Infrared thermography for convective heat transfer measurements

The wavelength λ* at which the black body emits its maximum spectral emissive power is a function of the absolute black body temperature according to:i.e., the maximum value of I ^b moves toward shorter wavelengths as the body temperature increases. E.g., at liquid nitrogen temperature (77 K) λ* ≈ 38 μm, at room temperature λ* ≈ 10 μm, while the sun (at about 6,000 K) emits yellow light peaking around 0.5 μm in the visible light spectrum. This explains why IR cameras mainly operate in MWIR and LWIR bands.

The total (over all wavelengths) hemispherical emissive power E ^b (W/m²) also depends on the absolute black body temperature alone, according to:where σ is the Stefan–Boltzmann’s constant, which is equal to 5.6704 × 10⁻⁸ W/m²K⁴ . However, since infrared camera detectors capture only a limited band of the whole electromagnetic spectrum, while making measurements with IR thermography, Planck’s law (2), rather than Stefan–Boltzmann’s law (4), has to be applied.

Real objects almost never comply with the above-described laws even if they may approach the black body behavior in certain spectral bands and conditions. A real object generally emits only a fraction I(λ) of the radiation emitted by the black body I ^b (λ) at the same temperature and wavelength. For the sake of ease, I(λ) is always referred to the spectral hemispherical emissive power. By introducing the spectral emissivity coefficient, defined as:

Equation (2) can be rewritten for real bodies by simply multiplying its second term by ε(λ):

Bodies having their emissivity independent of λ are called gray bodies. Kirchhoff’s law states that the spectral emissivity coefficient is equal to the spectral absorptivity coefficient α _r (λ), which is the absorbed fraction of the radiation of wavelength λ. Therefore, for non-transparent bodies, such as those generally used in infrared thermography, Eq. (1) becomes:

Besides, real objects almost never emit in a diffuse (isotropic) way, the emissivity coefficient ε being dependent also on the angle θ (directional emissivity) between the direction of emission and the normal to the emitting surface (viewing angle). The directional emissivity behavior of dielectric materials is quite different from metallic ones.

As shown in Fig. 1 for Macor™, dielectric materials, at angles θ generally less than about 60°, have a quite constant and relatively high emissivity, while they emit poorly at large angles away from normal direction. Vice versa, electric conductors (such as platinum) have usually a low emissivity, with a relative minimum in the normal direction. To evidence viewing angle effects, the thermogram of the wall of a hot vertical PVC (dielectric) cylinder under natural convection conditions is shown in Fig. 2. Wall temperature, which is constant cross-wise (along the broken line), appears to decrease toward the cylinder edges, due to high viewing angle and dropping emissivity there. Since infrared measurements are often performed with dielectric materials at low θ values and because of the limited wavelength band captured by camera detectors, the emissivity of viewed surface is often assumed to be a constant. Being necessary to work at high θ’s, a careful calibration for ε as a function of θ must be performed and viewing angles have to be very well known.

The core of the IR camera system is the radiation detector. Detector technologies are mainly separated into two classes: thermal detectors, which are sensitive to the incident energy flux and quantum detectors, whose sensitivity depends on photon absorption.

A currently common type of thermal detector is the uncooled microbolometer, made of metal compound or semiconductor material. The microbolometer typically has a lower cost and broadband IR spectral response but is less sensitive and quite slower (response time in the milliseconds domain) than quantum detectors. The latter ones are made from materials such as InSb, HgCdTe (MCT), and layered GaAs/AlGaAs for QWIP (Quantum Well Infrared Photon) detector. Quantum detectors have a low response time (microseconds domain) and higher sensitivity than thermal ones but their strong cooling is still required. In actual cameras, miniature Stirling coolers easily achieve temperatures around 70 K.

In Fig. 3, the spectral responses of some of most sensitive, largely used, cooled and uncooled infrared detectors and their relative detectivity are indicated. The response curves are shown in terms of D* (detectivity star) for a specific exposure time, as a function of the spectral wavelength. D* is the sensitivity figure of merit of the infrared detector detectivity, so that higher D*s indicate better performance. Modern quantum detectors and QWIP tend to approach the ideal (top curves) detector behavior.

Nowadays, non-cooled microbolometers are typically employed in both MWIR and LWIR spectral bands. Instead, because of their, respectively, higher D*s (see Fig. 3), quantum detectors usually utilize InSb in MWIR band and HgCdTe, or QWIP, in LWIR band.

To carry out IR thermography, the choice of the most appropriate working spectral band (MWIR, or LWIR) depends on several factors often linked to object surface nature and to atmospheric absorption. Cameras in LWIR band, because of their band low atmospheric absorption (except for very high water vapor content) and high thermal contrast, generally allow for high accuracy measurements; in particular they are able to take data also in the presence of air plasma that typically does not emit in 8–12 μm band (Cardone 2007). However, frequently MWIR cameras are preferred because of their lower cost detectors and optics, higher detectivity D* for quantum detectors and since some surfaces have higher emissivity coefficients in the middle infrared band. It has to be noted that, for temperatures higher than about 10°C, temperature sensitivity is generally better for MWIR than for LWIR quantum detectors. Should high sensitivity and very short response time not be required, the best and cheapest actual choice is a camera with non-cooled microbolometers.

The standard instantaneous output of each thermal image is generally constituted by a matrix of data from 100 k up to 1 M elements. Therefore, as already stated, a digital data processing is compulsory, which is easy to perform because practically all cameras have a digital output. Temperature range that can be usually measured spans from −20 up to +1,500°C, but it can be further extended to higher values by filtering the oncoming radiation. Typically, MWIR cameras use silicon optics, while LWIR ones germanium optics. Most of the available IR cameras offer also telescopes, expander lenses and supplementary close-up microscope lenses, i.e., the possibility of changing their optics, so as to adapt working distances to the scene one is looking at.

The performance of an infrared camera is conventionally evaluated in terms of thermal sensitivity, scan speed, image resolution and intensity resolution.

Thermal sensitivity is generally defined in terms of (mean) noise equivalent temperature difference (NETD), which is the time standard deviation averaged over all pixels of a blackbody scene and is expressed in terms of mK. Some modern FPA systems are able to detect temperature differences of less than 20 mK at ambient temperature.

The scan speed represents the rate at which a complete image (frame) is updated and is expressed in terms of frame rate (Hz). FPA systems of the last generation are characterized by high standard frame rates (often greater than 100 Hz) and reducing the number of acquired pixels (i.e., by windowing the frame) and their integration time (i.e., detector sensitivity), frame rates can currently go up to several ten thousands of Hz.

The image resolution, which is the capability of a system to measure surface temperature of small objects, is usually defined as instantaneous field of view (IFOV), which is expressed in terms of mrad; theoretically, IFOV is the ratio of detector pixel width over lens focal length. However, this is only an ideal design parameter and does not fully describe the performance of the actual system. In fact, when a lens of reduced total field of view (FOV) is used, IFOV decreases, but the number of IFOVs in the frame remains the same. Then, the number of IFOVs (pixels) that describes the complete FOV gives a better description of the image resolution. Modern systems are able to produce images composed of up to several hundred thousands of pixels at standard frame rates. More rigorously, the spatial resolution of the IR camera may be defined in terms of the Modulation Transfer Function (MTF_IR), which is the mathematical description of the detected signal modulation (also due to the pixel finiteness) as a function of the spatial frequency. This point is further addressed in Sect. 5.2.

The intensity resolution, or dynamic range, is expressed in terms of the number of digital intensity levels the thermal image is composed of. The latest generation of cameras provides typically 14-bit A/D conversion, which allows measuring small temperature differences even in the presence of a large temperature range in the viewed scene.

The energy actually detected by an IR system depends not only on the emissivity coefficient of the surface under measurement but also on environmental conditions. In fact, the total radiation I′ detected by the camera can be written as:where τ _r is the transmissivity of the atmosphere between the surface and the camera, I _obj ^b is the radiation intensity corresponding to a black body at the object temperature T _obj, I _amb ^b is the black body radiation intensity corresponding to the (effective) temperature of the object surroundings T _amb, called the reflected ambient (or background) temperature and I _atm ^b is the radiation intensity corresponding to a black body at the temperature of the atmosphere T _atm.. In Eq. (8), the term τ _r εI _obj ^b is the emission from the surface captured by the radiometer, τ _r (1 − ε) I _amb ^b is the reflected emission from ambient sources, and (1 − ε) is the surface reflectivity (T _amb is assumed constant for all emitting surfaces of the half sphere seen from the object surface). The term (1 − τ _r ) I _atm ^b is the emission from the atmosphere, with (1 − τ _r ) being the atmosphere emissivity. For the sake of simplicity in the Eq. (8), the dependence from T and wavelength is not indicated.

Generally, the transmissivity of the atmosphere τ _r is assumed to be equal to unity, which simplifies Eq. (8). Thus, using Eqs. (2) and (8), a semi-empirical adaptation of Planck’s law with the parameters R, B, and F can be found. The typical calibration function of an IR camera can be put in the form:where U _D is the detected signal, R is a function of integration time and wavelength, B is a function of wavelength alone, and F is a positive value very close to 1. If the object used for calibration is a black body, the calibration constants R, B, and F, besides taking into account the sensed wavelength band and the radiation constants, consider only emission and absorption from atmosphere.

A simpler way to perform the calibration, which does not take in account T _amb variations, is the in situ calibration proposed by Sargent et al. (1998), which practically neglects the second term of the second member of Eq. (9).

Needless to say that, if a window exists in the optical path between test section and IR camera (as may happen in wind tunnel measurements, e.g., see Fig. 11), the constants of Eq. (9) depend also on the transmissivity through such a window.

Errors due to sensor are mainly associated with radiation that it emits toward ambient, tangential conduction within the sensor itself and losses from its back surface, as illustrated in Fig. 4. When standard techniques are used to measure wall temperature, it is possible to have a very low surface emissivity coefficient (e.g., by gold plating the sensor surface) so as to neglect the radiative heat flux to ambient. Obviously, because of what is stated in Sect. 2, this cannot be the case when using an IR camera, since surface emissivity should be high.

Radiative heat flux is computed with the so-called radiosity law which derives from Eq. (4):where ε _t is the front surface total hemispherical emissivity coefficient; T _w and T _amb are the temperature of the sensor surface and of the experimental ambient, respectively.

For the heated-thin-foil sensor and isotropic foils, by retaining the assumption that sensor is thermally thin (i.e. isothermal at temperature T _w across its thickness s) and ideal, it is possible to evaluate the equivalent tangential conduction heat flux Q _k per unit sensor area by means of Fourier’s law:Therefore, to extend the heated-thin-foil sensor to the multi-dimensional case, one must include in the no longer one-dimensional energy balance this contribution as well.

It is important to remark that infrared thermography (intrinsically two-dimensional) allows, in principle, to directly evaluate the Laplacian of Eq. (12) by numerical computation. However, since in the evaluation second derivatives are involved, this can be accomplished only after filtering the camera signal, typically affected by noise (Astarita and Cardone 2000).

As already mentioned, in many applications of the heated-thin-foil sensor, a spatially constant Joule heating can be obtained by using a printed circuit board (Fénot et al. 2008). The printed circuit is generally manufactured with several adjacent thin (down to 5 μm) copper tracks, closely spaced, arranged in a Greek fret mode (see Fig. 5) and bound to a fiberglass substrate. However, due to the high conductivity coefficient of copper, the board exhibits an anisotropic thermal conductance behavior (along, or across, the tracks) so that it is not correct to evaluate Q _k by means of (12).

By still retaining the assumption that T _w is independent of coordinate z normal to the board, it is, therefore, necessary to generalize Eq. (12) to take into account this effect:where Λ is the thermal conductivity tensor. To simplify Eq. (13) and by neglecting the top and bottom edges of the board, it is feasible to roughly separate the effect due to copper tracks from that of fiberglass support. In particular, by choosing a Cartesian coordinate system with its axes directed along the two principal axes x and y of Λ (see Fig. 5), one may split the effects into two directions, normal to tracks x and parallel to them y. This problem is addressed by Astarita and Cardone (2000).

Also for both thin-skin and thin-film sensors, the temperature within the sensor was supposed to be one-dimensional. Under the assumption that the sensor material is isotropic, or (as already done before) by choosing a Cartesian coordinate system with its axes directed as the two principal axes of the thermal conductivity tensor, it is possible to split conduction effects along the two tangential directions. Therefore, since the extension to any arbitrary convective heat flux is straightforward, for the sake of ease, in the following it is assumed that convective heat flux harmonically varies only along one direction parallel to the sensor surface x, that is:where Q _h is the heat flux amplitude and ξ = 2π/L the wave number (L being the wavelength).

To correct measured temperatures so as to take into account tangential conduction effects, it is convenient to use the ratio between the temperature amplitudes with and without tangential conduction Temperature Amplitude Transfer Function (F), which, according to De Luca and Cardone (1991), is reported in Fig. 6, for the two sensors as a function of a modified Fourier number Fo _ξ = ξ ² /αt, where α is the thermal diffusivity coefficient of sensor material.

The amplitude of each harmonic component of the measured temperature may be thus corrected and the corresponding harmonic component of the heat flux can be evaluated by using the classical one-dimensional formulae. A direct comparison between the two sensors has practically no meaning because they are basically realized with materials having different thermal conductivities (high for thin-skin and low for thin-film). Nonetheless, it has to be noted that, for the thin-skin sensor, the tangential conduction correction can be directly computed as in the case of the heated-thin-foil with Eq. (12), as a function of time.

If back surface is diabatic as indicated in Fig. 4, data reduction has to be performed by subtracting to Q _j also the total heat flux from sensor to external ambient Q _a, via the back surface. Typically, this heat flux results to be the sum of radiative and natural convection heat fluxes. Radiative heat flux can again be computed by means of radiosity law (11), while convective heat flux to external ambient may be evaluated by using standard correlations tables. However, to carefully evaluate Q _a, it is much better to perform some ad hoc tests with thermally insulated front surface and which include the radiative contribution as well (Astarita and Cardone 2000).

The relation between the original thermal object o(x, y) and the recorded degraded image r(x, y) is given by the two-dimensional point spread function PSF(x, y), where x and y are the spatial coordinates. Function PSF describes the response of the measuring process to a point source (or point object). A general expression for r(x, y) is:where ⊗ is the convolution operator and n(x, y) indicates an additional noise term. If it is assumed that the main subsystems of the whole measurement process, thermal sensor and IR camera (which includes optics, detector and electronics) are shift invariant, PSF may be expressed as:where h _TS(x, y) is the impulse response of thermal sensor and h _IR(x, y), the one of IR camera. After Fourier transform, the convolution product of Eq. (15), in the frequency domain ζ _x , ζ _y , reduces to an ordinary product:where STF is the System Transfer Function, which expresses the overall degradation.

In the presence of imaging degradations only, STF coincides with the Optical Transfer Function, which normalized magnitude (with unit value at zero frequency) is generally defined as the Modulation Transfer Function (MTF_IR) of the camera. A discussion on the MTF_IR of IR scanning systems is reported by de Luca and Cardone (1991) and of modern FPA systems by Boreman (2001). Instead, in the most general case, under the assumption that the different modulation processes are cascaded, the product of the various transfer function yields the STF. E. g., for thin-film and thin-skin (see Sect. 5.1) the STF is equal to MTF_IR × F.

It has to be recalled that, for the heated-thin-foil and thin-skin sensors, the sensor modulation (heat flux losses due to tangential conduction and radiation) may be directly appraised as already indicated (see Sect. 5.1). It is important to point out that MTF_IR of an IR camera is a property of the entire system. In fact, all components (lens assembly, FPA, A/D converter, cabling, etc.) contribute to the final MTF_IR of the system. Assuming that all subsystem are cascaded, the system MTF_IR is given by: MTF_IR = MTF_Optics · MTF_FPA · MTF_Electronics.

In Fig. 7, the measured MTF_IR of an IR camera, based on 1,024 × 1,024 square pixels MWIR QWIP (Gunapala et al. 2005), is shown as a function of the spatial frequency ξ normalized with respect to Nyquist frequency ξ _N (1/2 pixel pitch). The MTF_Optics of the spot scanner optics at ξ _N is 0.2, thus the MTF_FPA at Nyquist frequency should be around 30 and 45% along horizontal and vertical direction, respectively. The MTF_IR difference along horizontal and vertical directions is also present in the differently shaped PSFs (not shown herein). Since MTF_Optics data do not show a large variation between horizontal and vertical directions, the difference is most probably due to the electronic readout integrated circuit.

From Eq. (17), the degraded image can be restored with a restoration (inverse) filter W(ξ _x , ξ _y ), which is the reciprocal of STF, yielding the restored image \( \tilde{o}\left( {x,y} \right) \):where F ⁻¹ indicates the inverse Fourier transform. Restoration with the inverse filter W(ξ _x , ξ _y ) results in unlimited amplification of the response when modulation approach zero. This undesired amplification can be prevented by stopping the restoration process just before the noise frequencies or using the Wiener filter W _w(ξ _x , ξ _y ) according to Jain (1989):where STF*(ξ _x, ξ _y) is the complex conjugate of the STF and \( \Upphi_{\text{noise}} \) and \( \Upphi_{\text{image}} \) are the power spectral densities of noise and image, respectively. The additional ratio \( \Upphi_{\text{noise}} /\Upphi_{\text{image}} \) (image signal to noise ratio) attenuates high noise components. The Wiener filter becomes the exact inverse filter for noise-free images.

An example of image restoration for the thin-skin sensor is presented by Bougeard (2007) who studies the local heat transfer on a plate fin which had two-tube rows normal to it. Heat transfer measurements are corrected for radiation and tangential conduction effects. The fin is warmed up to 42°C and then cooled down by airflow with a fixed entrance temperature of 22°C. The IR camera records temperature variations during a 6.5-s duration (about one hundred thermal images). In order to reduce noise, Bougeard computes the integral (between initial and final time of test) of the terms which are present for the thin-film sensor and evaluates the tangential conduction with Eq. (12).

By indicating with e _tot, the integral term corresponding to the total internal energy per unit area lost by the fin (J/m²), e _cond the integral of the conductive term, e _rad the integral of the radiative term, and i _temp the term corresponding to the integration of the difference of fin temperature and T _ref (Ks), the local convective heat transfer coefficient can be computed from the ratio:

Moreover, a specific digital image restoration technique is developed to enhance the camera spatial resolution. The restoration technique uses a two-dimensional Wiener filter (Bougeard et al. 1994). The e _tot image (Fig. 8a) shows the fin energy density lost during the experiment. High values are found at the fin leading edge because of the developing boundary layer and in front and around of the second tube row which are due to the horseshoe vortex presence. The e _cond image (Fig. 8b) reveals high heat transfer by conduction around the tubes because of high spatial temperature variations due to the vortex structures. On the fin’s remaining part, the conduction is quite small, isolated sharp variations being due to the presence of noise in infrared images. The e _rad image (Fig. 8c) shows that radiation heat transfer is fairly low (temperatures are relatively low), representing only a few percent of the total energy exchange, and is predominant downstream of the tubes, where convection is low. The convective heat transfer coefficient distribution (Fig. 8e), computed according to (20), shows that: the first row of tubes has a very small horseshoe vortex effect; a heat transfer increase is found at the fin leading edge; the staggering disposition of tubes decreases the wake size behind their first row.

As an example of image restoration for the IR system modulation applied to the thin-film sensor (de Luca et al. 1990a, b), Fig. 9a shows the coarse footprints (T in °C) of Goertler vortices on a solid 15° RTV™ elastomer ramp as recorded by the camera. The ramp is placed downstream of a delta wing in hypersonic flow at M = 8.15 (with fluid moving from thermogram bottom upwards) and vortices are barely evident by the periodic horizontal variation of wall temperature. Even if the IR used interlaced camera (AGEMA 880LW) with extension rings had a limited spatial resolution (140 × 140 pixels), the restored image of Fig. 9b allows detecting the rather regular vortices structure which shows a mean pitch of about 2 mm. Horizontal striping is due to camera interlacing and transient heating.

The heated-thin-foil technique for analyzing transient natural convection on a vertical plate is described by Carlomagno and de Luca (1989). A vertical stainless steel foil (245 mm high, 960 mm wide, 40 μm thick), coated on the viewed side with a thin layer of high emissivity (ε = 0.95) paint, is electrically step heated (Q _j  = 0–80 to 270 W/m²). By measuring the apparent temperatures on both foil sides, the uncoated side emissivity is evaluated. In fact, for the tested conditions, the radiative heat flux is of the same order of magnitude of the convective one and therefore, it must be definitely subtracted from the Joule heat input.

For a step Joule power input 0–130.5 W/m², the time evolution of the foil temperature vertical profile is shown in the pseudo-thermogram of Fig. 10 where abscissa is time (for a total of 80 s), ordinate is position along the foil central vertical segment (0–245 mm) and colors represent temperatures (21–42°C). The thermogram’s, left region, characterized by a sequence of colored vertical bands, points out an initial uniform time increasing of foil temperature which indicates a prevalent conductive heat transfer regime between foil and ambient air. Temperature evolution agrees well with theoretical calculation. The temperature variation, which later occurs in the vertical direction reveals the progressive onset of the natural convection flow. When steady state is reached, measured data agree within ±5% with the theoretical prediction of Sparrow and Gregg (1956) for laminar flow.

High-pressure ratio and high temperature rise are required to improve the performance of modern gas turbines and impose strong challenges on combustor and initial turbine stages design. The combustor and the blades’ leading edge are largely cooled by effusion (film) cooling that maintains adequate metal temperatures. This is achieved by injecting through a large number of holes cold air which produces a shielding film on the hot side surface. The performance of such a method is measured by the surface adiabatic film cooling effectiveness η, which in the most general case is defined as:where T _w is the measured surface temperature, T _aw∞ is the free-stream adiabatic wall temperature, and T _oc is the coolant stagnation temperature.

One of the first test rig to measure η by means of IR thermography is presented by Leger et al. (1996). The test facility (Fig. 11) has a multi-hole cooling set up on a flat plate simulating the combustion chamber wall. The plate is subjected on one side to hot gases resulting from combustion (débit chaud) and on the other side to the cooling airflow (débit froid). The CaF₂ infrared window (hublot IR) for the MWIR band is also visible. Calibration has to also take into account the presence of the IR window.

A recent study by Dhungel et al. (2009) deals with the film cooling performance of a flat plate with a row of simple holes and with the same holes, either complemented with two smaller symmetrical anti-vortex holes, which branch out from the main hole, or shaped at their exit. The proposed anti-vortex design requires only easily machinable round holes, unlike shaped holes, and is intended to counteract the detrimental vorticity associated with standard circular cross-section holes. Experiments are performed at four different coolant-to-mainstream blowing ratios BR from 0.5 to 2 by using the transient thin-film sensor.

The baseline test plate has six holes (d = 12.7 mm) in each row, inclined at 30° along the flow direction, hole spacing between adjacent holes being three-hole diameters. The anti-vortex holes are branching out of the main holes which have the same orientations and geometry as the baseline. Only the features of the anti-vortex holes are altered in six different geometries, some of their aspects being evident in the η maps of Fig. 12. The shaped (diffuser exit) holes still have an inclination angle of 30°; the length of the cylindrical inlet portion twice the diameter of the hole and a compound angle of 15°.

For the baseline case, the jet streaks are barely visible at high BR where flow separation due to jet liftoff appears to occur, the highest effectiveness taking place when the jet has the lowest momentum flow rate, i.e. at BR = 0.5. Case 1 has the anti-vortex holes with their exit located upstream of the main hole and 1/4 the diameter of this one. The trend is similar to the baseline case except for the overall higher η. The anti-vortex pair causes reduced flow through the main hole and also supplements the film coverage in the region between main holes.

For Case 2, the anti-vortex holes are 1/2 the diameter of the main holes and their entry is halfway into the main hole. The best film cooling effectiveness occurs for BR = 1. The two holes from the adjacent anti-vortex pairs interact and produce another jet streak similar to the main holes. Downstream, the various streaks coalesce producing a quasi-uniform spanwise effectiveness distribution. However, as the blowing ratio increases, the effectiveness downstream gets worse. In Case 3, the anti-vortex holes have the same exit location and diameter as in case 2 but branch out from the base of the main holes so as to produce a more developed coolant flow. High film cooling effectiveness can be seen even for higher blowing ratios. The spanwise and downstream coverage increases with blowing ratio, the only drawback being that the region adjacent to the main holes remains uncooled.

Case 4 is similar to Case 3 except that the exit of anti-vortex holes is somehow more downstream than for Case 3. The result looks similar to that of Case 3, with a good attachment of the film even at higher blowing ratios. The additional length to the anti-vortex holes does not provide significant benefit even if there are some minor differences between Cases 3 and 4. Case 5 has the exit of anti-vortex holes at the same streamwise location of Case 3 but closer to the main holes. For all blowing ratios, the jets from the anti-vortex holes mix with those from the main holes, thus creating a thicker coolant streak footprint than in the other cases. However, the effectiveness distribution has not the lateral spread of Cases 3 and 4 and appears to peak at BR = 1.5 with similar levels at BR = 2.0.

The anti-vortex holes coming laterally outward from the base of the main holes, for Case 6, have their exit at the same spanwise position of Cases 2–4 but much more upstream. At higher blowing ratios, the jets seem to clearly liftoff, but their presence causes a momentum decrease in the jet from the main hole, thus restricting the liftoff even at BR = 1.5. This causes a slightly better effectiveness than baseline but does not contribute to significant effects, such as those seen for Cases 2–4.

For shaped holes, the effectiveness distributions for blowing ratios of 1 and 1.5 indicate good lateral and downstream coverage. The larger exit area of these holes reduces the exit velocity of the coolant jet and hence the film remains adhered to the plate surface. However, for the highest blowing ratio, the coolant jet has greater momentum to liftoff, producing lower effectiveness than for BR = 1.5. At high blowing ratios, a classical separation, resulting in skewed effectiveness profiles inside the diffuser, exists especially on the right side.

Impinging jets receive great attention from both industrial and academic points of view. Industrial interest is justified by the many applications such as to dissipate heat in electronic circuits, achieve high heat transfer coefficients at the leading edge of turbine blades, dry textiles, temper glass and heat zones which are critical for ice formation over aircrafts. Research attention derives from the complex fluid flow occurring in impinging jets.

With regard to IR measurement for a round impinging jet, the works by Meola et al. (1995, 1996, 2004), who report measurements of adiabatic wall temperature T _aw and of heat transfer coefficients performed with the heated-thin-foil sensor, must be mentioned. The sensor (impingement plate) consists of a thin constantan foil (200 mm wide, 470 mm long, and 50 μm thick), Joule heated and held flat by a stiffening fixture. Truncated cone nozzles are adopted with several exit diameters d and nozzle-to-plate distances z. The jet Mach number M ranges from 0.04 to 0.91 and the Reynolds number Re = Vd/ν from 10,000 to 173,000, both based on the nozzle exit velocity V. Total jet temperature is kept equal to the ambient one.

Meola et al. (1995), through measurements of adiabatic wall temperature T _aw (not heated foil), observe instability developing for high M values, such phenomena also depending strongly on the impingement distance. For z/d < 6, as M increases, the vortex ring, which is located in the shear layer at r ≈ 1.2d (r is the radial coordinate), strengthens up and breaks (Widnall instability) entailing entrainment of warmer ambient air and giving rise to the formation of structures. Snapshots of the T _aw map (d = 5 mm, z/d = 4) at different Mach number values are shown in Fig. 13, where several thermograms are reported. For M = 0.3 (Fig. 13a), the minimum T _aw at r ≈ 1.2d has the shape of a completely developed and stable annulus. This annulus, which is the location of the vortex ring, for M = 0.4 is transformed into an unstable semicircle. As M increases, the vortex ring reinforces and, for M = 0.71 (Fig. 13d), breaks up in the impact with the plate, entraining warmer ambient air and giving rise to secondary minima at about 0.9 and 2.2d, with a maximum between them at about 1.6d. As M further increases, such structures become stronger and reach their highest magnitude for M = 0.85 (Fig. 13e). As M further increases, the structures break up into numerous smaller structures, which tend to coalesce giving rise to a transient alternate circumferential movement.

The recovery factor is defined as r _f  = (T _aw − T _j )/(T _oj  − T _j ), where T _oj and T _j are the initial jet total and static temperatures, respectively. Carlomagno and de Luca (1989) report tests performed with T _oj equal to ambient temperature and Fig. 14 shows the relief map of the recovery factor r _f , corresponding to d = 10 mm, z/d = 8, Re = 130,000 and M = 0.52. The recovery factor has a peak value on the jet axis and a local minimum in the annular region at r/d ≈ 1, which is attributed to the vortex ring in the shear layer surrounding the jet. A local r _f maximum is located at r/d ≈ 1.8 which is followed by another minimum at r/d ≈ 3.8. For further r/d increasing, the recovery factor attains a unity value.

The relief map of the Nusselt number, for d = 10 mm, M = 0.11, Re = 28,000 and a much lower distance z/d = 2, is represented in Fig. 15. When the jet flow impinges on a wall relatively close to the nozzle exit, moving along the radial direction two local minima and two local maxima values are found. The minima are located one at the jet axis and the other one at r/d ≈ 1.5 (practically where also the minimum of r _f is placed). Instead, the inner maximum is positioned at r/d ≈ 0.5 and the outer one at r/d ≈ 2.5. This behavior confirms results documented in the literature.

An example of multi-jet impingement is described by Fénot et al. (2008), who report experimental measurements of heat transfer due to a row of hot air jets impinging on a concave semi-cylindrical surface performed by using a printed circuit board to implement the heated-thin-foil technique. They state that the effects of tangential conduction through the board are small. The influence of high relative curvature (d/D = 0.1–0.2) is investigated by changing jet tube diameter d, the impinging surface diameter D remaining constant. Reynolds number based on d and jet exit velocity, injection temperature, jet-to-jet spacing P and impingement distance z are also made to vary. Nusselt number is based on jet tube diameter d.

Typical effectiveness defined as η = (T _aw − T _amb)/(T _j  − T _amb), where T _amb and T _j are ambient and jet temperature, respectively, together with Nusselt number Nu maps are presented in Fig. 16. The small circular zones without results (mainly visible in the (map) are zones covered with reflective adhesive used as spatial references. Spanwise periodicity and symmetry look satisfactory. The curvature produces a confinement of the jet flow that gives high η values at the impinging point so adiabatic wall temperature T _aw is nearly equal to injection temperature.

The Nusselt number map around impinging points has an eight-form and, going along the s direction, Nu shows a local minimum at the impinging point, then attains a maximum at s/d = 0.4 and afterward decreases. The maximum location roughly corresponds to the half-width of the jet potential core. Going along the Y direction, at the impinging point Nu has a maximum, then weakly decreases and finally shows a small local maximum halfway between two adjacent jets.

Another example of multi-jet impinging is presented by Roger (2007) who describes a periodic transient technique for high-resolution heat transfer measurement. In contrast to other measurement techniques, this one requires neither homogenous heating nor quantitative measurement of surface or fluid temperatures. The heat transfer coefficient is determined by periodically heating the sensor and evaluating the phase shift between the heat flux penetrating the sensor surface and the resulting temperature response. The technique is applied to a hemispherical solar receiver window, with a 5-mm thick fused silica sensor, a radius of 0.31 m and multiple air jets cooling the concave surface.

The convective heat transfer coefficient map with a six-nozzle (d = 8 mm) symmetric window-cooling configuration is shown in Fig. 17. The bottom window edge is assigned a zero h value because no measurements are possible there. Since IR camera has a limited field of view and measurements are periodic, the map of Fig. 17 is composed of six identical 60° slices. High heat transfer coefficients are observed where jets impinge with a kind of Coanda effect on the wall, while, between the jets, the heat transfer is much lower. At the window top, a stagnation point causes only fair heat transfer.

The knowledge of the temperature distribution over an aerodynamic body is of great interest because of the contained information which can be related to heat transfer and skin friction at the wall through Reynolds analogy and to detect transition, separation and reattachment zones.

de Luca et al. (1990b) study the flow field over a Göttingen 797 airfoil (with a 180 mm chord) at several angles of attack. The wing model is made of a glass–epoxy skin (≈ 3 mm thick) over polyurethane foam. In order to perform measurements by means of the heated-thin-foil sensor, the wing leeside is coated with a Joule heated thin (30 μm) stainless-steel foil, 155 mm wide, which starts 13 mm away from the leading edge and is coated with a very thin layer of thermally black paint (ε = 0.95). Tests are carried out in a Göttingen type closed-return tunnel with circular open test section 1.1 m in diameter. Results are reduced in non-dimensional form in terms of the Stanton number St defined in the conventional way.

The chordwise St profiles at leeside for chord based Reynolds number Re = 259,000 and different angles of attack α (in the range −12° to 20°) are shown in Fig. 18. The beginning of the plateau may be assumed to coincide with the point of laminar separation and its end with the beginning of transition in the separated shear layer. As α increases the minimum St value moves upstream following the movement of the laminar separation point deriving from the adverse pressure gradient on the airfoil leeside. At the highest α value, the plateau disappears from the measured zone. Data are slightly affected by tangential conduction in the model wall and by the modulation transfer function of the IR scanner that, as stated by the authors, has a limited spatial resolution. They were both not corrected at the time.

Ricci and Montelpare (2005) carry out similar tests on the laminar bubble occurrence by also using the heated-thin-foil sensor. The laminar bubble is a local boundary layer separation phenomenon that mainly exists at low Reynolds numbers. Three characteristic points of the bubble are searched for: the laminar separation point, the transition point and the turbulent reattachment point. The laminar bubble behavior is tested for an RR3823HL airfoil at Reynolds number based on the airfoil chord equal to 200,000.

In order to individuate the searched points in a simple and objective way, results are presented in terms of a modified Stanton number. In fact, to enhance with greater detail the Stanton number variations along the chord, instead of computing St with the free stream speed V _∞, the authors calculate its values with the inviscid speed V _i (s), i.e., the speed the flow attains outside the boundary layer along the curvilinear chordwise abscissa s. V _i (s) is evaluated with the inviscid solution of Xfoil code, the choice deriving from the fact that the computed speed is independent of the code used. Once measured the St profile along the chord (see Fig. 19), the laminar separation point is localized as the flex point that comes before the absolute minimum. In fact, since the laminar separation represents a fluid dynamic singularity, this also reflects in a singularity for the thermal heat exchange. The boundary layer transition point is localized at the absolute minimum St value because it corresponds to the point of maximum bubble height, where the convective heat transfer coefficient reaches its lowest value. The turbulent reattachment point location is similarly individuated by the maximum heat transfer coefficient because the flow behaves there like an impinging jet. The upper part of Fig. 19 shows the recorded thermogram of the airfoil (blue: low temperature, high heat transfer; red: high temperature, low heat transfer).

Zuccher and Saric (2008) perform a qualitative study on the boundary-layer transition in supersonic flows by testing several models (having an initial temperature difference with respect to the oncoming flow) of swept wings in a blow-down facility at Mach number 2.4. They observe effects of wing sweep and other parameters such as angle of attack, leading edge contour and presence/absence of surface roughness. The IR technique is revealed to be very effective for flows sensitive to surface roughness, such as transitional boundary layers, since it does not require interaction with the model or the flow and because it can be applied also by researchers not very familiar with IR thermography and heat transfer.

Figure 20 shows a typical IR image acquired for a swept angle equal to 20°, α = 0°, M = 2.4 and Re _u = 31.2 × 10⁶/m. Since the external flow is at a lower temperature than the model and the (downstream) laminar boundary layer has a low heat transfer coefficient, the laminar region appears warmer (about 12°C) than the turbulent one (about 8°C). The transition front is visible at about 50 mm from the leading edge, i.e. ~8.5% of the chord but is not uniform because of the presence of turbulent wedges, originating from very small disturbances on the leading edge, which move when the model is polished. A reflected wave is also visible in the upper-right portion of the image, together with an anticipated transition region. The authors claim that the leading edge is much colder (even if a narrow warmer strip appears at its periphery) than the rest of the model not because of turbulent flow, but because of its very low thermal inertia which lets it reach the external lower temperature much faster than the rest of the model. They seem to overlook the fact that, in laminar flow, the Stanton number tends to peak up moving toward the wing leading edge (as shown e.g. in Figs. 18 and 19), nor do they mention the adiabatic wall temperature variation between laminar and turbulent flow, which, for high Mach number such as the one they are testing at, is very relevant (see Sect. 4).

As already affirmed in Sect. 6.2, to improve the performance of modern gas turbines, high temperatures are required. Often, to cool blade surface, air from the compressor goes through the hub section into the blade interior and, after flowing through serpentine passages, is discharged into the external gas. These passages are mostly made of several adjacent straight ducts, spanwise aligned along the blade and connected by 180° turns. The turns cause flow separation and reattachment and induce secondary flows so that the convective heat transfer coefficient exhibits high local variations with consequent increased wall thermal stresses.

With the heated-thin-foil sensor, Astarita and Cardone (2000) obtain local heat transfer measurements on a 180° sharp turn of a square smooth channel. Reynolds number Re is based on hydraulic diameter (D = 80 mm). Heat transfer coefficients are presented in terms of the normalized local Nusselt number Nu/Nu*, where Nu* is the Nusselt number as predicted by Dittus and Böelter correlation for channel flows.

The Nu/Nu* distribution is presented in Fig. 21 for Reynolds number Re = 30,000. Data is corrected for radiation, tangential conduction and natural convection at the sensor backside, which is the viewed surface. Flow enters the duct from the left channel (inlet) and exits from the right one (outlet). At the inlet channel, the flow is fully developed so the heat transfer coefficient is about that predicted by Dittus and Böelter correlation. The flow field in the turn region, and downstream of it, is highly three-dimensional and the normalized Nu map shows zones with a relatively low heat transfer coefficient, corresponding to recirculation bubbles, as well as zones with high heat transfer coefficient, which are due to flow reattachment and/or an increase in the flow mean turbulent level. A first recirculation bubble is located just before the first outer corner and attached to the external wall. Two other regions with relatively low heat transfer coefficient may be noticed, the first nearby the partition wall tip and the second by the end wall by the outlet channel axis. Three high heat transfer zones are also observed: the first placed near the end wall; the second downward of the second outer corner and extending for about 3 diameters; the third about 2 diameters after the second inner corner and attached to the partition wall. They are due to the jet effect of the flow through the bend.

Rib turbulators attached to the heat exchanging walls enhance convective heat transfer and completely modify the channel flow field as well as the local heat transfer coefficient distribution.

For the channel described earlier with angled rib turbulators, Astarita et al. (2002a) and Astarita and Cardone (2003) present detailed quantitative maps of the heat transfer distribution again obtained with the heated-thin-foil sensor. The aluminum ribs have a square side (e = 8 mm), are placed on the two opposite walls, at an angle of 60° with respect to the duct axis and at a pitch P = 80 mm. Data are corrected for radiation, tangential conduction and natural convection at the sensor back side.

The two-dimensional map of the local normalized Nusselt number Nu/Nu* is shown in Fig. 22 for Re = 30,000. Ribs are clearly visible due to the higher heat transfer rate occurring over them. The low Nu value spots on the last rib of the inlet duct and on the first rib of the outlet duct, near the partition wall, are due to a partial detachment of the ribs glued to the wall, owing to high local thermal stresses difficult to avoid. The authors believe that this has little influence on the local nearby measurements, but it has to be highlighted that it is easily revealed by IR thermography. Before the turn, the thermal pattern in the inlet duct appears to be recurring (a kind of thermally fully developed flow) except for some edge effects at the duct entrance and exit, due to the quite strong tangential conduction owing to dissimilar nearby zones there. The map also shows that the sharp turn presence already induces a slight modification of the shape of the contour lines before the inlet duct last rib.

In the inlet duct, the reattachment downstream of the ribs can be identified as the locus of the normalized Nusselt number local maxima when moving streamwise. The reattachment distance increase going toward the sidewall is due to the interaction of the main flow with the secondary one. The separation zone after each rib is strongly influenced by the secondary flow impingement toward the partition wall. Instead, the separation zone ahead of each rib remains well visible and it is not much influenced by the secondary flow, its width remaining practically constant along the ribs.

The heated-thin-foil sensor to determine local heat transfer distributions is used also by Gupta et al. (2008) in a double wall ribbed square channel for several configurations and by varying the pitch to rib height ratio (P/e) and the rib height to hydraulic diameter ratio (e/D). Reynolds number based on D ranges from 10,000 to 30,000. Results are again presented in terms of normalized Nusselt number Nu/Nu*.

For P/e = 10, local profiles of Nu/Nu* for the 60° V-broken rib configuration in the streamwise direction are presented in Fig. 23a. The corresponding Nu/Nu* maps are shown in Fig. 23b, where some asymmetries appear. Spanwise variations are high indicating that the presence of ribs distorts a lot the thermo-fluid-dynamic field. Lobes of heat transfer enhancements along the streamwise direction are ascribed to the secondary flow developed in the channel due to the rib shape. The generated vortices strongly mix the flow and hence heat transfer rates from the surface are enhanced.

Blades rotation changes the channel fluid dynamic behavior because there is an interaction between the Coriolis forces, pressure gradients causing main flow and centrifugal forces. For a radially outward flow, the Coriolis force produces a secondary flow (i.e., a symmetric pair of secondary vortices) in the plane normal to main flow direction which pushes the particles in the channel center toward the trailing (that follows) wall, then the flow continues along the sidewalls and finally gets to the leading (that goes ahead) wall. When the flow is reversed, i.e. for a radially inward flow, one has to change the role played by the leading wall with that of the trailing one and vice versa.

One of the first attempts to measure convective heat transfer coefficients h in a rotating air channel with IR thermography is performed by Cardone et al. (1998). The apparatus concept is a direct consequence of the used heated-thin-foil sensor. Since the foil back surface (to be viewed by the IR camera) cannot be thermally insulated, to avoid here high thermal losses by forced convection, the channel rotates in a vacuum tank (below 100 Pa).

Also Gallo et al. (2007) measure h maps nearby a 180° sharp turn of a rotating channel with the heated-thin-foil sensor. Their experimental apparatus (Fig. 24) consists of a Plexiglas two-pass water channel with a sharp 180° turn, mounted on a revolving platform whose rotational speed can be continuously varied in the range 0–60 rpm. The channel has a square cross-section 60 mm on a side, its length of 1,200 mm ahead of the 180° turn ensuring a hydro-dynamically fully developed flow before the turn. The central partition wall dividing two adjacent ducts is 12 mm thick. Water from a tank is pumped through an orifice meter, a rotating hydraulic coupling and, after flowing in the test channel, is discharged back into the tank. A magnetic pick-up synchronizes IR image acquisition. The classical heated-thin-foil reducing technique is modified because water presence makes the Biot number not sufficiently low. The apparatus is capable of reproducing both Reynolds numbers and rotation numbers Ro = ϖ D/V (where ϖ is the rotational speed of the channel) values typical of turbine blades.

In Fig. 25, the segment-by-segment average Nu/Nu* profiles at the leading and the trailing channel walls, for Re = 20,000 and rotation number Ro in the range 0.0–0.3, are reported. The length of a segment is half channel side. In the inlet duct, the flow results fully developed for both walls being Nu/Nu* practically constant in the first four segments.

For the leading wall (Fig. 25a), Nu/Nu* values are lower than those relative to the static case and decrease for Ro increasing. At the fifth segment, i.e. about one hydraulic diameter before the turn, the Nusselt number starts to increase and reaches a maximum value in segment seven. In fact, in the turn zone, the radial velocity component suddenly decreases and changes sign with a consequent decrease and an inversion of the Coriolis force. This inversion makes the flow to separate by the trailing side and to abruptly reattach toward the leading side, with a strong increase in Nu/Nu* at reattachment. For all rotation numbers, profiles in the turn region and outlet duct exhibit analogous trends with values of the normalized Nusselt number increasing for rotation number increasing.

At the trailing wall (Fig. 25b) of the inlet duct, the Nu/Nu* values are higher than for the static case and slightly increase as Ro increases. In the first corner and in the first half of the second corner (segment nos. 7, 8 and 9), the profiles relative to all rotation numbers present the same trend of the curve pertinent to the static case but with higher Nu/Nu* values. For rotation number increasing, in the outlet duct, it is possible to note that the maximum of the convective heat transfer coefficient (located downstream of the leading wall case) increases and tends to move upstream, i.e., toward the tip of the partition wall.

Rotating systems are quite relevant in several applications and the rotating disk is their simplest configuration. As a matter of fact, flywheels, turbine disks to which blades are attached, disk brakes and even modern high-speed CD-ROMs are all examples of practical applications of this model. Often, the fluid resistance due to rotation is irrelevant but there are a number of cases where the disk thermal behavior may be important.

Astarita and Cardone (2008) perform convective heat transfer measurements on a heated rotating disk, with a relatively small centred jet impinging on it. The disk section consists of a printed circuit board glued on a 20-mm-thick polystyrene foam slab contained in a 450-mm-diameter steel cup, which rotates in the range ω = 100–4,400 rpm. Air, passing through a heat exchanger and a rotameter, goes through a nozzle to produce the jet. The heat exchanger ensures a jet bulk temperature practically equal (±0.1°C) to the temperature of the ambient air the jet mixes with. Several nozzle exit diameters d and nozzle exit to disk distances z are tested. The jet always impinges perpendicularly at the center of the disk.

This topic gives the chance to present authors to report a case where the intrinsic two-dimensionality of IR camera is reduced to a single dimension only, during tests performed with the just described apparatus to detect the spiral vortices (attached to the disk surface) which occur in the transitional regime of a simply rotating disk (with no jet) and cause h azimuthal variations. Since during a full frame acquisition time for the tested conditions, the disk would rotate about two turns thus producing a blurred image, the vortices attached to the surface are detected by the line-scan option of the used Agema 900 IR camera (Astarita et al. 2002b). While the disk is rotating at thermal steady state, the temperature profile along one radius is acquired as a function of time. Then, the temperature map of the disk surface is reconstructed by taking into account its rotation, i.e. by azimuthally displacing the acquired radial profile sequence so as to generate the thermal map attached to the disk surface. Fig. 26 shows such a map, obtained by azimuthally displacing about 30,000 profiles, where the footprint of the vortices is clearly visible. The disk diameter is equal to the side of the externally black square since the temperature range to detect the vortices is very low.

Before treating the disk with the jet, the importance of the adiabatic wall temperature T _aw in high-speed flows is illustrated with thermograms obtained in the normal way (2D) in the same apparatus. The upper half of Fig. 27 (Cardone et al. 1996) shows the thermogram of the disk rotating at 4,390 rpm with a Joule heat flux Q _j  = 871 W/m². A relatively small region (≈16% of the disk surface) at the disk center, with a constant wall temperature T _w, and where the flow is laminar, is clearly evident. In fact, since the laminar solution of Millsaps and Pohlhausen (1952) predicts that the convective heat transfer coefficient h has to be constant over the surface, from Eq. (10) it follows that, for a constant heat flux boundary condition and constant T _aw distribution, the wall temperature T _w must be constant. Actually, in the low subsonic regime, T _aw coincides with fluid temperature and near disk center speed is low.

Outside the laminar zone, the temperature T _w decreases, first rapidly in the transitional regime and then, more slowly in the turbulent one. Immediately after, the wall temperature trend is reversed as T _w begins to slowly rise while, according to the turbulent correlation law (Cardone et al. 1997b), the convective heat transfer coefficient should increase (T _w decrease) for increasing local radius.

This behavior is explained by examining the lower half of Fig. 27, which shows the adiabatic wall temperature T _aw map (simply obtained with Q _j  = 0) at the same disk angular speed. In the map, T _aw is practically constant (and equal to T _amb) only within the circumference whose radius is about 60% of the disk radius; afterward T _aw shows a significant increase (about 4°C over T _amb near the disk edge). Since for the tested conditions, T _w − T _aw is of the same order of magnitude as T _aw − T _amb, Eq. (10) explains the T _w behavior.

Then, the tests of a rotating disk with the centred jet performed by Astarita and Cardone (2008) are described. In order to reduce the number of governing parameters and because of the lack of theoretical analysis, they made the assumption that heat transfer coefficient depends on the ratio between the two momentum flow rates (one due to jet, the other one to disk rotation). By assuming a jet width proportional to the distance from the nozzle and laminar flow over the disk, they put such a parameter in the form:where ν is the fluid kinematic viscosity coefficient, ϖ is the disk rotational speed, other quantities being already defined. The convective heat transfer coefficient at the jet stagnation point h _o is examined.

By considering only the disk rotation, the flow is always laminar at the disk center and in the case of a jet impinging on it, the h _o departure from the single rotation value should be a function of χ only. Therefore, the dimensionless quantity \( h_{o} /k\sqrt {{\nu \mathord{\left/ {\vphantom {\nu \varpi }} \right. \kern-\nulldelimiterspace} \varpi }} \), with k fluid thermal conductivity coefficient, is plotted in Fig. 28, where tests, performed by randomly varying disk angular speed, nozzle diameter, jet initial flow rate and nozzle-to-disk distance, are reported as a function of χ.

The two correlation curves, also shown in Fig. 28 with continuous lines are: The two correlations (23) and (24) are, respectively, obtained by using 42 and 122 data points.

Miniaturized systems are being progressively applied in more and more sectors, such as the electronic, mechanical, pharmaceutical, and medical industries, as well as in the military sector e.g., for biological and chemical warfare defense. As these areas continue to grow, it becomes more and more important to understand the influence on micro-channel flows of various effects such as entrance length, wall roughness, nano-bubbles on the wall surface, viscous dissipation, electric double layer, etc. Miniaturization, once restricted to space, has become a key word in many advanced technologies as well as traditional industries.

As a general comment, it has to be pointed out that, when using IR thermography for convective heat transfer measurements in micro systems, one has to be very cautious and consider three important aspects. The first one is that the convective heat transfer coefficient h can be very high; e.g., having the Nusselt number for channel laminar flow a constant value, since the tube diameter is small, h increases. The second aspect is that, because of the limited dimensions of the thermal sensor, for non-uniform sensor temperature, tangential conduction may become very relevant. Finally, when working with very small dimensions, another drawback is that, especially for IR cameras working in the LWIR band (8–12 μm), the expected spatial resolution easily reaches the system’s physical limitations.

As an example of IR thermography application to micro systems, the thermogram of a meniscus (liquid–vapor interface) topping ethanol contained in a vertically oriented capillary tube is reported in Fig. 29 from the work of Buffone and Sefiane (2008). Due to ethanol evaporation, below the meniscus they find by PIV a toroidal vortex (convection cell) where the fluid particles travel along the meniscus from its center toward the capillary walls; from there, particles move down along these walls to the bulk phase, returning after to the center and finally, via the capillary axis, back toward the meniscus.

A low resolution scanning camera (140 × 140 pixels) with a microscope (minimum FOV 1.4 × 1.4 mm²) is used to record the thermogram of Fig. 29, where the meniscus surface temperature of evaporating ethanol inside an unheated capillary tube (600 μm ID) is presented; indicated temperature is the difference with the ambient one. The blue circle nearly coincides with the tube wall (100 μm thick), also pinpointed with black broken lines. The thermogram shows a practically constant temperature for large part of the meniscus with strong temperature variations only nearby the tube walls. However, it has to be pointed out that ethanol has a very low contact (wetting) angle and, therefore, the low measured temperatures nearby the walls could be also due to the high viewing angles there (see Sect. 2). Besides the authors do not report any data on ethanol radiative transmissivity even if the convection cell (where temperature gradients are present), whose top they are observing, has a depth of only few hundredths of microns.

Flow patterns of the evaporating two-phase flow in heat absorber tubes are of special interest since the tubes are inclined and dryout may occur at low flow velocities because of gravity. Generally, the term dryout indicates a local continuous contact of the gas phase with the pipe surface. In the presence of dryout, large circumferential differences of the heat transfer coefficients result in temperature differences, which, in solar collectors, may produce severe thermal stress in the pipe wall and/or damage the covering selective paint. It has to be stressed that two-phase flows often involve unsteady heat transfer so that, for real-time measurements, the choice of the thermal sensor is crucial.

Hetsroni et al. (2003) carry out experiments to study the flow regimes and heat transfer for an air–water flow in 8° inclined tubes of 25 mm ID by using high-speed video technique, conductive tomography and infrared thermography. Under the studied conditions, disturbance waves of different forms are observed. The analysis of the heat transfer coefficient behavior, together with flow visualization and conductive tomography shows that, at certain superficial liquid velocity, dryout takes place in the open annular flow regimes, with motionless or slowly moving droplets. Experiments are carried out with a heated-thin-foil sensor (50 μm thick), which has a frequency response of 15–20 Hz so, being the highest cluster frequency higher, the authors confine their measurements to average values. The difference between wall and flow temperatures never exceeds 20 K.

Figure 30 shows a typical temperature map and the corresponding circumferential heat transfer coefficient distribution h _θ over the periphery of the pipe, in the angle range 0 < φ < 180° (where φ = 0° is at the tube top). The heat flux is Q _j  = 8,000 W/m², superficial gas velocity is V _G = 36 m/s and superficial liquid velocity V _L = 0.016 m/s. The flow moves from right to left. Color shades of the map (see scale of the upper half of Fig. 30) indicate wall temperature.

The temperature distribution along the pipe perimeter shows a maximum at the top and a minimum at the bottom of the pipe. The circumferential profile of the heat transfer coefficient h _φ , computed according to Eq. (10) where T _r is the fluid bulk temperature and T _w the average wall temperature, is shown in the bottom half of Fig. 30. Comparison with other measurements shows that the distribution of heat transfer coefficient corresponds to dryout on the upper part of the pipe.

The shock-wave/boundary-layer interaction (SWBLI) is a widely studied problem of hypersonic flow, its importance stemming from applied problems, such as efficient design of control surfaces, high-speed air inlets or thermal protection systems in re-entry vehicles.

De Luca et al. (1995b) analyze some aspects of SWBLI in a two-dimensional hypersonic wedge flow over a flat plate/ramp configuration. Flow conditions are only geometrically two-dimensional because, due to formation of Goertler type vortices (see Fig. 9), some spanwise heat flux periodic variations over the ramp at reattaching region are observed. Measurements are performed on a flat plate followed by a ramp in a blowdown wind tunnel at Mach number M = 7.14 and unit Reynolds number Re _u = 8.6 × 10⁶/m.

The mean Stanton number St profiles, measured over a flat plate (90 mm × 90 mm) followed by a ramp with angles α of 10°, 15°, and 20° are shown in Fig. 31. The increase in the flap angle moves the location of the (laminar) separation upstream. The Stanton number over the ramp attains its highest values for the highest ramp angle of 20°, where the very clear St peak denotes the presence of a turbulent reattachment. It has to be stressed that Stanton number distributions over the ramp of Fig. 31 refer to spanwise averaged values since, in all of the tested flow conditions, the heat transfer coefficient exhibits a spanwise periodic variation to be ascribed to Goertler type vortices developing in the reattaching flow region.

Cardone (2007) tests SWBLI in a high-enthalpy arc-heated tunnel which produces M = 6 flows with a specific total enthalpy up to 2.5 MJ/kg and a nozzle exit (to the test chamber) diameter of 60 mm. The tunnel operates in a pulsed, quasi-steady mode, with running time up to 200 ms and the model consists of a flat plate followed by a compression ramp with a spanwise dimension of 100 mm. The hinge line is positioned at 50 mm from the leading edge, the ramp angle is 15° and MACOR^® is chosen as model material for its relatively low thermal conductivity, as required to use the thin-film sensor model. A thermal map recorded about 80 ms after starting of the wind tunnel is reported in Fig. 32 (flow is from left to right), the temperature distribution being almost two-dimensional only near the model’s leading edge. Moving downwind, the continuous decrease in wall temperature shows the boundary layer development. By the hinge line, a region is clearly visible where the temperature attains a minimum due to the presence of a flow separation region. Continuing to move along the symmetry axis, after the hinge line, the temperature reaches a maximum due to flow reattachment on the ramp. Fig. 32 is mainly reported to show how IR thermography allows an easy detection of a non-uniform flow, which, in the present case, is due to the expansion fan starting from the lips of the nozzle exiting in the low-pressure test chamber.

A complex problem regarding hypersonic flow (M = 5.3) is studied by Gulhan et al. (2008) who report an experimental study on aero-thermo-dynamic effects associated with the injection of a lateral jet into a hypersonic cross flow around a generic missile model, with and without angle of attack. The model consists of a cone, followed by a PEEK™ cylindrical main body (which includes a single side jet hole normal to the cross stream) and a flare. Heat transfer measurements, presented in terms of Stanton number distributions, are performed with the thin-film sensor. The flow is also analyzed by oil film visualizations, schlieren images and measuring wall pressure distribution.

The upper part of Fig. 33 shows the Stanton number profiles on the model at circumferential angles φ equal to 180° (jet location) and 150°, M = 5.3, angle of attack α = −10° (windward injection) and p _oj /p _∞  = 300, where p _oj and p _∞ are the jet total and the free stream pressures, respectively. The lower part of the figure gives the projected oil film image (from the top half of the model) and Stanton number distribution (bottom half) on the model. Downstream of the cone shoulder (placed at x/D = 2.8), the Stanton number drops sharply to a plateau, followed by another drop. As it is evident from the oil film image and the Stanton number map, the separation shock is located at about x/D = 3.6, downstream of the cone shoulder. The final drop is caused by the separated horseshoe vortex. Upon reattachment of the vortex, the Stanton number profile, for φ = 180°, shows a pronounced peak. Downstream of the injection site, the Stanton number rises again, reflecting the fact that the temperature of the jet exceeds that of the free stream. Stanton number profiles for both φ angles are similar up to the horseshoe vortex formation. In the area nearby the jet, Stanton number exhibits major differences in the circumferential direction.

At 150°, in the region of the horseshoe vortex wrapped around the jet, the heat transfer is less intense, with Stanton numbers reaching a pronounced minimum there. Farther downstream, outside the area affected by the horseshoe vortex, the Stanton numbers rise markedly due to the impact of the free stream with the flare. The oil film image shows the horseshoe vortex separation line marked by the yellow line that wraps around the fuselage in the outward direction.