sðkÞ ¼ 1
ð5Þ
where q(k) is the monochromatic reflectance and s(k) is the monochromatic transmittance. Opaque materials are those which the transmittance is null. Combining Eqs. (4) and (5) for opaque bodies results in qðkÞ ¼ 1 eðkÞ 3. Infrared radiometric thermometry and imagery
1 0.9
Air Transmittance
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
1
2
3
4
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8
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Wavelength (μm) Fig. 3. Air spectral transmittance for a 10 m atmosphere layer.
13
14
15
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Useful Emissive Power Fraction
0.55
0.50
0.45
LENS 0.40
HOT OBJECT
Fig. 6. Array sensor receiving image from the specular reflecting target with intervention of a hot object reflection, beyond the expected surrounding thermal radiation.
0.35
0.30
0.25
0.20 280
320
360
400
440
Temperature (K) Fig. 4. Useful emissive power fraction between 7 lm and 14 lm for different blackbody temperatures.
SOURCE 1
SOURCE 2
S2
S1
TARGET S3
τS1
ρS2 DETECTOR
εS3
Fig. 5. General scheme for infrared radiant energy transfer showing that the detector receives transmitted, reflected and emitted radiation from the target.
reflection and transmission. Dependent on the optics of the detector, the radiosity is the value that IR sensors are able to measure, not the temperature directly. If the target were a blackbody, only the emitted energy (S3) would strike the sensor, because the transmittance and reflectance would be null. For any other body, reflected or transmitted radiant energy can contribute to the infrared radiation leaving the surface. Because of this, it is very important to know the body’s surface properties. Considering Eq. (6), an opaque material with high emittance in the sensor sensibility spectral band reflects very little in the same band. However a material with a smaller emittance e will have a reflectance (1 e) and its radiosity will be strongly influenced by the radiance of the surfaces that constitute its neighborhood. In the case of the detector is a thermal imager system, these surround reflections can interfere in the image formation
and in the temperature measurements. If the target surface is a diffuse reflector or else if the surrounding source is a uniformly extended source, the image can stay without deformations, being sufficient to correct the temperature values with a mathematic algorithm that takes into account the background radiance. Fig. 6 shows the path of the radiation beam striking the sensor pixels in the case of a specular reflecting target. The pixel in the sensor sees the directional radiosity of determinate area in the target, including just the emissive power of the target and the specular direction reflected image. The resulting image in the detector’s focal plane array is a superposition of the target thermal image and the surroundings reflected image. If one pixel receives the reflection of a hot object it sees only the target emissive power and the hot object reflected radiation, i.e., the surrounding for it is that hot object. The intensity of the radiant power arriving on the sensor can be estimated using the useful emissive power fraction M and the transfer constant factor KT to modulate the target radiosity. The transfer constant factor is the fraction of the total target radiosity that strikes the sensor. It comprises the view factor, the lens transmittance and all the other practical restrictions but M. I p ¼ M K T ½eT rT 4T þ ð1 eT ÞeS rT 4S
ð8Þ
where Ip is the intensity in detector pixel, eT is the target emittance, eS is the surrounding source emittance, TT is the target temperature and TS is the surrounding temperature. 4. Optical properties and thermographic thermometry on glass Glass is one of the few solid materials that are transparent to visible radiation. Because of this, glass is manufactured in smooth flat sheets and is used mainly in building windows. Glass is very transparent in whole solar energy band and is used as cover in solar thermal collectors and photovoltaic modules. The glass sheets are specular reflectors and the reflection intensity depends directly on the glass refractive index. Eq. (9) gives the Snell’s law of refrac-
A. Krenzinger, A.C. de Andrade / Solar Energy 81 (2007) 1025–1034
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tion, where h1 and h2 are, respectively, the incident angle and the refracted angle and n1 and n2 are the refractive indexes of the incident mean (air, n1 = 1) and the refracted mean (glass). Eq. (10) gives the reflectance, for non-polarized light, at the interface air–glass as derived from the Fresnell equations (Lorrain and Corson, 1970). n1 sinðh1 Þ ¼ n2 sinðh2 Þ ð9Þ 2 2 1 n1 cosðh1 Þ n2 cosðh2 Þ 1 n1 cosðh2 Þ n2 cosðh1 Þ q¼ þ 2 n1 cosðh1 Þ þ n2 cosðh2 Þ 2 n1 cosðh2 Þ þ n2 cosðh1 Þ
ð10Þ
Ordinary glass is opaque to the infrared radiation with wavelength larger than 4 lm. This fact assures that glass transmittance is null and the incident radiation must be either absorbed or reflected. After Kirchhoff’s Law, Eq. (6) can be used to determine the emittance from the reflectance. Typical values for float glass refractive index in function of wavelength are given in Fig. 7, where the one-interface reflectance obtained from Eq. (10) is also plotted for normal incidence (dash line). Note that a glass sheet reflects more in the sensitivity band of the most of IR cameras than in visible band. In the visible band, because the light absorptance is very low, the effective reflectance is a combination of two-interfaces reflection coefficients (in the case of air–glass–air interfaces), resulting in values about 8%. For wavelengths longer than 4 lm the reflectance is produced in only one interface, so the results shown in Fig. 7 are valid for a single thin sheet as well as for glass covering applications. The effect of the specular reflection on glass can produce two kinds of errors that can induce to wrong judgment in the values of measured temperature. The first concerns to the formation of the image itself. In spite of the IR glass 4
0.4
3
0.3
2
0.2
1
0.1
0
Normal Reflectance
Refractive Index
Typical values for Float Glass Refractive Index n Normal Reflectance
0 0
5
10
15
20
25
Wavelength (μm) Fig. 7. Typical spectral values for reflectance and refractive index of float glass.
Fig. 8. Thermography of a uniform temperature glass, showing the heat reflection of the operator of the equipment.
reflectance is not very strong, its specular characteristics can alter significantly the image. Fig. 8 shows a thermographic image of a uniform temperature glass sheet where is possible not only to perceive the reflection of the thermograph operator in the glass, but also that he is wearing glasses. The glass actual temperature in this image is 21.5 °C while the effect of the reflection of the operator skin (35 °C) produces the temperature reading 24.0 °C. In cases like this is easy to perceive the occurrence of the effect, because is evident that there is not a thermal picture printed in the glass surface, but the reflected image can be more confused and then more difficult to detect. The second kind of error occurs only in outdoor conditions measurements and is caused by the fact of the sensibility wavelength band of the thermographic cameras corresponds to an atmospheric transmitting band. Under clear sky conditions there is no significant radiation emitted by the atmosphere in this band. This means that the sky equivalent blackbody temperature for the camera is drastically low. In this condition, even if the sky reflection effect do not modify the image (clouds form images in their reflection), the error exists because several camera software do not support so low background temperature or because the user is not informed about this reflection consequences. The interest in use of thermography for determining temperature fields in solar collectors or photovoltaic modules and other system components in operational conditions is quite obvious. There are innumerable applications in system thermal analyses and scientific development applied to solar engineering. However, solar collectors are glass covered and normally are tilted towards the sky. The thermographic thermometry of the glass that covers a solar collector or a PV module is subjected to both mentioned kinds of error. There are three completely different situations to be analyzed: (a) overcast sky condition, when the surrounding equivalent temperature is easy to determine and the thermal image have fidelity to the temperature field of the glass
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target; (b) partially cloudy sky condition, when the thermal image of the glass is very deformed by the reflection of the cloud boundaries; and (c) clear sky condition, when the thermal image is no influenced by the sky reflection but the difficulties on the calibration of the camera can yield errors up to 15 K in the glass temperature determination. For overcast sky condition the resultant IR images, generally, have quality enough to consider that the error is depreciable and the cares in the procedures are the same than in indoors experiments. In this case, as well as in all the cases here described, is very important to observe other than sky infrared sources, because depending on the angle of view, specular reflected radiation from other sources is expected. In the case of partially cloudy skies, if the analysis is performed during the day time, is recommendable to take a visual picture at the same time and from the same angle than the IR image. This way is possible to compare the two images and to eliminate wrong conclusions during the analysis. Fig. 9 shows a thermographic image of a PV module few minutes after to be exposed to the sun at horizontal. Both images show the cloud boundaries, but because of very different causes. Visual image contrasts the blue of the sky with the light gray of the clouds while IR image contrasts the cloud temperature with the clear sky temperature. Fig. 9 shows a thermographic image of a PV module reflecting the sky with the presence of a cloud. The glass is at 20 °C, although the regions corresponding to the reflection of clear sky are reported by the camera as 11 °C, but in the region where the reflection corresponds to the cloud image the temperature reported is near the true value. The module was recently exposed to the sun and it is warming when the thermography was taken. The lighter region in the center of the bottom of the module surface image is caused by the back connection box, which introduces a better thermal insulation so that area is warmed up. Note that there are dark points marking the vertices
Fig. 9. Thermographic image of a PV module reflecting the sky with the presence of a cloud.
of the photovoltaic cells, which are caused by colder points in the small areas not covered by the silicon. The darker region at the top of the thermal image is consequence of the effect of the sky reflection angle. At larger incident angles the glass reflectivity is stronger and the effect of the sky effective temperature is more accentuated. In the case of clear sky condition, depending on the view angle, there is no care to be taken, except about other IR sources, in order to obtain a relative image dependent only on the target temperature distribution. In spite of the image bright is proportional to the temperature, the value presented by the camera software can be very far from the actual temperature. Fig. 10a presents thermographic images of a PV module in short circuit during a thermal analysis under clear sky condition. Fig. 10b shows the IR image taken from the back side of the same module few seconds after the first image has been taken. The module was under thermal steady state condition. The front side is glass covered and the emittance was set to 0.85. The backside of the PV module is covered by Tedlar, a polymeric material, diffuse reflector with emittance assumed to be 0.9. In both cases the background temperature setting
Fig. 10. Differences between front side (a) and backside (b) thermographic thermometry of a cell in a photovoltaic module, in a clear sky day. The back measurement is more accurate.
A. Krenzinger, A.C. de Andrade / Solar Energy 81 (2007) 1025–1034
was kept in 25 °C, because the objective was to observe the sky reflection error anterior to possible intern algorithm correction. The difference in the registered temperatures for both sides in the same region was about 8 °C, as can be seen in the pictures. Of course the same temperature is not expected, because of different thermal resistances for heat transfer to the ambient, but a theoretical analyses show that the difference between front and back temperature in this experimental particular condition is not larger than 2 °C. Moreover, this difference can be easily confirmed by using a cheap non-contact thermometer, which can use the same measuring principles but, because it can be positioned very near the glass cover, do not allow the sky reflection interference. To set the background temperature parameter to the inferior limit (T = 20 °C for the used equipment) was not enough to plenty correct this error, but this produce the rise in measured front temperature from 41 °C to 45 °C. Depending on the relative position of the camera operator respect to the target, the effect of the reflection angle has to be corrected. This effect was already shown in Fig. 9 where a darkening is noted along the PV module surface. 5. Correction of the thermal image reflection effect To obtain the temperature from the value of the radiosity given in Eq. (8), it is necessary first understand that for the element sensor that are receiving reflected image from a hotter (or colder) object, the external source is the only surrounding source, because the pixel is unable to see anything beyond the external source by reflection on the target, so eS and TS are substituted, respectively, by eE and TE and: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Rp ð1 eT ÞeE rT 4E 4 KT TT ¼ ð11Þ eT r However, because there are others pixels in the image, whose reflected image is not the external but the surrounding source, the camera algorithm produce a temperature correction based on TS. Then it is necessary to revert the temperature information to radiosity again in order to introduce a suitable correction. This last can be implemented directly through the addiction of the correct reflected part of radiosity and the subtraction of the surrounding reflected term: Rp ¼ K T r eT T 4T ð1 eT ÞT 4Se þ ð1 eT ÞeE T 4E ð12Þ and sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 4 4 4 eT T M ð1 eT ÞeE T E þ ð1 eT ÞT Se TT ¼ eT
ð13Þ
where TM is the absolute temperature measured with the camera, inside the external source reflection image area. Note that eS no longer appears in Eqs. (12) and (13). Most infrared camera software make use of the equivalent black-
1031
body temperature TSe for the background radiation, as given by Eq. (14), because this quantity is easily obtained directly from the own camera. sffiffiffiffiffiffi 4 4 T S T Se ¼ ð14Þ eS Eq. (13) gives the corrected target temperature inside the external source reflected image. In order to apply it, the external source temperature or its radiosity must be known, as well as the settings of the camera, including eT and TSe. Nevertheless, if the real target temperature and emittance are known, it is possible to determine the external source equivalent blackbody temperature through the same camera that is being calibrated. 6. Experimental Before performing experimental tests to confirm these proposed corrections, the effective infrared reflectance was determined trough a simple experimental mounting. The camera was set to emittance e = 1 and background temperature TS = 22 °C. A blackened thick aluminum disk, with an electrical heater resistor installed in its back side, was used as blackbody source. It was warmed to about 38 °C while the ambient and surroundings temperature was 22 °C. The disk was set over a table inside the laboratory, in front of a photovoltaic module at ambient temperature which acted as the reflector target. The reflection angle was determined using trigonometric relations from measured distances in the setting. Fig. 11a and b shows examples of thermographic images obtained during this experimental setting, respectively for incident angles of 10° and 74° respect the normal. This setting was repeated for nine different incident angles, and the reflectance was obtained from Eq. (15), where TR is the absolute temperature reading inside the reflected image of the disk and TD is the absolute temperature reading directly from the disk, TT is the absolute temperature reading from the target (PV module) and TS is the temperature of ambient and surroundings (TS = 294 K). During these experimental procedures the PV module was kept at ambient temperature, so TT = TS. q¼
T 4R T 4T T 4D T 4S
ð15Þ
Fig. 12 shows the reflectance as measured and calculated from Eq. (15) and as calculated from Eq. (10) considering a mean refractive index n2 = 2.25. Error bars was inserted in order to show the effect of uncertainties of ±0.2 K in temperature measurements. Surely there are angular errors too, which are not shown in the picture and were estimated to be about ±3° (see Fig. 13). In order to validate the proposed correction method, it was assembled an experiment using a 20 l glass beaker filled with water with adjustable temperature as external source and a plane wall of an aquarium, also filled with adjustable
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Glass Reflectance
0.4
Glass Infrared Reflectance 8 -14 μm band Experimental Theoretical for n=2.25
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0.1
0 0
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20
30
40
50
60
70
80
90
Incident Angle (°) Fig. 12. Results of glass infrared reflectance in function of incident angle obtained from thermographic thermometry in a photovoltaic module illuminated with a warmed blackbody surface, and comparison with theoretical prediction.
aquarium IR-camera Fig. 11. Infrared images from a blackbody surface disk and its reflected image through the glass of a PV module for: (a) 10° incident angle and (b) 74° incident angle, with temperatures indicated in Kelvin.
temperature water as the glass reflector target. The objects are arranged to set a 30° angle from the camera objective and the target normal. The mounting is presented in Fig. 13. The procedure adopted was to slowly change the temperatures in the beaker from ambient temperature (25 °C) to warm water (50 °C) keeping initially the target temperature constant and posteriorly warming the target as well. The camera was mounted on a tripod support and thermographic images were taken at different beaker and target temperatures, reaching 30 images at the end. For each target image, the camera was rotated to the beaker in order to register its external temperature under the same conditions. In this camera position, the image of the external source is not affected by the reflection of the target, only by the background surrounding temperature. From each IR image the temperatures were read inside and outside the reflected image of the beaker and the difference, which is the reflection error, plotted against the IR measured beaker temperature. Fig. 14 shows the comparison between the true target temperature and the temperature measured inside the beaker reflected image. Fig. 14 shows also the
Fig. 13. Schema of the experimental mounting, showing a warmed beaker as external source and a smooth glass aquarium wall as target.
values of the temperature corrected with Eq. (13). Fig. 15 shows the errors before and after the correction. Errors as large as 4 °C were recorded in this experiment and the results show that the errors are clearly correlated with the difference of the beaker temperature and the surrounding temperature, as it was expected. 7. Measuring effective sky temperature One of the requisites for the accurate temperature measurement using thermograph techniques is to inform the surrounding temperature in order to allow the software of the equipment to correct its effects. The surrounding temperature can be estimated either by scanning around the target with the own camera or, as it is recommended in the user’s manual (Thermoteknix, 2001) and as proposed
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mittance window. In this case is possible to measure the effective sky temperature using the previously presented relations. The methodology consists in to expose a sheet of glass, which temperature is known, to the incident sky light in order to reflect the sky image to the camera. The glass sheet should be installed in the shadow avoiding direct solar radiation absorption and so keeping the glass near ambient temperature. The emittance parameter in the camera is set to e = 1. The error in the glass temperature reading depends on the sky effective temperature and on the incident angle for the image. Considering TM the measured absolute glass temperature and TG the actual absolute glass temperature, the effective sky temperature, TSKY, is given by Eq. (16): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 4 4 T M ½1 qðhÞ T G ð16Þ T SKY ¼ qðhÞ
60
Target Temperature (°C)
50
40
Measured temperature True Target Temperature Corrected Temperature
30
20 0
5
10
15
1033
20
25
Beaker Temperature - Surrounding Temperature (°C) Fig. 14. Temperature of the aquarium wall measured with a thermographic camera, showing the effect of the reflection error. True target temperature is determined outside the reflection area.
5
Measured Raw Difference Difference After Correction
As an example of using this technique, the effective sky temperature in the conditions of the thermography presented in Fig. 10 was determined to be TSKY = 204.7 K. This value was then used as external source temperature TE, assuming emittance eE = 1, in Eq. (13). The result is the correction from 39.6 °C to 47.4 °C, which agree with the actual glass temperature. 8. Conclusion
Reflection Error (°C)
4
3
2
1
0
-1 0
5
10
15
20
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Beaker Temperature - Surrounding Temperature (°C) Fig. 15. Reflection error as function of the difference between the external source temperature and surrounding temperature, before and after to apply the proposed correction.
by Datcu et al. (2005), by using an aluminum diffuse mirror beside the target to represent the averaged surrounding source radiation. For outdoor applications in clear sky conditions, depending on the incident angle, both methods can be ineffective because the camera can present underload saturation as consequence of the atmospheric trans-
Thermographic thermometry is a very important technique for performing evaluation of solar energy conversion equipments, but its utilization has to be carried out with care and attention in order to obtain accurate results. When performing outdoor thermographies, two kinds of errors can arise: one of them concerns to anomalous image formation due to the reflections of surrounding objects and the other concerns to the bad estimation of the equivalent sky temperature. Both are related to the glass infrared specular reflectance which importance is often neglected. This paper propose a correction method for reflection errors which is based in preliminarily to revert temperature to radiosity information, and then subtracts the external object emissive power reflected in the target as part of the whole considered radiosity, tuning it temperature again. The method was validated for a number of experimental situations, always using glass as the reflector target. As a subsequence of this method it was shown that a thermographic equivalent sky temperature can be determined for use in correction procedures for the own thermographic measurements. Acknowledgements The authors acknowledge the financial support granted by the Brazilian Scientific and Technologic Development Council (CNPq).
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A. Krenzinger, A.C. de Andrade / Solar Energy 81 (2007) 1025–1034
References Al-Kassir, A.R., Fernandes, J., Tinaut, F.V., Castro, F., 2005. Thermographic study of energetic installations. Applied Thermal Engineering. 25, 183–190. Bazilian, M.D., Kamalanathan, H., Prasad, D.K., 2002. Thermographic analysis of a building integrated photovoltaic system. Renewable Energy 26, 449–461. Datcu, S., Ibos, L., Candau, Y., Mateı¨, S., 2005. Improvement of building wall surface temperature measurements by infrared thermography. Infrared Physics & Technology 46, 451–467.
Dereniak, E.L., Boreman, G.D., 1996. Infrared Detectors and Systems. John Wiley & Sons, New York, p.34. Gruner, K.D. 2003. Principles of non-contact temperature measurements. pdf brochure www.raytek-europe.com. Lorrain, P., Corson, D.R., 1970. Electromagnetic Fields and Waves, second ed. W.H. Freeman and Company, San Francisco, pp. 508–519. Thermoteknix Systems, 2001, TherMonitor Infrared Reporter User manual, Appendix B: determining the background and emissivity.