monitoring, over time, of the surface temperature of an ice accretion during its formation under different atmospheric icing conditions. For a non-rotating cylinder ...
Proceedings of The Thirteenth (2003) International Offshore and Polar Engineering Conference Honolulu, Hawaii, USA, May 25 –30, 2003 Copyright © 2003 by The International Society of Offshore and Polar Engineers ISBN 1 –880653 -60 –5 (Set); ISSN 1098 –6189 (Set)
Infrared Laboratory Measurement of Ice Surface Temperatures during Experimental Studies on the Formation of Ice Accretions Anatolij R. Karev and Masoud Farzaneh NSERC/Hydro-Québec/UQAC Industrial Chair on Atmospheric Icing of Power Network Equipment (CIGELE), Département des Sciences Appliquées, Université du Québec à Chicoutimi Chicoutimi, Québec, Canada
ABSTRACT the “wet” regime, whereas for the “dry” regime values would fall between the temperature of water fusion and a certain minimum around ambient temperature. An alternative model based on the dynamics of a supercooled water film flowing over an icing surface was proposed by Kachurin (1962). This model, incorporating a Couette shear layer and the concept of eddy diffusivity in a flowing water film, was also initially developed for aircraft icing. It predicted supercooling of icing surfaces in both icing modes: with and without a water film. A series of experiments with artificial hailstones grown in laboratory simulations of natural conditions (List et al., 1989; Garcia-Garcia and List, 1992; Greenan and List, 1995) confirmed that the temperature of the water film on an icing surface in the wet mode is always below 0 oC. Angular temperature distribution from pole to equator was also observed, depending on the applied hailstone mode of motion, such as spin or nutation, and the prevailing thermodynamic conditions. This investigation is an attempt to draw a parallel between the various processes of ice accretion, involving hailstone growth, atmospheric icing on structures, and aircraft icing, by recording the supercooling at the surface of a water-film moving on the accreting ice surface. Ice was accreted on the surface of rotating and non-rotating horizontal cylinders by placing them within a supercooled aerosol cloud, produced and set flowing inside an icing wind tunnel under controlled thermodynamic parameters. To avoid any inadvertent influence on the ice accretion process, a non-destructive remote sensing technique was applied using industrial infrared (IR) pyrometers as detectors of electromagnetic waves emitted from the surface under investigation.
A non-destructive remote sensing technique was used to measure the temperature of an almost circular accreting ice surface in two icing regimes, i.e. both with and without a water film on it. Two industrial infrared pyrometers for the detection of electromagnetic waves within an 8 to 14 µm atmospheric window were used in the permanent monitoring, over time, of the surface temperature of an ice accretion during its formation under different atmospheric icing conditions. For a non-rotating cylinder, a 2-D angular distribution of the surface temperature was recorded starting from the stagnation line position. The temperature of the icing surface was found to be supercooled in the majority of cases, depending on the dynamic conditions in the boundary layer created by air shear on the icing surface. KEY WORDS: Non-destructive evaluation; infrared technique; supercooled water film; icing surface. INTRODUCTION Current atmospheric icing models are based entirely on the heat balance calculation of an icing surface, where the temperature of water fusion, Tm=273.15 K, is taken as the reference point, distinguishing the solid from the liquid states of water. This theoretical concept was first introduced into the investigation of the thermodynamics of cloud hailstone accretion (Schumann, 1938), and was further developed for application to aircraft icing (Messinger, 1953). When the entire amount of dispersed supercooled liquid water impinging upon the icing surface does not convert into ice immediately, the remainder forms a water film which is set in motion by aerodynamic and gravitational forces. The icing regime occurring with such a liquid film is referred to as “wet”. The “dry” regime is characterized by the instant complete freezing of the impinging water without the prior formation of a liquid film. According to this theoretical concept, upon measuring the temperature of icing surfaces, one would expect values close to the temperature of water fusion for
INRARED TECHNIQUES FOR THE NON-DESTRUCTIVE MEASURING OF SURFACE TEMPERATURES Jarvis and Kagarise (1962) measured the temperature of a water surface at room temperature by using a commercial IR radiometer and a thermistor probe. The results obtained from each technique were
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compared, and advantages of the IR technique were emphasized, particularly regarding the rapid response to changes in surface temperature, the possible recording water film motion, and the representative depth of the surface sub-layer measured. Thermal IR remote sensing in the long wavelength infrared (LWIR) band has already been successfully used for detecting newly formed ice surfaces and for surface phase-state analysis during night-time (Dey, 1980), since the contrast between the emissivity of water as opposed to thin bare ice is considerably less distinct in other IR and visible wavebands. This sensing method, however, is harder to apply when distinguishing between old ice and water, since any water surface is generally warmer than that of ice. This fact may eliminate possible differences in brightness temperatures produced by differences in the emissivity of ice and water. Rees and James (1992) measured the angular variation of the IR emissivity of ice and water surfaces in the LWIR band corresponding approximately to an 8 to 14 µm atmospheric window. The results showed that, in the range of electromagnetic wavelengths considered, both emissivity distributions are descending functions of the angle formed with the surface normal. These functions may, however, be roughly approximated as constant up to an angle of 30o with a drastic drop in both emissivity distributions beyond this angle. The emissivity of the ice surface is noticeably lower than that of water up to a 65o angle, with a maximum difference between the two functions of about 0.045 recorded for a 45o angle. Beyond a 65o angle, the emissivity of ice is equal to that of water or higher. Inagaki and Okamoto (1996) proposed a method for the non-destructive measuring of surface temperatures of non-metallic materials using three IR radiometers working in different detection wavelength ranges. This combined detection method, based on the observably different behavior of the emissivity of materials in different wavelength bands, is an invaluable tool for evaluating the characteristics of a given material. The nineties were marked by the increased use, not only of low-cost infrared detectors such as pyrometers, radiometers and thermocouples, but also of state-of-the-art infrared cameras. These latter were used for global infrared imaging of ice surfaces with different degrees of roughness during icing accretion (Hansman et al., 1991), and also of water surfaces during water film spreading processes (Saylor et al., 2000). Penetration depth for thermal IR radiation is very low: about ten micrometers for ice and several tens of micrometers for water according to various authors (McDonald, 1960; Horwitz, 1999); this fact facilitates obtaining temperature fields averaged over water surface depths. Fuller and Wisniewski (1998) used an infrared camera for investigating ice formation and the propagation of the crystallization front in various plant species. In their experiments, the moment and location of initial ice nucleation was detected by a sudden drastic increase in the negative temperature observed, i.e. lessening of supercooling. By processing different infrared images and comparing them, it became possible to distinguish between flat and rippled water surfaces. By using an infrared camera, a wavy water-film surface may be observed and successfully distinguished at both negative (Greenan and List, 1995) and positive (Saylor et al., 2000) ambient temperatures. In the former case, water film motion was registered on the surface of accreting ice; in the latter, water film spreading was observed on the surface of other materials at room temperature. Henry et al. (1995) used an infrared camera combined with infrared heat lamps for investigating enhanced heat transfer from hemispherical roughness elements on a flat plate placed inside a wind tunnel to the laminar and turbulent boundary layer of an air stream flowing above the plate. This makes it possible to understand the increased convective heat transfer mechanism on irregular ice surfaces, particularly during the regime of glaze ice formation. The potential in applicating infrared techniques is even greater than the simple nondestructive evaluation of materials and their surface-state. Peake et al. (circa1976), by applying infrared imaging in aerodynamics,
showed that, for negligible heat transfer and pressure gradient, the image obtained may be used for deriving the recovery temperature on a flat surface, and may subsequently be used to define the extent of the transition region. THEORETICAL BACKGROUND Figure 1 shows the design of the experiment. The surface, S, of ice accreting on a cylinder placed inside the test section of an icing
emission Surface S, Ts
reflection
radiosity Sensor R, TR
Walls of tunnel, Twl Figure 1. Diagram of conceptual model: IR measurements wind tunnel, is considered as a graybody with a surface temperature, Ts. The object under investigation, S, is surrounded by the surfaces of a second graybody with a surface temperature, Twl, where the walls of the test section are made of Plexiglas. The sensor, R, with a surface temperature, TR, is the third thermal factor participating in the radiant heat transfer from surface S to R. Radiosity of the surface S on the path from S to R is defined by Okamoto et al. (1993) as the sum of emissive and reflective energy. The multiple reflections between R and S from the negligibility of corresponding radiant energy (Horwitz, 1999) are disregarded. Optimum operation of the infrared pyrometer involves maintaining constant ambient temperatures throughout the experiments. The manner of maintaining constant ambient temperatures was, however, eliminated from the schedule of operation, since some minimal oscillation was unavoidable throughout the duration of the experiments. This may be ascribed to the capacity of the system to regain the target temperature in the tunnel after supplementation of the coolant to the cooler. It was, thus, planned to collect the data without any additional efforts to cool the surroundings or the sensing head so as to obtain an ideal measurement field. Reflection from the surroundings should, however, be taken into account adequately, when operating in this way. The problem of measuring Ts may therefore be solved with precise temperature measurements of all factors involved: ambient temperature Ta; temperatures Twl and TR, defined above; and total radiant incident energy, qΣ (W/m2), measured by the infrared sensor. This radiant energy registered by the sensor may be written as follows: ∞ ∞ qΣ = AdΩ∫ ε λ ,s (λ )Wλ ,b (Ts , λ ) + ∫ rs (λ )ε λ ,wl (λ )Wλ,b (Twl , λ ) + b(TR , λ ) f (λ )dλ 0 0 (1) where: Wλ ,b (Ts , λ ) and Wλ ,b (Twl , λ ) represent the intensity of
incident radiation with wavelength λ, emitted by a black body (represented by subscript b) at temperatures Ts and Twl, respectively, per unit of solid angle dΩ, per unit of detector area A, per unit wavelength interval and per unit of time; f(λ) is a filter function of the detector defining cutoff wavelengths of spectral response, λ1 and λ2; ελ,s and rλ,s are the spectral emissivity and reflectivity of the object under investigation, respectively; ελ,wl is the spectral emissivity of the second non-blackbody, made of Plexiglas; b(TR,λ) is the term representing background emission with a characteristic temperature TR. The temperature of air, Ta, is not included in this formula, since the emission of air within the waveband of spectral response of the pyrometer is disregarded in this study. The assumption is valid in its entirety for the wavelength range from 8 to 13 µm, where the air does not absorb radiation. Because of the evident CO2 absorption in the
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wavelength range from 13.5 to 17 µm, the assumption is valid only partially in the remaining short interval of the detection wavelength range from 13 to 14 µm. Since the object investigated could be either ice or water, depending on the regime of ice accretion, ελ,s and rλ,s represent spectral emissivity and reflectivity of ice (ελ,i and rλ,i) or water (ελ,w and rλ,w). The first term in (1) represents the radiation energy emitted directly by the object investigated with a characteristic temperature Ts; while the second term represents the energy reflected, or re-emitted, by the object after it was initially emitted from the walls with a characteristic temperature Twl. For both the non-blackbodies listed, TR should be taken as representative of background emission. The third component of the total radiant energy representing its transmitted part is omitted, since all three mediums involved, namely ice, water and Plexiglas, are considered opaque to infrared radiation. Opacity together with the significant postulate ε s = α s , makes it possible to express Kirchhoff’s
By combining (5) and (6), one obtains the relationship between i) the temperature indicated by the instrumentation and measured in the units specified, T s′ ; ii) real temperature Ts; and, iii) the various radiant factors involved:
law for an opaque body in thermodynamic equilibrium with its surroundings as follows:
ε s + rs = 1
(2)
where εs and αs are integral emissivity and absorption of the object inspected, respectively. As may be seen from (2), the emissivity and reflectivity in Kirchhoff’s law do not generally pertain to specific wavelengths; in practice, however, this formula is used for spectral data with a high degree of accuracy (Salisbury et al., 1994), and is intended for use in such a way in this study. Equation (1) may be rewritten by substituting (2) into (1), by taking into account formulas (A.4) and (A.6) presented in Appendix A, and by accounting for TR as the temperature of the surroundings relative to emission from both the nonblackbodies defined earlier, represented by the surface under investigation S and the Plexiglas walls of the test section:
{ (
)
(
qΣ = AdΩσ ε s K1,sTsns − K1,RTRnR + (1 − ε s )ε wl K1,wlTwlnwl − K1,RTRnR
)} (3)
In general, the power factors ns, nR and nwl are different for all characteristic surfaces having distinguishable temperatures. For this investigation, however, the value n=4.9, from an earlier study (Rees and James, 1992) for temperature T=273.15 K, will be adopted in this article. This same consideration may be applied to the use of the recurring constant K1: it is assumed that K1 is the same for both first and second combinations of a graybody with emitting surroundings. The radiant energy detected may also be expressed through the coefficient of radiosity, as, of the measuring system for this combination of radiant-energy emitters with the real surface temperature Ts of the object investigated, as follows:
qΣ q= = σ K 1 a s T sn dΩ A
(
)
T ′ n − (1 − ε s )ε wl Twln − TRn (7) Ts = TRn + s εs From the last series of expressions, (5), (6), and (7), it may be concluded that defining the radiosity of the measuring system plays a pivotal role in the infrared measurement of surface temperatures. It may also be supposed that both expressions can be considerably simplified if the sensor were cooled, making it possible to disregard the temperature TR. Since cooling below 10oC is not recommended for this type of pyrometer, however, the temperature TR should figure in all considerations. Finally, from (7) it may be concluded that calibration adjustment must be made prior to taking the measurements, thus making it possible to compare real temperatures, as measured by a reliable instrument such as a thermocouple, with the readout from the infrared instrument. The procedure to be carried out at the calibration stage will be described in further on. Surface temperature values calculated using (7), as may be indicated by an IR instrument, T’s, are presented in Figure 2 and correspond to a different real surface temperature, Ts, and different sensor temperature, TR. Data for water and ice emissivity, from Irvine and Pollack (1968), and from Schaaf and Williams (1973), respectively, were used to calculate their integral emissivity over the detection waveband by integration with 0.1 µm. From this figure, it may be observed that the temperature indicated by the IR instrument is a fairly weak function of the temperature of the Plexiglas walls in the tunnel, Twl. Similar conclusions were drawn by Horwitz (1999). This is due to the fact that both water and ice are very good emitters over the entire detection waveband with an emissivity approaching that of a blackbody. A further conclusion, drawn from observation of the theoretical results in Figure 2 and considered a disadvantage, is that, for Twl~ 0oC, the distinction between water and ice surfaces of an order of only 0.1 to 0.7 o C, may be recorded for supercooled surface temperatures, while for surface temperatures around Tmthis difference is even lower than 0.1oC. 1n
230
T's (K)
220
1 2 3 4 5 6 7 8
210 200 190 180 170 255
(4)
260
265
270
275
280
285
Ts, (K)
where the coefficient of radiosity is defined by the ratio of measured Ts′ and real Ts temperatures, as follows:
Figure 2. Theoretical graph: correspondence between real and indicated hypothetical temperature of scanned surface for different ambient thermal condition: 1., 5. Twl=0oC, TR=-15oC; 2., 6. Twl=20oC, TR=-15oC; 3., 7. Twl=20oC, TR=-10oC; 4., 8. Twl=20oC, TR=-20oC; 1., 2., 3., 4.- ice; 5., 6., 7., 8.- water.
n
T′ (5) a s = s Ts By substituting (3) into (4) and taking into account each of the recently discussed assumptions, the coefficient of radiosity may be expressed through the temperatures and emissivity of all essential factors involved, as follows: T n T n −T n (6) a s = ε s 1 − R + (1 − ε s )ε wl wl n R Ts Ts
The distinction is much more noticeable for Twl~ 20oC because of the increased influence of re-emitted energy. Though this condition may occur outside the tunnel, it is counterproductive for icing experiments inside the tunnel, since it would affect heat transfer processes considerably. Typical wall temperatures inside the tunnel, maintained
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throughout an icing experiment, range from –7oC to 5oC.Changes in the sensor temperature, TR, have the greatest influence on the temperature 1 255
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inside the tunnel just below the lid of the test section. To introduce the tube containing the pyrometer probe from below, an ellipsoidal opening was made in the 0.6 cm thick Plexiglas base of the tunnel and, once
1 2
as (-)
3 4 0,1
5 6 7 8
0,01 Ts (K)
Figure 3. Radiosity of measuring system as a function of the ambient thermal parameters: all symbols are the same as in Figure 2. recorded by an IR instrument.Thus, 5oC-changes in sensor temperature, produced by uncontrolled oscillations in the ambient temperature, will generate changes in the read-out of the TS′ of about 10oC to 12oC for a temperature of the scanned surface of about Tm. This tendency emphasizes the importance of maintaining TR relatively constant throughout the experiment, and as low as possible in relation to the scanned surface temperature. In practice, however, after thoroughly cooling the tunnel and the control room surrounding the test section, we were able to maintain ambient temperature oscillations within a 1.5oC to 2oC range. The importance of maintaining TR considerably below Ts may also be further deduced from Figure 3, showing the calculated values of the radiosity coefficient for the same conditions as Figure 2. When TR is kept at least 20oC below the expected surface temperature of the material investigated, it is still possible to collect information from this surface for use in extracting Ts. In this case, there is a considerable increase in the importance of the calibration curves U(mV)/Ts for certain constant values of TR, as expected during the experiment. Calibration curves of this type will be discussed in the next section.When the sensor temperature approaches Ts, however, the extraction of the data related to Ts becomes increasingly difficult, and then impossible to obtain when the radiosity coefficient drops below 0.1.
Figure 4. Schematic diagram of technical design: IR measurements tested, the tube was sealed into the bottom of the test section. For ease of maneuvrability, a double sliding palette-like tab made of Plexiglas, with an ellipsoidal hole for the tube, is set under the Plexiglas bottom of the test section. The angles covered by this system range from 45o to 90o below this line. A manually operated rail-and-tread system rotates the sensor tube within the prescribed angular range and also makes it possible to adjust the penetration distance between the sensor and the surface investigated. The cylinder is placed horizontally across the test section and inserted into two bearings mounted on each wall of the test section. Rotation of the cylinder is produced by an AC electrical motor transferring the angular momentum to the inner ring of one of the bearings, and, from there, to the aluminum cylinder screwed into it. The other end of the cylinder remains unriveted inside the second bearing. The second experimental set-up was designed to collect temperature data from the upper half of the cylinder. Two circular Plexiglas plaques, whose diameters are approximately equal to the height of the walls of the test section, are placed inside the tunnel against both walls. The plaques are mounted on the same bearings as those used for rotating the cylinder in order to use the same pivotal point to rotate the experimental construction around the surface to be investigated. The tube with the second probe is mounted on an especially designed metallic crossbar, whose ends are fitted into the circular plaques. To make it possible for the tube-with-probe combination to reach the top position above the cylinder, a rectangular opening was made in the cover of the wind tunnel and protected by a fiberglass hood which was sealed in with special rubber cement. Rotation of the circular plaques is carried out manually outside the tunnel by using an aluminum handle. The handle is connected to the plaques through 135o arc-like slots in each wall of the tunnel composed of 0.6 cm thick Plexiglas plates and reinforced with aluminum posts at the joints between the bottom and wall plates. This set-up makes it possible for the probe to be rotated around the cylinder at angles of 0o
EXPERIMENTAL SET-UP The infrared pyrometers used in this investigation were Omega Technologies Co. models OS65 with mV/degree output type. The optical system, which has a focal length of 6 inches (~15.24 cm) and effective focal ratio 24:1, makes it possible to collect the average signal from a focal point emitted by a ¼-inch (~0.6 cm) diameter circular area. The detector operates within an ambient temperature interval of – 18 oC to 85 oC. The influence of air humidity inside the test section may be disregarded here, since the spectral response of the model is within an 8 to 14 µm atmospheric window. The emissivity of the object investigated may be digitally adjusted within a range of 0.10 to 0.99. Figure 4 shows a vertical cross-section schematic of specifically adapted improvements to the test section of the icing tunnel for carrying out infrared measurements. In order to protect the probes from icing over during the experiments, each one was placed inside a plastic tube darkened with epoxy blacking. To discover the best way for the sensors to penetrate the test section area and reach to the measuring surface, two independent mechanical systems were designed as follows: a lower system situated beneath the test section with its controls on the outside of the tunnel, and an upper system inserted
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to 90o as measured from the perpendicular line to the stagnation line, for the top half of the cylinder, and at angles of 0o to 45o measured from the same perpendicular line to the stagnation line, for the bottom half of the cylinder. From the outset of the experiment, both sensors are positioned at a distance equal to the focus length from the surface investigated. As the ice surface moves in radial fashion during the experiment, this distance decreases and cannot be adjusted for the top sensor, but it may be regulated for the bottom sensor according to the ice thickness predicted.
surface (Rees and James, 1992). The sub-series makes it possible to explore the role of potential roughness elements occuring on the icing surfaces, with their capacity for changing the signal; also deviation of the sensor axis from the line perpendicular to the scanned surface which may result in data acquisition at a grazing angle. For this and subsequent calibration sub-series a special measuring device was designed. A shallow box-like tray made of Plexiglas 20x20x8 cm3 is rigged centrally between two sections of a cylinder adjusted and locked in place. Water or previously prepared flat ice samples are placed inside the tray which is aligned horizontally before cooling in the wind tunnel is initiated. During exposure of the samples to varying ambient temperatures, the top infrared sensor is rotated around the device starting from a position perpendicular to the scanned surface up to a 7080 degree maximum achievable grazing angle. A control thermocouple was placed in contact with the water surface by means of a Styrofoam float; for flat ice samples, the thermocouple was kept on the surface with special fastenings on the walls of the Plexiglas tray. This subseries proved that the influence of the angular variations of ice and water emissivity on the read-out of the IR instrument, up to a 45o angle, falls within the instrument accuracy range. As a result, it was not taken into account... It may be noted that for a non-equilibrium thermodynamic state when the temperatures of the ambient and scanned surfaces are different, condensation on the latter or evaporation from it, produces additional heating or cooling, respectively, of the thin surface layer. A non-equilibrium thermodynamic state is the most frequent state occurring in nature and in this calibration sub-series.
CALIBRATION SERIES Calibration of both infrared systems was carried out by the simultaneous measuring of the surface temperatures of several representative patterns of control bodies using pyrometers and thermocouples. This method of calibration (Jarvis and Karagarise, 1962) is a typical preparatory stage preceding the pyrometer measurement of surface temperatures, and involves testing on a body of known emissivity. Based on equations (6), and (7), the following factors were taken into consideration in the calibration series. In order of their expected significance they are: distance from the object investigated; angular position of the sensor relative to the line perpendicular to the surface investigated; shape of the control body, whether flat or curved, and the radius if so; emissivity of the object investigated within the detection waveband of the pyrometer, or the phase state of ice surface; ambient thermal conditions, including supplementary and background emitters. The entire calibration series consists of specific parallel measurements made by a pyrometer and a reliable thermocouple under conditions where all the factors mentioned, except one, are maintained constant. The deviations of the sensor readout as a result of the variations of each unsteady parameter should provide the degree of significance of the parameter observed. A further incentive for carrying out this calibration series is to explore and evaluate in greater detail the extent of the potential effects each of the parameters may have on the accuracy of the results. Only the most important calibration series will be presented in a graphical manner.
20 15 10
1 2
t (oC)
5
3 4
0 -15
-10
-5
-5 0
5
10
15
20
5 6 7
-10
t=U
-15
Distance from Object During the experiment, ice accretes on the surface of a cylinder and consequently the radiant ice surface progresses in a radial direction towards the sensor head. According to the inverse-square law, the intensity of the radiation emitted from a point-source varies as the inverse square of the distance between the source and the receiver. The Stefan-Boltzmann law (Eq.A.3) defines the total IR energy radiated into a hemisphere. The optics of the sensor, however, makes it possible to collect the data from the narrow aperture close to the focal point. A flat piece of wood covered with dull black masking tape was used for the verification of the reading of both pyrometers as a function of variations in distance. A control thermocouple was taped in place between the last two surface layers of the masking tape. The absolute accuracy for a relatively uniform temperature field was seen to remain the same. The surface scanned cannot be considered as a point-source; accordingly, the influence of the distance variation on the difference between the temperature values recorded by the pyrometer and those measured by the thermocouple may by considered as negligible. It falls within the accuracy limits of the instrument. For cylinders of small diameter (D< ½ inch), however, the difference was seen to increase as a result of the partial acceptance of approximation with the pointsource.
-20 U ( mV)
Figure 5. Calibration curves for several materials at positive ambient temperatures: 1., and 2. darkened wood; 3. piece of Plexiglas; 4. saline water; 5., 6., and 7. distilled water. During a similar calibration series Jarvis and Karagise (1962) tried to avoid this problem by covering the water surface with thin film of oleic acid (1 to 2 mm). The final calibration curves for clean and contaminated surfaces, however, were found to lie very close to each other. A more exacting problem is the precise settling of the junction of the thermocouple as close to the water/air interface as possible, while still remaining in the water medium. This exactitude is necessary for the readouts of the thermocouple to be representative of a thin surface layer, the average temperature of which is measured by the sensor. The problem was solved by periodical checking the junction point near the surface using a microscope. In Figure 5 the calibration curves are presented for several for several materials involved in IR measurements for a 0o incident angle. Data acquisition was done at positive ambient temperature (24oC~25.8o). Several supercooled water samples were obtained by dissolving NaCl in distilled water. Seawater has a 2% lower emissivity than distilled water in an 8-14 µm waveband (Salisbury and D’Aria, 1992) due to the distinct behavior of optic constants in both cases (Pinkley and Williams, 1976); this is illustrated
Incident Angle and Emissivity of Object This calibration sub-series was necessitated by the results of recent measurements of ice and water emissivity as a function of the angular position of the sensor relative to the line perpendicular to the scanned
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considerations.
in Figure 5 by changes in the degree of slope for data concerning the saline solution.
RESULTS AND DISCUSSION Shape of Icing Object and Ambient Thermal Conditions In Figure 6, the calibration curves for the flat ice sample, obtained stage of the calibration for a 0o incident angle, are compared to the mV/oC relationships for 3-D ice samples. Samples were obtained either through refrigeration or by real ice accretion processes in the icing wind tunnel. A Plexiglas tray was used for placing the samples in the focal point of the infrared sensors. The ice samples were i) 3 and 6 cmdiameter solid cylinders; ii) a 4 cm-diameter hollow cylinder; iii) an open cylindrical cavity with a 3 cm inner diameter; and, iv) a 4 cmdiameter hollow cylinder with a slit about 30o in aperture. All data were collected at supercooled ambient temperatures. The calibration curves are obtained from continuous changes in the ambient temperature during experimental IR sensor readings and further comparison with parallel experimental thermocouple measurements. The differences recorded in the behavior of these curves may be explained theoretically (Bramson, 1968). Supplementary sub-series was carried out to investigate the difference between temperature readings made by thermocouple and by infrared sensor as a function of the diameter of a cylinder covered with dull black masking tape when it was placed at
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t (oC)
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Experiments with a Non-rotating Cylinder The data-set presented in Figure 7 is acquired from the ice accretion surface on a non-rotating cylinder formed during the icing experiment. The following ambient conditions were applied during the experiment. The temperature and air speed were –15oC and 10 m.s-1, respectively. The droplet size distribution (DSD) with a median volume droplet diameter (MVD) of 57 µm was used. The combination of
temperature (oC) or U(mV)
2
Two complete typical data-sets are presented here from a number acquired under various thermodynamic conditions from the surface of both rotating and non-rotating 3.5 cm-diameter icing cylinders. The diameter of the cylinder was chosen in accordance with the results obtained from the calibrations series. Only the data collected by the upper IR set-up system are presented in this article.
0 0
1000
2000
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3000
1 2 3 4
-15 -20 time (s)
Figure 7. Data-set acquired during an icing experiment: 1. temperature of walls of tunnel, Twl; 2. air temperature, Ta; 3. temperature of sensor TR; 4. time-averaged voltage, U (mV), as an output of IR instrument.
t=U
-20 U (mV)
dynamic nozzle parameters (Karev et al., 2002), used to obtain this DSD, for an air speed of 10 m.s-1, gives a liquid water content (LWC) at the mid-point of the cross-section of about 8.7 g.m-3. The spatial IR data were collected around the cylinder every 10o from 14 separate equidistant radial points starting from the top position and to an angle of 135o as measured from the highest point. Data collection from each single point lasted about 30-45 seconds with an approximate time interval of 15 to 20 seconds between two consecutive measurements to allow for changes in the position of the system. As a general rule, this method of procedure leads to performing a 135o-rotation in approximately 10 to 12 minutes. During the rotation of the IR system, data acquisition may be halted temporarily using software written in VB specifically created for the purpose of data-collecting selectively and punctually, i.e. at given points. After completion of data acquisition, average values for 30-45 second time interval for a specific point were obtained. The thermodynamic conditions presented correspond to “wet” ice growth, as may be calculated from any of the classical icing models. Extracting the information acquired by using calibration curves presented earlier with taking into account changes of TR during an experiment, one may obtain, however, a negative surface temperature throughout the duration of the experiment. Since data acquisition proceeded over time, for the purposes of this experiment, the resulting temperature distribution may be called the spatio-temporal distribution of surface temperatures, which is presented in Figure 8. From time to time, shedding of droplets could be observed visually
Figure 6.Calibration curves for variegated ice shapes:1. hollow half of cylinder with an inner diameter 4 cm; 2. and 3. a 6-cm diameter cylindrical ice; 4. and 5. a 3cm-diameter cylindrical ice shape; 6. 7. 8. and 9. flat ice samples at –12oC to –15oC ambient temperature. the focal point of the sensor and kept at room temperature. With a decrease in the diameter of the cylinder, the difference between the two temperatures measured by different means was found to be generally increased. This fact may be attributed to the different ratios between cylinder diameters and the diameter of the spot from which the data were gathered for the cylindrical samples of different diameters. The temperature difference registered is maximal for the smaller ¼-inch cylinder, when the diameter of the scanned spot may be even larger than the cylinder diameter, and minimal for the largest 1½-inch diameter cylinder. Some of the calibration curves for flat ice samples and for a 3 cm-diameter cylinder presented in Figure 6, were obtained during data acquisition under different ambient temperature conditions. Thus, the curves are distinct only as a result of the influence of the thermal factors involved; the influence of the oscillation of the ambient temperature, Ta, is investigated in this sub-series, producing corresponding changes in the sensor temperature, TR. This impact displays itself by shifting the calibration curves up or down and changing its slope. This was observed also during theoretical
395
CONCLUSIONS
temperature (oC)
during the experiment, and a thin water film flowing on the icing surface was also registered.
Spatio-temporal remote IR measurements were presented and discussed in this investigation on the surface temperatures of an ice-covered cylinder during the process of experimental ice accretion in an icing wind tunnel. It was demonstrated that the surface temperature of accreting ice remains supercooled at all times during the experiment. The angular surface temperature distribution for a non-rotating cylinder was observed and recorded, providing evidence of a nonhomogeneous heat transfer process around the cylinder. In spite of the theory (Messinger, 1955) which proposes the assumption, that the surface temperature is 0oC for the icing regime with a water film on the ice surface, the temperatures measured were supercooled even when shedding occurred from the ice surface. It should be noted that, the terminology “wet” and “dry”, which since the time of Schumann’s theoretical work (1938) has usually been applied in various models in order to distinguish between the ice accretion icing regimes with and without a water film on the icing surface, now has become obsolete and misleading in the light of further research. Finding an alternative to the contemporary distinction between the two icing regimes mentioned should be the main objective of subsequent research in physics of atmosphere and atmospheric icing. To date, only one theory (Kachurin, 1962), mentioned in the Introduction, satisfies the requirements, and with certain modifications, should be tested in future experimental work.
5 3 1 1rotation -1 -50 0 50 100 2rotation -3 3rotation -5 -7 -9 -11 -13 -15 Angle from stagnation line (degrees)
Figure 8. Spatio-temporal distribution of temperature of ice surface during an experiment extracted from output of IR pyrometer. Experiments with a Rotating Cylinder Data presented in Figure 9 were collected during ice accretion on the surface of a cylinder rotating at 1 rpm while exposed to a supercooled aerosol cloud. During the rotating cylinder experiment, the upper IR system remained in the top position, scanning the same spot from different locations of the rotating cylinder. The MVD of the DSD in the experiment was 43 µm. The air temperature and speed were –10oC and 10 m.s-1, respectively. The combination of dynamic nozzle parameters used to obtain this DSD, for an air speed of 10m.s-1, results in the LWC at the mid-point of the cross-section of about 6 g.m-3. These thermodynamic conditions correspond also to “wet” ice growth. Extraction information using calibration curves presented earlier from the data-set, indicates, however, a negative surface temperature throughout the experiment. Shedding of droplets again was observed visually during this experiment.
ACKNOWLEDGEMENTS This study was accomplished within the framework of the NSERC/Hydro-Quebec Industrial Chair on Atmospheric Icing of Power Network Equipment (CIGELE) at the University of Quebec in Chicoutimi. The authors would like to thank the associates of the CIGELE for financial support. Valuable help provided by CIGELE technician P.Camirand and S. Vaslon, undergraduate, in designing and manufacturing of experimental set-up for infrared observation is gratefully acknowledged. We are also most grateful to M. L. Sinclair for editorial assistance. REFERENCES
temperature (oC) or U (mV)
6 4 2 0
-2 0
700
1400
2100
2800
3500
1 2 3 4 5
Bramson, M (1968). Infrared Radiation: A handbook for applications, Plenum Press NY, 624 p. Dey, B (1980). “Applications of satellite thermal infrared images of monitoring North Water during the periods of polar darkness,” J Glaciol, Vol 25, pp 425-38. Fuller, MP, and Wisniewski, M (1998). ”The use of infrared thermal imaging in the study of ice nucleation and freezing of plants,” J therm Biol, Vol 23, pp 81-89. Garcia-Garcia, F, and List, R (1992). “Laboratory measurements and parametrizations of supercooled water skin temperatures and bulk properties of gyrating hailstones,” J Atmos Sci, Vol 49, pp 2058-73. Greenan, BJW, and List, R (1995). ”Experimental closure of the heat and mass transfer theory of spheroidal hailstones,” J Atmos Sci, Vol 52, pp 3797-15. Hansman, RJJr, Yamaguchi, K, Berkowitz, B, and Potapczuk, M (1991). “Modeling of surface roughness effects on glaze ice accretion,” J Thermophys, Vol 5, pp 54-60. Henry, RC, Hansman, RJJr, and Breuer, KS (1995). “Heat transfer variation of proturberances and surface roughness elements,” J Thermophys Heat Transfer, Vol 9, pp 175-80. Horwitz, JW (1999).” Water at the ice point: a useful quasi-blackbody infrared calibration source,” Appl Optics, Vol 38, pp 4053-4057. Inagaki, T, and Okamoto, Y (1996). “Surface temperature measurement near ambient conditions using infrared radiometers with different
-4 -6 -8
-10 -12
time (s)
Figure 9. Data-set acquired during an icing experiment with a rotating cylinder : 1. temperature of walls of tunnel, Twl; 2. air temperature, Ta; 3. temperature of sensor TR; 4. time-averaged voltage, U (mV), as an output of IR instrument; 5 temperature of ice surface obtained from experimental data.
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detection wavelength bands by applying a grey-body approximation: estimation of radiative properties for non-metal surfaces” NDT&E Internat, Vol 29, pp 363-69. Irvine, WM, and Pollack, JB (1968). “Infrared optical properties of water and ice spheres,” Icarus, Vol 8, pp 324-360. Jarvis, NL, and Kagarise, RE (1962). “Determination of the surface temperature of water during evaporation studies. A comparison of thermistor with infrared measurements,” J Colloid Sci, Vol 17, pp 50111. Kachurin, LG (1962). “On airplane icing theory,” Izv Akad Nauk SSSR, Ser Geofiz, Vol 6, pp 823-32. Karev, A. R., and Farzaneh, M. (2002) Evolution of Droplet Size Distribution in an Icing Wind Tunnel, 10th IWAIS, Brno, Czech Republic, 16-19 June 2002. List, R, Garcia-Garcia, F, Kuhn, R, and Greenan, B (1989). “The supercooling of surface water skins of spherical and spheroidal hailstones,” Atmos Res, Vol 24, pp 83-87. McDonald, JE (1960). “Absoption of atmospheric radiation by water films and water clouds,” J Meteorol, Vol 17, pp.232-238. Messinger, BL (1953). “Equilibrium temperature of an unheated icing surface as a function of air speed,” JAS, Vol 20, pp 29-42. Okamoto, Y, Inagaki T, and Sekiya, M (1993). Surface temperature measurement using infrared radiometer (1st report, radiosity coefficient and radiation temperature), Trans Jpn Soc Mech Eng Ser B, Vol 59, pp 232-237. Peake, DJ, Bowker, AJ, Lockyear, SJ, and Ellis, FA (circa1976). “Nonobtrusive detection of transition region using an infra-red camera,” AGARD CP, paper 29. Pinkley, LW, and Williams, D (1976). “Optical constants of sea water in infrared,” J Opt Soc Am, Vol 66, pp 554-558. Rees, WG and James SP (1992). “Angular variation of the infrared emissivity of ice and water surfaces,” Int J Remote Sensing, Vol 13, pp 2873-86. Salisbury, JW, and D’Aria, DM (1992). “Emissivity of Terrestrial Materials in the 8-14 µm atmospheric window,” Remote Sens Environ, Vol 42, pp 83-106. Salisbury, JW, Wald, A, and D’Aria, DM (1994). “Thermal-infrared remote sensing and Kirchhoff’s law 1.Laboratory measurements,” J Geophys Res, Vol 99B, pp 11897-11911. Saylor, JR, Smith, GB, and Flack, KA (2000). “Infrared imaging of the surface temperature field of water during film spreading,” Phys Fluids, Vol 12, pp 597-02. Schaaf, JW, and Williams, D (1973). “Optical constants of ice in the infrared,” J Opt Soc Am, Vol 63, pp 726-732. Schumann, TEW (1938). “The theory of hailstone formation,” Quart J Roy Meteorol Soc, Vol 64, pp 3-21.
x =
4 ) = 2 π k3 T2
∞
4
∫
h c
0
x 3 dx 2π k 4T = x e −1 h 3c 2
4
(A.2)
J3
where the value of the integral J3 may be defined in optics as J 3 = π 4 15 (Bramson, 1968). The expression (A.2), after insertion of the value of the integral J3, transforms into the well-known StefanBoltzmann law of blackbody radiation with a temperature T: (A.3) q b (T ) = σ T 4 where σ =5.67.10-8 W.m2.K-4 is the Stefan-Boltzmann constant. The radiant emittance per unit area of a non-blackbody with a temperature Ts, when the emission of the surroundings is appreciable, may be defined as follows: 4 (A.4) q nb (T ) = σε s Ts4 − Tsur
(
)
λ2
where ε = 1 ε dλ is the integral emissivity of a non-blackbody; λ ,s s
λ λ∫
1
ελ,s is its spectral emissivity within the range confined by cutoff wavelength limits λ1 and λ2; and, Tsur is the temperature of the surroundings. In (A.4), the subscript “nb” stands for non-blackbody. The radiant energy qnb,nr(T) per unit of solid angle dΩ, as emitted by a non-blackbody and detected per unit of detector area by an IR sensor with a narrow detection waveband, and when the emission of the surroundings is negligible, may be written as follows: 3 ∞ 2 π k 4 T 4 ε λ , s f ( x )x dx (A.5) x 3 2 ∫ h c e −1 0 where f(x) is the filter function of the detector depending on the variable x = hc λ kT . In (A.5), the subscript “nr” stands for narrow range. The simplest solution of the integral (A.5) may be obtained when the filter function f(x) is a non-zero constant within the detection waveband, and zero everywhere outside this interval, i.e. the relative spectral response is in the shape of a delta- function with cutoff wavelength limits λ1 and λ2. In such a case, the radiant energy from (A.5) may be written as follows:
q nb , nr (T
)=
q nb , nr (T
)=
2π k 4T h 3c 2
4 x2
∫ελ
,s
g ( x )dx = K ε s T
n
(A.6)
x1
where g ( x ) = x 3 (e x − 1) , and the new boundaries of integration x1 and x2 are defined as x 1 = hc λ 1 kT and x 2 = hc λ 2 kT , respectively; K (W.m-2.K-n) is a constant defined through the Stefan-Boltzmann constant σ and constant K1: K = K 1σ ; n is called the power factor ( n > 4 ); and the integral emissivity is averaged only over the spectral response band of the detector. The power factor n may be defined from an empirical relationship as follows :
Planck’s spectral radiant emittance W (W.m-2.µm) of a blackbody at temperature T and wavelength λ, emitted per unit of wavelength, is postulated as follows: (A.1) 2 λ , b (λ , T ) =
, one may obtain the total radiant emittance qb(W.m-2)
q b (T
APPENDIX A: Energy Detected by IR Sensor
W
hc
λ kT
(A.7) n = 14388 λ eq T where λeq is called the equivalent wavelength, taken in microns in this empirical relation. Another way of defining n is by using the abovedefined filter functions (Rees and James, 1992) as follows: (A.8) x1 g ( x1 ) − x2 g ( x2 )
2 π hc hc 5 λ exp − 1 λ kT
where h=6.626.10-24 J.s and k=1.3807.10-23 J.K-1 are the universal Planck and Boltzmann constants, respectively; c=2.9979.108 m.s-1 is the speed of light in a vacuum. In (A.1), the subscript “λ” stands for the spectral value, and “b” stands for a blackbody. By integrating expression (A.1) over all wavelengths and using the new variable
n=
x2
∫ g(x)dx
+4
x1
Within an 8 to 14 µm atmospheric window n ≈ 4.9 (for T=273.15 K).
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