total radiation intensity E is obtained (Stefan-Boltzmann law):. E =ear. (2) where e ... coefficient) and a is the Stefan-Boltzmann constant. .... 20H X lOV. Horizontal ...
CHAPTER
34
Infrared Thermography in Convective Heat Transfer Giovanni Maria Carlomagno and Luigi de Luca
BASIC PRINCIPLES OF INFRARED THERMOGRAPHY Thermography is a measurement technique of thermal maps. Accurate quantitative analysis of thermal images acquired in real time is an essential performance requirement of a thermographic system. The technology of modern infrared (IR) thermography can currently attain this goal to a considerable extent. Basically an IR thermal imager is a camera that detects the electromagnetic energy radiated in the IR spectral band from an object (whose temperature has to be measured) and converts it into an electronic video signal. In particular, starting from the object, IR energy is first radiated through a medium (typically the atmosphere). It then enters the sensing system, passing through a lens and an aperture (or a filter), and finally impinges on a single IR detector or a focal-plane array (FPA) sensor, which transduces the radiation into an electrical signal. The IR systems of the first generation, which typically are equipped with a single detector, need also a scanning mechanism (see later); for this reason they are conventionally termed IR scanning radiometers (IRSRs). Infrared (staring) cameras based on FPA sensing elements do not generally require any scanning device; nevertheless, since the image may be still thought of as the output from electronic scanning, hereafter they will be also referred to as IRSRs. The standard instantaneous output is represented generally by a matrix of data having a number of elements typically of the order of 20-60 thousand or more. Consequently, it is necessary to treat the data by means of numerical techniques. As a result, the procedures and the algorithms generally referred to as digital image
processing may be conveniently applied-in particular, image enhancement and image restoration. Monochromatic radiation intensity EA, emitted by a surface having an absolute temperature T, is given by Planck's law: E - e E A -
A Ao -
eACI )._5(eC2 fAT _
1
)
(1)
where EA is the spectral hemispherical emittance, CI and C2 are the first and second radiation constants respectively, A is the wavelength of the radiation being considered, and EA.o is the blackbody monochromatic radiation intensity. By integrating Planck's law over the entire spectrum, the total radiation intensity E is obtained (Stefan-Boltzmann law): E =ear
(2)
where e is the total hemispherical emittance (or emissivity coefficient) and a is the Stefan-Boltzmann constant. Measurements made by means of spectral radiometers or pyrometers are generally based on Eq. (1). Infrared cameras are often classed as total-radiation radiometers, although Eq. (2) does not apply, since their detectors sense radiation in a limited bandwidth (window) of the IR spectrum. In fact, IRSRs typically perform measurements in two different windows of the IR band: the short-wave (SW) window and the long-wave (LW) one. In the first case, the radiometer generally uses silicon optics with a coating having a transmittance peak at a radiation wavelength of about 5 J.Lm; the detector is typically manufactured from indium antimonide (InSb) and gives a spectral response between 2 and 5.6 J.Lm. A broadband coating of the optics of an SW system increases the relative response of the scanner by bringing the lower edge of the SW window
547
548 Giovanni Maria Carlomagno and Luigi de Luca down to 2 ~-tm, the short-wave broad (SWB) band. This is an advantage when spectral filtering is required, e.g., when reading the temperature of semitransparent objects, for obtaining a target signature, and in laser applications. However, broadband systems are most susceptible to atmospheric losses. In the LW band, the radiometer uses germanium optics with a peak coating at about 10 ~-tm; the detector is typically manufactured from mercury cadmium telluride (HgCdTe), which gives a spectral response between 8 and 14~-tm wavelengths. Mercury cadmium telluride detectors can be used also in the SW window. The choice of an appropriate spectral band (SW or LW) depends on different factors. Some surfaces have a higher emissivity factor in the SW window; moreover, low-cost detectors and/or thermoelectrically cooled detectors are also available in this band. However, in spite of the relatively high atmospheric transmission coefficient, usually the SW region requires some compensation while performing high-accuracy measurements at viewing distances greater than 1 m. On the other hand, the LW region exhibits a very low coefficient of atmospheric absorption, except in the case of very high water-vapor content. Due to a higher thermal contrast or sensitivity in this window, higher overall system performances can be achieved. The detector is the core of the IR thermographic system. The most frequently used detectors are the so-called photon detectors, in which the release or transfer of electrons is directly associated with photon absorption. The main characteristic of photon detectors is that they have a very short response time (of the order of microseconds), but they require cooling well below the ambient temperature to allow for high sensitivity and rapid scanning (if needed). Therefore, the sensor is frequently located in the wall of a Dewar chamber, which is cooled by liquid nitrogen (LN 2 ). To increase the operating time of the radiometer, a demand-flow Joule-Thompson cryostat using high-pressure nitrogen (or argon) gas or a Stirling closed-cycle cryogenic refrigerator can also be employed. An alternative method, based on a thermoelectric (Peltier) cooling effect, eliminates the use of detector cooling agents. This, however, generally yields a less sensitive radiometer. When the sensing element is a single detector or point detector, in order to have it receive energy from different parts of the field of view (i.e., to scan the object), a proper electromechanical scanning mechanism must be used. This scanning mechanism may consist of moving mirrors, refractive elements (such as prisms), or a combination of the two. For two-dimensional imaging, such a mechanism allows object scanning in both vertical and horizontal directions. Infrared scanning radiometers that scan the object in only one direction (one-dimensional IRSRs) are also available. They are convenient when measuring temperatures of objects moving in a direction perpendicular to the scanning one or to have very high scanning speed in the
study of fast transient phenomena (e.g., heat transfer in shock tunnels). More recently, the focal-plane array (FPA) sensor has been introduced. The FPA technology avoids the need for scanning mechanisms employing a highly reliable and very simple two-dimensional matrix of sensors, which may range from 120 x 120 elements up to 1040 x 1040 elements. In addition to detectors and cryocooler assembly, generally the sensor unit also contains all of the electronics associated with operation and control of FPA, and provides the mechanical and electrical interface to a variety of optic assemblies. In contrast to the traditional dewar-..) d>..]' (t- A//2
0
(24)
where ¢ is the temperature difference Tw(t)- Twi, Twi being the initial value of the wall temperature Tw; here p, c, and k are the mass density, the specific heat and the thermal conductivity coefficient of the model material respectively. Usually the integral of Eq. (24) is evaluated numerically by using one of the algorithms accepted for aerospace application [20 ]. In practice, a heat-flux sensor is a slab of finite thickness L; hence the thin-film model is applicable only for relatively small measurement times (i.e., there is a lower limit to the frequencies at which the sensor gives valid results). On a quantitative basis, if tM is the measurement time, it has to be verified (Figs. 6 and 7) that (25) In this case the boundary condition on surface 2 is irrelevant, since the assumption of a semi-infinite wall is valid. Since the IR radiometer has a typical response time of the order ofO.Ol-0.1 s, much larger than typical thin films, by taking into account the result enforced by formula (25), severe limitations arise from the relatively high response time of IRSR. In particular, the use of IRSR requires relatively thick sensors and/or materials of low thermal diffusivity. Another very practical transient technique is the thin-skin one, where the model wall behaves as an ideal calorimeter. In this method the sensor-a thin plate in practice-is modeled as an ideal calorimeter (isothermal across its thickness), heated on one face and thermally insulated on the other. If the heat flux Q 1 is constant in time, the relation linking Q 1 to the time rate of change of T (sensor temperature) is dT
Q1 = pcLdt
(26)
If the heat flow varies in time and does not contain harmonic component with frequencies greater than 2ajL 2 , the following equation can be used [13]:
QI (t ) =peL
VI
2
557
dT2 (t
+ L2 j6a) dt
(27)
where T2 is the adiabatic face temperature, usually measured. In the case of convective heat transfer, in order to calculate the heat transfer coefficient, it is necessary to know the temperature T 1 of the heated surface. This latter can be correlated to the temperature T2 by the formula (28)
558
Giovanni Maria Carlomagno and Luigi de Luca
Heat flux may also be correlated to temperature T1 by means of the formula Q I() t =peL
dT1(t+L 2 j3a) dt
(29)
Both Eqs. (28) and (29) are valid in the same range of frequencies as Eq. (27). Analysis of the frequency-response results (Figs. 6 and 7) shows that, within the assumption made, it is preferable to measure the heated-surface temperature instead of the insulated one because, at higher frequencies, T2 becomes smaller than T1• The use of IRSR in the wall-calorimeter technique seems advantageous because one can measure the temperature on either side of the model wall. Further, in this technique, the possibility of evaluating tangential conduction errors, due to edge effects and/or nonuniform heat flow, is very valuable. For both· thin-skin and thin-film models, the heat flux within the sensor is assumed to be one-dimensional. This hypothesis is rigorously satisfied when the heat flux on the sensor surface is uniform. Unfortunately, in many thermofluid-dynamic situations, the heat flux involved varies along the surface. A suitable expression for steady convective heat fluxes harmonically varying in one direction is Q(x)
= Ou +OJ, coskx
(30)
where: Ou represents the uniform part of the heat flux, OJ, is the amplitude of the harmonic part of the flux, k = 27rI L is the wavenumber of this latter, and x is the spatial coordinate along which the heat flux varies. For the two sensors, the response due to the harmonic spatial variation of the heat flux is given by de Felice et al. [21] in terms of the difference between the surface temperature T(x, t) at time t and the initial uniform temperature T;: &(x, t) = T(x, t) - T;. For sensor j (j = f, s), we have: (31)
where Fo =~at, the suffix s denotes the thin-skin sensor, the suffix f the thin-film one, and B.= Qhf>..~s. Be= QhfAk,
f.= fr
1- exp(-Fo)
of Ou but in the absence of tangential conduction (which is given by the classical one-dimensional solutions). We call this ratio the temperature-amplitude transfer function · (TATF). For the two models, we have respectively TATF.
=1-
exp(-Fo) Fo
(33)
and TATFe
= ..fii erf.JFo 2
(34)
JFO
The amplitude of each harmonic of the measured temperature may be thus corrected, and the corresponding harmonic of the heat flux may be evaluated by means of the classical lD formulae. Figure 9, where TATF5 and TATFr are plotted as functions of the Fourier number, shows that the thin-film sensor has to be generally preferred to the thin-skin one. This conclusion is reinforced by the fact that, for the thin-film sensor, the maximal amplitude is approached at lower Fo than for the thin-skin one. However, since sjL « 1, the ratio of the maximal temperature amplitudes is favorable to the thin-skin sensor.
VII
MEASURING HEAT TRANSFER IN WIND TUNNELS
Heat-transfer rates to aerodynamic shapes are often measured in wind tunnels. For high-Mach-number flows (high enthalpy), the model typically starts at ambient temperature, and is suddenly exposed to the stream; the increase of the wall temperature versus time is then measured. For low-Mach-number flows, a temperature difference must generally be created between model and stream. For example, a common method consists in preheating the model and studying the subsequent convective cooling by the stream. If the thermal properties of the wall are known, TATF
(32)
= erf(.JFO)
In Eq. (32), s the thickness of the thin skin, and>.. and a are the thermal conductivity and diffusivity coefficients of the sensor material, respectively. Equation (31) states that, in both cases, there is no phase difference between the incident harmonic heat flux and the surface temperature response. The maximal amplitudes, obtained for Fo --. oo are B5 and Be, respectively. For finite values of Fo, they are lowered by the attenuation factors f. and fr, respectively. In order to correct the measured temperatures to take into account tangential conduction effects, it is convenient to evaluate the ratio of the temperature amplitude Bjj(Fo) given by Eqs. (32) to that corresponding to the same value
:.:1···················.,·. . . . . . .. ··... 0.4
···.... ·······
0.2
2
3
4
5
VFo Fig. 9 Temperature-amplitude transfer function for thin-skin and thin-film sensors.
Infrared Thermography in Convective Heat Transfer on the basis of the results reported in the previous sections, the study of the heat conduction in solids can be used to determine a relationship between the heat transfer rate and the measured wall temperature history. Often it is desirable to obtain a quick survey of the distribution of the heat-transfer rate in complicated shapes. In this case, the use of classic sensors makes instrumentation of the model time-consuming and expensive. In certain cases, moderate accuracy can be tolerated, so alternative methods to measure surface-temperature distribution have been developed. The use of paints that change color at certain temperatures has been described in Refs. [22-25). The temperature at which the paints change color depends on the rate of change of the temperature, on the pressure, and in some cases also on the humidity absorbed by the paints. It is therefore usual to calibrate the whole technique with experiments on hemispheres for which the results are known. In any case, including when liquid crystals are used [15], only one isotherm at a time can be detected. Moreover, it is necessary to paint the model before each test run. Another method [26) makes use of a thin opaque coating that melts to a clear liquid at given temperatures. In this case, care must be taken to keep the liquid from flowing along the surface with the risk of creating accumulations that may disturb the flow. It is important to remember that surface-temperaturesensing techniques for wind tunnel facilities can be classed, in general, either as mounted or unmounted (remote or noninvasive sensing). Models having surfaces unsuitable for attachment of a sensor require remote methods using pyrometers and/or radiometers. A wide-field measurement with good spatial resolution, wide thermal-response range, and strong high-frequency response is mandatory whenever the experimenter does not know the optimum location or is unable to mount surface sensors. The technology of IRSR currently available fills this need. The use of IR thermography allows not only measurement of the distribution of local heat-transfer coefficients but also visualization of the local flow condition, i.e., in particular, the location of the boundarylayer transition and the location and extent of the flowseparation region. Moreover, IRSR constitutes a rapid and accurate technique for determining thermal loads as a function of the model geometry (e.g., when the flow around an aircraft or space vehicle is simulated). A typical experimental arrangement showing the model and camera installation in a wind tunnel is shown in Fig. 10 [27). A lens of appropriate focal length has to be chosen; this will depend on the dimensions of the tunnel and/or the model, or on the desired spatial resolution [28). Deciding on the material for the optical-access window is probably one of the main problems to be solved when IRSR is used in a wind tunnel facility, since neither standard glass nor quartz can be used for the wavelengths for which the IR detector is sensitive. In the case of test runs simulating
.,,,., fr011
559
llfiiCI~
Fig. 10 Typical model and IR camera installation in a wind tunnel [27].
supersonic or hypersonic flow regimes, the choice of the window material is determined by both optical and mechanical considerations. In fact, in these cases, the window must resist the stresses that originate in it because of the temperature and pressure differences existing between the wind tunnel and the environment around it. The temperature differences across the window can be minimized, as shown in Fig. 10, by having it in a remote position. Figure 11 gives the transmittance of some of the most frequently used materials. Other materials are also possible: i.e., calcium fluoride (CaF 2 ), cadmium telluride (CdTe), and potassium bromide (KBr). Germanium's primary transmission range is from 2 to 15 f..Lm, making it useful for IR laser applications, particularly in the LW band. It is opaque in the visible region, and because of a high surface reflectivity of 36% (related to its high refractive index, which is greater than 4), Ge should have an antireflective (AR) coating. Silicon (Si) is similar to germanium but with greater resistance to mechanical and thermal shocks. Its use in the LW region requires extensive calibration due to the strong variation of the transmission coefficient. Arsenic trisulfide (As 2 S3 ) has a transmission range from 0.5 to 13 f..Lm, but is quite soft and brittle. Its coefficient of thermal expansion is very similar to that of aluminum. Zinc selenide (ZnSe), with a transmission range from 0.58 to 15 f..Lm, is useful for IR applications in both SW and LW bands, permitting visual alignment. An AR coating is required to decrease the 17% single-surface reflection loss. Calcium fluoride (CaF 2 ) [30) and magnesium fluoride (MgF 2 ) [29] have excellent transmission over a broad spectral range. The former is usable from 0.15 to 9 f..Lm, and the latter from 0.11 to 7.5 JLm. Both of these materials are slightly water soluble. Their low index of refraction allows them to be used without AR coatings;
560 Giovanni Maria Carlomagno and Luigi de Luca
100 80
......., 60 ~ L-J
w 40
0
z
30
.... ien
20
j$
z c
... Gil:
10 1
1.5
2
3
8 4 6 WAVELENGTH [p.m]
10
15
20
30
Fig. 11 Transmittance of some IR optical materials (thickness 2 mm).
MgF2 is more durable than CaF 2 , and both are sensitive to thermal shock. Sapphire (Al 2 0 3 ) [28], also known as 9752 IR glass, has an extremely hard surface, is chemically inert, and is insoluble except at very high temperatures. It exhibits high transmittance (all the way from 0.15 to 6 J.Lm}, which makes it useful in the SW band and allows visual alignment. Because of its great strength, the sapphire window can safely be made much thinner than windows of other material. The sapphire window is therefore useful even at wavelengths very close to its transmission limits. Because of sapphire's exceptionally high thermal conductivity, thin windows made of it can be effectively cooled by forced air or other methods. A simple solution for the optical-window problem, described in [31], makes use of a thin plastic foil supported by a perforated force-carrying metal sheet. If the sheet is far away from the focal plane of the camera, although it decreases the IR radiation intensity, its interference with the optical quality of the picture is acceptably low. In the specific application where this system was tested, in which IRSR was used to measure the heat transfer rate on a paraboloid in a hypersonic blowdown wind tunnel, the foil had to support a pressure difference of about 1 bar. Holes of 8-mm diameter were used. No difficulties due to heating of the foil were encountered, since it was far from the hot jet boundary. When testing conditions do not impose any particular restriction, such as pressure differences, more simple solutions can be considered. The simple thin plastic (e.g., vinylidene-chloride-vinyl-chloride copolymer} foil may often be used as an IR window in room-temperature lowspeed wind tunnel environments [32]. A block diagram of the entire recording and datareduction system, as used by Bynum et al. [27) to obtain model surface temperature and heat transfer coefficient distributions, is shown in Fig. 12.
To circumvent the problem of measuring absolute radiation from the model surface, a relative method of measurement is frequently adopted [27, 29, 32], requiring known temperatures within the scanned field of view. Reference thermocouples are embedded in the subject surface at fixed points, and the rate of the strip chart used to read the reference thermocouple output can be synchronized with the tape-footage indicator of the video recorder of the thermal images. This allows continuous direct comparison of the intensity level and the subject temperature in the zones near the reference thermocouples. The scanner aperture setting, thermal range, and thermal level can also be noted at each test point. To achieve a high accuracy of absolute temperature measurement, modem IRSRs include a microprocessorcontrolled measuring system. One or more miniature reference sources are built into the scanner and, by scanning these references, the gain and level of the system can be precisely controlled. Calibration of the IRSR is generally accomplished with a blackbody calibration source mounted with the aperture on the centerline of the wind tunnel test section and in the center of the field of view of the camera. The radiation from the source is viewed with the camera through all the system's optical components, thus obviating corrections for transmission and reflection losses. In order to enhance the thermal-image detection of theIR system, it may be necessary to increase the emissivity coefficient of the surface to be measured, especially when the model is constructed of metallic material. The use of a thin coat of matte black paint raises the emissivity coefficient to 0.95-0.98 [29, 32]. To minimize interference and collimate radiation from the test model's hot surface, measuring the temperature of the tunnel walls in order to evaluate their influence on the measurements is recommended. In any case, it may be useful to keep the tunnel
Infrared Thermography in Convective Heat Transfer 561 AULD& VIDEO TAPE SYSTEM
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Fig. 12 Data-recording and digitizing system for heat-transfer measurements in a wind tunnel (27]. walls near the test section very cool compared with the model surface, and/or to coat them, using selective coatings. It is also recommended that the optical-access window be AR-coated also on the side facing the camera so as to avoid reflection of infrared radiation coming from the environment. When particular model shapes such as cones or cylinders are tested, certain regions at the edge of the model are often viewed with a great angle of incidence (measured from the normal). Such regions may appear cooler or hotter than they actually are, since all materials exhibit a dependence of the emissivity on the angle of incidence (directional emissivity). In particular, electric conductors and nonconductors exhibit contrasting behavior. For conductors, the emissivity first increases and then decreases as the emission angle approaches 90°. Nonconductors, on the other hand, have a practically constant emissivity for angles of 60° or less. Beyond 60° the emissivity falls off rapidly. The interpretation of the heat-transfer contour maps therefore needs proper correction for varying emissivity at different emission angles. Thin-film and thin-skin models are generally employed in wind tunnel testing.
A Wind Tunnel Applications A wide-ranging review of the applications IR imaging has seen in aerodynamic research may be found in the paper of Gartenberg (33].
The earliest application of an IR imaging system to measure and map aerodynamic heating parameters is probably that reported in Ref. [31], in which an IR camera was used to measure heat-transfer rates on a paraboloid in a hypersonic blow-down wind tunnel. The thin-film datareduction technique was used to determine the heat transfer data. The measured distribution of the Stanton number St = h/ Poo V00 Cp along the surface of a paraboloid at Mach 7.1 agrees in a satisfactory way with similar results obtained using melting coating (Fig. 13). Both are about 30% below the results from Ref. [34]. The agreement between the two methods indicates common sources of error, the main one being the uncertainty of the physical properties of the wall material. Another source of error is the nonuniform walltemperature distribution. The thin-film method was also selected in Ref. (27], which describes the IR system used to acquire and reduce the heating data, and the results of the measurement and mapping of aerodynamic heating parameters in the AEDCVKF continuous wind tunnels. Heat-transfer data were obtained on a cone and on a hemisphere-cylinder model at zero angle of attack for Mach 8 and free-stream Reynolds numbers ranging from 2.4 x 106 to 3.5 x 10 6 • Figure 14 reports the longitudinal centerline Stantonnumber distribution obtained from a 6° cone with laminar and turbulent boundary layers. The measured distributions are in reasonably good agreement with the calculated values. A typical Stanton contour map is presented in Fig. IS. Since these data were obtained at zero angle of
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attack, the isotherms would be expected to appear as straight lines normal to the body axis. These data, indeed, show an apparent gradual change in heat transfer at the edge of the model, from the lowest contour value to the higher ones. This is attributed mainly to the directional emittance of the model surface. Similar measurements performed in hypersonic flow on a slender 5° half-angle cone, to evaluate the accuracy and test procedure of an IR thermal-mapping system, are described in Ref. [35]. The application of infrared thermography to the measurement of heat transfer over models tested at the Von Karman Institute in the H-3 hypersonic wind tunnel at a Mach number of 6 is described by Simeonides et al. [36]. The performance of the IR technique in quantifying heat-transfer rates over aerodynamic surfaces was found to be comparable to that of discrete point gauges, such as thin-film surface-resistance thermometers and coaxial thermocouples. Significant results referring to flow visualization and heat transfer measurements performed with an IRSR in the blow-down hypersonic wind tunnel of CEAT in Poi tiers (France) at Mach number 8.15 on simple and double
ellipsoidal models are discussed in Ref. [37]. Data are reduced by means of the thin-film technique. Figure 16 shows a typical map of iso-Stanton contours measured over a double ellipsoid, on the leeward side, for an angle of attack of 30°. The full lines in the picture represent the edges of the two ellipsoids. The Stanton-number map well agrees with the oil film flow visualization (not reported herein). The thermogram reported in Fig. 17 shows the side view of the tested double ellipsoid. It gives detailed information about the aerodynamic heating mainly on the lower ellipsoid, due to the higher temperature attained here. The temperature field recorded on the cockpit (the upper ellipsoid) appears in this case substantially flat except at the reattachment zone. The dark blue region extending in the direction of the principal axis of the ellipsoids corresponds to the cockpit-lower ellipsoid junction, where the model seems colder mainly because of the directional emissivity effect. The spanwise oscillations of the heat transfer occurring in hypersonic flow on· a two-dimensional compression ramp following a flat plate (Goertler vortices-type structures) was studied by using IR thermography in the ONERA wind tunnel [38]. In particular, parameters like
Infrared Thermography in Convective Heat Transfer Mllltl oil I cand lly wlndo w tr1111
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Giovanni Maria Carlomagno and Luigi de Luca
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30.00
20.00
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Fig. 16 Map of iso-Stanton contours referring to a double-ellipsoid leeward side [37].
Fig. 17 Temperature map of double ellipsoid side view 1.60 s after model injection into the stream [37].
t is indicated in Fig. 19. Since the temperature values attained on the ramp and on the wing are quite different, and the dynamic range of the system is limited to 8 bits, for each testing condition two thermal-image sequences were recorded by setting two thermal values of the scanner's thermal range. As a matter of fact, the plot was obtained by matching the two image sequences including details about the wing and the ramp. The X and Y coordinates are streamwise and spanwise respectively. The Stanton number shows a steep ascent on the ramp, where the locus of maxima denotes nearly the reattachment line. The IRSR has also been evalu,ncd as a diagnostic tool for aerodynamic research. The results reported in the literature characterize the system's capability of performing a variety of experimental investigations, such as temperature transients, air-velocity distributions, capture of vortices, boundary layer flows, separated flows, .md wakes [431 . In particular, the IR technique has been applied to the detection of boundary-layer transition in wind tunnel settings [44, 45). Since turbulent flow evinces an increase in skin friction, heat-transfer rates are greater in turbulent flow
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Fig. 18 '-,mow- fidd IR th.:rmn!;rJph)' optk.1l ":t up l"cd 0:\l R,\\ IU( h wind tunnd I~
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Infrared Thermography in Convective Heat Transfer the relative amplitude modulation of the heat-lransfer coefficient, the amplitude modulation of the local recovery temperature, and the spatial frequency of these modulations were obtained from the time-resolved thermography oi the model surface. The two modulations were fou nd in phase opposition. The camera, with a 7 ' x 7o or 12e x 12" len:., was placed in a pressurized vessel, and an extra lens could be positioned between the camera and the model to obtain a smaller field of view, when a better spatial resolution was needed (Fig. 18). The Goertler-type instability of a hypersonic boundary layer and its influence on the wall heat transfer were experimentally analyzed also in Ref. [39) . Infrared measurements refer to the flow over two-dimension
\ \._ _ .,...__ _
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Fig. 20 Heat transfer coefficient distribution on the airfoil su rface; positions are measured from the leading edge [46).
Infrared Thermography in Convective Heat Transfer 567 (a)
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14 Stx10E3 12 10 8
6 4 2 0 0
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x/c Fig. 21 Chordwise distributions of the Nusselt number (based on wing chord) over the wing upper surface for various angles of attack n: (a) -12" 0.7 for Taw and Tw are of the same order of magnitude, the radial distribution of the Nusselt number, aver-
aged along circumferential patterns, does not seem k> depend upon the Mach number, as can be seen in Fig. 26c. It should be emphasized that the two-dimensional character of the present measurements performed by means of IR thermography, having a sufficiently high spatial resolution, made it possible to obtain these results. The study of free convection by IR thermography was addressed by Vermeulen and Baudoin [57]. These authors present correlations of free-convection heat transfer obtained, in the case of air, over a vertical and an inclined flat plate as well. as over a vertical plate with transverse disturbing elements located in the laminar boundary layer. The measurements were also completed with some flow visualizations. Cardone, di Leva, and Carlomagno [58] carried out surface flow visualizations and heat-transfer measurements in turbulent flow over a backward-facing step on both sides of the channel downstream of the step. At relatively high Reynolds numbers, a three-dimensional zone of separation was found, especially in the proximity of the upper wall, just downstream of the step location. In particular, the thermograms seem to indicate the presence of more vortices, which rotate about an axis normal to the lower and upper walls of the channel. The number and the position of such vortices appear generally random. However, at Re = 35,000, they seem to assume a regular symmetric pattern, as shown in Fig. 28. Some other IR measurements of the wall heat transfer at the reattachment point behind a backwardfacing step are in the paper of Dumoulin et al. [59]. Heat-transfer measurements on a rotating disk were performed by making use of the heated-thin-foil technique and by measuring temperature maps with an infrared scanning radiometer [60 ]. IR data were discussed in terms of the influence of the edge effects with particular regard to the tested configuration. Corrected heat-transfer results were presented in terms of Nusselt and Reynolds numbers based on the local radius; they show a good agreement with previous experimental and theoretical analyses. Transition to turbulent flow was found at about Re = 250, 000. Recently IR studies of thermal anti-icing systems were reported by Buchlin et al. [61] and Meola et al. [62].
NOIVIENCLATURE Biot number hLfk specific heat coefficient or wing chord (Sect. VII) specific heat of test gas at constant pressure Planck's constants nozzle diameter or impulse response as defined by Eq. (3) total radiation intensity monochromatic radiation intensity
Infrared Thermography in Convective Heat Transfer
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