Differential infrared thermography (DIT) in a flashing...

Differential infrared thermography (DIT) in a flashing jet

by G. Lamanna*, H. Kamoun*, B. Arnold*, B. Weigand* and J. Steelant**

*ITLR, Universitaet Stuttgart, Pfaffenwaldring 31-70569 Stuttgart, Germany, [email protected] **ESTEC-ESA, 2200 AG Noordwijk, The Netherlands, [email protected]

Abstract

This paper discusses the feasibility of differential infrared thermography for performing quantitative temperature measurements in a flashing jet. First a methodology is defined to determine locally the spray emissivity, independently from a detailed knowledge of the drop size distribution. Thanks to the differential operation, the spray emissivity can be determined very accurately both in the optically dense and dilute regions of the spray. Second all factors, which may hamper quantitative data interpretation, are carefully reviewed. The analysis includes the choice of the background temperature, multiple scattering effects and the spatial resolution of the optical system. Finally, the experimental temperature data are validated through comparison with theoretical predictions, showing a remarkable good agreement.

1. Introduction

This paper discusses a novel application of infrared thermography, aimed at obtaining quantitative temperature data from the analysis of thermograms in liquid sprays. It is explicitly noted that to date the application of thermography to spray systems has been extremely rare and mostly limited to a qualitative mapping of the temperature distribution. This limitation is mainly due to the following factors: 1) the difficulty of determining the local distribution of the spray emissivity; 2) the impossibility to distinguish between the emitted and transmitted contribution to the total radiation acquired by the camera. One of the first application of thermography to disintegration studies was made by Yildiz et al. [1], who tried to characterise the thermal behaviour of a flashing jet through infrared imaging. However, due to the difficulties of calibrating the infrared camera and of determining the emissivity of the evaporating spray, only qualitative information could be extracted from the thermograms. A similar attempt was made by Laverriere [2] for a kerosene spray in a high-pressure chamber. In order to calculate the spray temperature distribution, the spray emissivity was set to 1 and the attenuation from the high-pressure surroundings neglected. Even though the obtained temperature profiles were plausible from a physical point of view, the assumption of a constant emissivity is not very realistic and may induce significant errors on the calculated temperature, which the authors were not able to quantify. First quantitative measurements have been performed by Saha et al. [3]. The authors applied infrared thermography to map the internal temperature field in levitated (distilled) water droplets in a size range of roughly 500µm. The authors estimated the emissivity for distilled water from literature data, which was found to be in the range of 0.95-0.98. This range of values was then confirmed by performing Fourier Transform Infrared Spectroscopy (FTIR). The measurement showed that the absorption coefficient did not change by more than 1% for the laser wavelength used in the experiments. For this level of emissivity, the error in temperature was found to be utmost 0.3°C.

A significant contribution towards quantitative interpretation of thermographic data for spray applications was given by Pawlowski and Kneer [4], who proposed an alternative method to calibrate the thermographs and determine the local distribution of the spray emissivity: the Differential Infrared Thermography (DIT) technique. A key feature of DIT is that the spray is imaged twice in front of a temperature-controlled background with a high emissivity. By varying the background temperature and applying image substraction, it is possible not only to distinguish between the portion of radiation emitted and transmitted by the spray, but also to determine the spray emissivity distribution. The authors [4] already demonstrated the advantages of DIT, briefly listed below:

• being non-intrusive • applicable to both dense and dilute regions of the spray • applicable to droplets and liquid ligaments of arbitrary shape • applicable to any fluid (including actual fuels), without requiring detailed knowledge of thermodynamic/

physical properties • no dopant is needed that may alter the thermodynamic behaviour of the fuel

In order to better comprehend the underlying assumptions and limitations in the practical application of DIT, we

summarise hereafter some major results from the theory of scattering, absorption and propagation of radiation in particulate media [5]. For a cloud of droplets of non-uniform size, characterised by a size distribution function N(rd), the spectral emission (or absorption) can be expressed as

€

ελ ,cloud = Qabs0

∞

∫ rd2 N (rd )drd (1)

11th International Conference on

Quantitative InfraRed Thermography

Similar relations can be written for the scattering and extinction of infrared radiation:

€

ρλ ,cloud = Qsca0

∞


€

βλ ,cloud = ελ ,cloud + ρλ ,cloud = Qext0

∞


If total (i.e. spectrally integrated) properties are required, as it is the case in most engineering applications (e.g. to evaluate the emitted radiation from a droplet cloud), Eqs.(1) to (3) may be integrated over the entire spectrum to obtain the Planck-mean coefficients, defines as

€

ycloud =π

4σT4I bλ

0

∞

∫ yλ ,clouddλ , y = ε,ρ,or β (4)

where Ibλ is the spectral radiation intensity. Since the efficiency factors Q vary rapidly across the spectrum, these integrations are generally quite cumbersome and require a detailed knowledge of the scattering phase functions for the different size classes. A first main advantage of DIT is that it enables the experimental determination of the spray emissivity independently from a detailed knowledge of the size distribution function for the droplet cloud. Equations (1) to (4) also show that in particulate media the total emissivity is strongly affected by the scattering processes within the droplet ensemble and hence is a strong function of the size parameter (α = 2 π rd / λ), which largely controls the direction and intensity of scattered radiation. Only in some limiting cases, the analysis of scattering phenomena and their influence on radiative heat transfer applications can be greatly simplified. For very large spheres (α >> 1), for example, almost all energy is scattered forward in a narrow cone around the direction of transmission and diffraction effects may be neglected. In this limit, it is possible to simplify the treatment of radiative heat transfer and treat it as transmission, as in the experiments of Saha et al. [3]. Only in this limiting case, the emissivity of the droplet can be assimilated to that of the bulk liquid. Another practical situation, where the description of the scattering behaviour greatly simplifies, is in the case of a highly polydispersed droplet size distributions. In this case, the scattered radiation is mostly concentrated in the forward direction (hence it can be assimilate to a transmission problem) [5-6] and only a very small fraction is scattered in the backward direction. The validity of this simplification for radiative heat transfer problems is verified in section 4.2. In the present paper, a detailed characterization of the DIT technique is presented with particular emphasis on all factors affecting the accuracy and quantitative interpretation of the measurements. The analysis includes the optimal choice of the background temperatures, the influence of scattering due to the granulometry of the spray, and the effect of the optical resolution on the accuracy of the measurement. To demonstrate the technique, superheated liquid sprays, atomising in near-vacuum conditions due to liquid boiling, are selected. In this way, the potential of DIT in performing temperature measurements in dense optical region can be explored, while excluding – in a first approximation - the effect of radiation and/or attenuation from the surroundings. The paper is organised as follows. Section 2 describes briefly the test facility and focuses mostly on the constructive details for manufacturing the temperature controlled backgrounds. Section 3 describes the principles of DIT and the post-processing algorithm. Section 4 presents the accuracy analysis and discusses the main simplifying assumptions in the implementation of the technique. Section 5 presents a validation of the technique by comparing the radial and axial temperature distribution to theoretical predictions.

2. Experimental setup

The test bench is designed for performing flash atomisation and vaporisation experiments at medium vacuum conditions (0.02 bar < pchm < 0.4 bar). A schematic layout of the facility is shown in figure 1. The injector chosen is a standard automotive fuel injector, which has been adapted to low-pressure applications. Thanks to a special nozzle design, injection pressures (pinj) as low as 6 bar can be attained. Note that a heating coil is wrapped around the injector body, thus enabling fuel pre-heating prior to an injection event. Fuel injection temperatures as high as 170°C can be obtained. The nozzle has an exit diameter D of 150 µm and an aspect ratio L/D approximately of 7. Four circular windows are installed in the vacuum chamber at 90 degree apart from each other to allow visualisation of the spray and optical diagnostics. Further details on the setup operations and instrumentation can be found in [6]. As test fluid, ethanol is employed. For the practical implementation of the DIT technique, two of the four circular windows are replaced with a temperature controlled background and with an infrared transmissive window made of sapphire (Diameter = 135 mm, thickness = 2 mm), respectively. The optical layout for the differential thermographic imaging is shown schematically in figure 2. For the two temperature-controlled backgrounds a base construction is used, as shown in figure 3. An aluminum disc acts as the housing for the temperature-controlled background (copper plate). The latter is embedded in MACOR frame to minimise thermal losses. For the heated background (figure 3 - left), an electrical heated foil is used. For a better contact between the foil and the copper plate, a heat-conductive paste is employed. In addition, a second MACOR

11th International Conference on Quantitative InfraRed Thermography, 11-14 June 2012, Naples Italy

plate placed behind the foil is used to avoid heat losses towards the surroundings. All these components are then pressed against the aluminum disk using a steel clamp. Since the heating foil requires a voltage supply of 230 V, a protective housing is used to isolate the construction from the surroundings. For the cooled background, two Peltier elements are used. The main advantages of Peltier cooling element (compared to a vapour-compression refrigerator) are its lack of moving parts or circulating liquid, and its small size and flexible shape (form factor). Its main disadvantage is that it is a relatively costly solution, if a high power efficiency is required. A ventilator is used to cool down the hot side of the Peltier elements. The overall assembly is shown in figure 3 (right). Similarly to the heated background, a steel clamp is employed to assemble all parts together.

Fig. 1. Left: Schematic of the vacuum chamber. Right: Details of the heating system.

Fig. 2. Optical layout for differential thermographic imaging.

Fig. 3. Construction layout of the heated (left) and cooled (right) background.

A FLIR-Orion SC7000 is used for acquiring the thermograms. The infrared camera is placed in front of the sapphire window and is sensitive to wavelengths between 3 and 5 µm. The camera has a resolution of 512x640 pixel at 100 fps (frame-per-second). For the present work, the camera resolution has been adapted to the region of interest 200x300 pixel resulting in a higher frame rate (250 fps). With the 50 mm objective, a magnification of 1:7 is achieved. For each injection, ten frames are recorded.


3. Principles of Differential Infrared Thermography

DIT is a line integral technique, which measures the thermal radiation emitted along a line path perpendicular to the CCD detector plane, as shown schematically in figure 2. In order to determine the spray emissivity, which varies locally with the droplet number density and size distribution, the spray is imaged in front of a temperature-controlled background with a high emissivity (ε = 1). A procedure is then established to determine the emissivity coefficient of the spray and eliminate the effect of background radiation from the surroundings on the measured signals. The emissivity can be computed at each pixel by acquiring the jet intensity radiation at two known background temperatures, obtained by uniformly heating (figure 4a) and cooling (figure 4b) the background, respectively.

(a) Heated background, TBack = 366K (b) Cooled background, TBack = 286K

Fig. 4. Thermographic images of a spray, acquired in front of a temperature controlled background, Tinj = 389 K, pam = 0.2 bar, pinj = 10 bar. Fluid: Ethanol.

Assuming that the spray temperature is the same in both images, the intensity captured by the infrared camera

can be expressed as the sum of different contributions:

€

ICam1 = τ atm εsprayI spray + 1−εspray( )I Back1[ ] +εatmI atm + ρsprayI tot (5)

€

ICam2 = τ atm εsprayI spray + 1−εspray( )I Back2[ ] +εatmI atm + ρsprayI tot (6)

where Icam1,2 is the radiation recorded by the camera, εspray and ρspray are the spray emissivity and scattering coefficients respectively, Ispray is the spray radiation, IBack1,2 is the background radiation, εatm is the atmosphere emissivity, Iatm is the atmosphere radiation and τatm is the atmosphere transmissivity. Note that all scattering effects have been incorporated in one single term ρspray Itot. The latter represents the total scattered radiation and includes both the fraction of emitted radiation and the portion of atmospheric radiation scattered within the spray. The underlying assumptions in Eqs. (5)-(6) are that neither the radiation emitted by the atmosphere nor the scattered fractions are affected by a change in the temperature of the background. This hypothesis is quite reasonable as long as the difference in the background temperature is relatively small, e.g. 20 < |TBackground1 − TBackground2| < 100 K and hence it is unlikely to induce a significant change in the amount of radiation absorbed and re-emitted by the atmosphere (or scattered by the spray). In other words, only the radiation transmitted by the spray is affected by a change of temperature in the background. Subtracting Eq. (5) from (6) and solving for εspray yields

€

εspray = 1− ICam2 − ICam1

τ atm I Back2 − I Back1( ) (7)

An example of the emissivity distribution calculated for an ethanol jet (injection temperature Tinj = 389 K, back pressure pam = 0.2bar, injection pressure pinj = 10bar) is plotted in figure 5a. As can be seen, the emissivity gradually evolves from the bulk liquid value of roughly 0.8 [7] - corresponding to the liquid core region - down to a value of 0.2 for the polydispersed spray regions. This dependency is in agreement with Eqs. (1) to (4), where the emitted radiation depends upon the droplet number density, size distribution and the scattering functions. Therefore, the application of infrared thermography to a spray requires a methodology for performing an in-situ calibration and determining the spray emissivity, which is de facto the key feature of the DIT method. Once the jet emissivity is known, its temperature


distribution can be determined from the intensity distribution (Eq. 5) using the Stefan-Boltzmann law. An example of a temperature distribution is shown in figure 5b.

(a) Distribution of the emission coefficient (b) Temperature distribution

Fig. 5. Thermographic images of a spray, acquired in front of a temperature controlled background, Tinj = 389 K, pam = 0.2 bar, pinj = 10 bar. Fluid: Ethanol.

Note that due to the differential operation, the determination of the emissivity coefficient is always quite accurate since any disturbance (e.g. misalignment, scattering, unwanted reflections) automatically cancels out. Problems arise in the quantitative extraction of temperature data. Referring to Eq. (5), scattering effects and/or radiation from the surroundings may cause a significant overestimation in the total measured radiative flux Icam1, thus compromising completely the temperature measurement.

4. Uncertainty analysis

This section discusses in details the different elements, which may potentially hamper the measurement of the spray temperature by DIT. Three different factors have been identified, namely: optical resolution of the imaging system, choice of the background temperature, influence of spurious radiation contributions, deriving either from the surroundings or from scattering effects associated with the granulometry of spray (see Eq. 5 as a reference). A separate analysis is presented for each source of uncertainty leading to a quantification of the corresponding temperature error. Due to their mutual independency, the total uncertainty in temperature measurement is then obtained by simply adding up the three different contributions.

4.1. Effects of radiation from the surroundings

With reference to Eqs. (5) and (6), the radiation from the surroundings can affect the measured radiation intensity Icam1,2 in two ways, namely through the background radiation (1-εspray) IBack1,2 and the atmosphere radiation (scattered or directly emitted) (1+ρspray) εatm Iatm. The latter term is particular relevant when the chamber is heated and irradiates the spray. In this case, the spray reflection of the ambient radiation ρspray εspray Iatm cannot be neglected and the determination of the spray temperature fails completely, as it is not straightforward to calculate the scattering coefficient ρspray. Furthermore, the directly emitted contribution εatm Iatm might be so intense as to overshadow completely the radiation emitted by the spray. This limitation is not expected to play any role in the measurement campaigns envisaged in this activity, as all tests are performed at ambient temperature. Even in the limiting case of low spray temperatures (e.g. (Tspray < Tam) the spray cools below the ambient temperature due to flash vaporisation), the spray reflection can still be neglected: being εatm << 1 and ρspray < εspray [5], we get τatm εspray Ispray,b >> ρspray εatm Iatm. Still, to avoid any undesired reflections, a good precaution is to blacken all walls of the test section.

A second hampering factor may occur in the dilute area of the spray, where the background radiation transmitted through the spray (1-εspray) IBack1,2 may overshadow completely the contribution emitted directly from the spray. In this case, the camera captures only the transmitted background radiance and a calculation of the spray temperature is highly inaccurate. Furthermore, the error in the calculation of the temperature due to this effect is amplified by an unfortunate choice of the background temperatures. To evaluate the uncertainty in the temperature measurement for a given pair of background temperatures TBack1 and TBack2, the method proposed in [4] is adopted to calculate the temperature error associated to an erroneous camera recording. By applying the Stefan-Boltzmann law to Eqs. (5) and (7) and neglecting the scattered and atmosphere radiation, we obtain

€

εspray = 1− TCam24 −TCam1

4

TBack24 −TBack1

4( ); σTCam1

4 = εsprayσTspray4 + 1−εspray( )σTBack1

4 (8)


By solving for Tspray, the following functional dependence between Tspray and Tcam1 can be derived

(9)

By deriving Tspray with respect to TCam1, it is possible to obtain the functional dependence dTspray /dTCam1 that relates the spray temperature error to the camera error. For a given spray and background temperatures, the measurement accuracy is plotted as a function of the spray emissivity in figure 6. The graphs can be interpreted as follows: 1K measurement inaccuracy in the determination of the temperature recorded by the infrared camera results inevitably in 10K inaccuracy in the spray temperature. Note that the error depends strongly on εspray. Generally the measurement accuracy improves dramatically with increasing emissivity. Figure 6a also shows that the measurement accuracy can be drastically improved by an optimal choice of the background temperatures. Typically the best results are obtained when the spray temperature is intermediate between the two background values (e.g. blue curve). In this case, the spray radiation dominates in at least one of thermographs and the enhanced contrast is crucial for the measurement accuracy. The optimal choice of the background temperature as a means to enhance the image contrast is particularly relevant for the spray regions exhibiting a low emissivity (typically εspray < 0.6), as can be immediately deduced by comparing e.g. the blue and green curves in figure 6a. By applying this uncertainty calculation method to an actual experiment, a spray temperature error map can be plotted for a given test condition (Tinj, pinj and pam) and background temperatures, as shown in figure 6b-c. As expected, the best results are obtained in the first case, where the spray temperature is intermediate between the two background values. In this case the max temperature error is below 4K.

(a) Measurement uncertainty versus εspray (b) TBack1 = 286K, TBack2 = 366K (c) TBack1 = 337K, TBack2 = 366K

Fig. 6. (a) Example of measurement uncertainty as function of spray emissivity; (b) & (c) Spray temperature error map, Tinj = 389 K, pam = 0.2 bar, pinj = 10 bar. Fluid: Ethanol.

4.2. Scattering effects

As mentioned already in section 3, multiple scattering effects – related to the granulometry of the spray - may lead to an overestimation of the emitted spray radiation and hence to an overestimation of the spray temperature. In order to evaluate in quantitative terms the influence of scattering, the radiative heat transfer problem is solved within the spray by including the interaction of the emitted thermal radiation with the droplet cloud. The physical processes included are Planckian thermal emission, scattering with arbitrary phase function, absorption, surface bidirectional reflection and direct radiation from the heated/cooled background. In this approach, the superheated jet is divided in horizontal regions, marked in red in figure 7a. Each region is then modeled as a non-isothermal, horizontally inhomogeneous, but vertically homogeneous media (figure 7b). For the simulations, the DISORT code [8] is employed, which numerically solves the radiative heat transfer equation by means of the discrete ordinate method. The code, developed by Stammes et al. [9-10] has been extensively validated and is extremely well-documented, therefore a detailed description is not reported here. In this context, we simply point out that DISORT considers the transfer of monochromatic unpolarized radiation in a multi-scattering, absorbing and emitting plane parallel medium. The medium can be forced by a parallel beam and/or diffuse incidence and/or Planck emission at either boundaries. Due to these characteristics, it was necessary to divide each region in small vertical sub-layers of thickness L = 100 µm and to specify the temperature and drop size distribution within each sublayer. As shown schematically in figure 7b, we have specified an input distribution for each region and then approximated them with step functions, such as each sub-layer has constant temperature and drop size. The input temperature distribution is taken from the DIT experiments, the droplet size data are estimated from literature data. For the present simulations, we assumed a Gaussian profile with a max droplet radius of 20µm on the spray axis and a minimum value of 5 µm at the spray border. Based on the chosen size distribution, the scattering/emission/extinction

€

Tspray = TCam14 −

TCam14 −TCam2

4( )TBack14

TBack14 −TBack2

41− TCam1

4 −TCam24

TBack14 −TBack2

4

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟

1/4


coefficients (Eqs. 1-3) can be evaluated in each sub-layer. For the sub-layers placed outside the spray, the optical properties of air are taken. Of particular interest is the extinction coefficient βi, shown exemplary in figure 7c. The latter multiplied for the sub-layer width (L), provides the total optical thickness of the spray:

€

β i = 2N iQextπrd2 , N i = N tot

Vnozzle

Vs

Vi

Vs

, δspray = β iL1

n

∑ (10)

where Vs is the volume of the spray region under consideration and Ni is the droplet number density in the sub-layer i. Ni is estimated from nucleation theory by assuming that the onset of nucleation takes place right within the nozzle and then scaling the total number of droplets Ntot by the volume of each sub-layer Vi. It is noteworthy mentioning that the spray optical thickness is one of the key parameter for estimating the effect of (multiple) scattering on transmission measurement. Lamanna et al. [11] have already shown that scattering is negligible either when the size parameter α << 1 (droplets much smaller than radiation wavelength) or when the optical thickness δ << 1 (rarefied clouds).

(a) Non-isothermal horizontal regions (b) Vertical sub-layers scheme (c) Exemplary β distribution

Fig. 7. Spray model for the multiple scattering simulations based on the solver DISORT.

Once the optical properties are derived for each horizontal region, two spray simulations are performed with and without scattering effects, respectively. As output, the radiative fluxes in the forward (detector plane) and backward direction are compared in order to obtain quantitative information on the influence of infrared scattering on the DIT temperature measurements. Figure 8 shows a first example of such simulations: the size parameter varies between (2 < α < 50) in each horizontal region and the optical depth decreases from 0.5 to 0.17 with increasing axial distance. Figure 8a shows the relative error between the forward fluxes Fscat (scattering included) and Ftrans (no scattering). As expected, the amount of scattered radiation strongly depends upon the optical thickness δ. For δ < 0.3 (x/D > 20), the influence of scattering on the transmission of thermal radiation is below 5%, even for value of α as high as 50. The scattered contribution to the total radiation becomes significant above 50% in the near nozzle region for x/D < 5 (δ > 0.4 and particularly for the large droplet class α ≈ 50). Note that the present simulation represents a worst case scenario for the estimation of the scattering effects. First of all, we compare here two extreme situations: Fscat represents the forward flux under the assumption that 99% of incident radiation is scattered and Ftrans assumes no scattering at all. Second, we have assumed that atomisation is instantaneous and concentrated an elevated droplet number density (Nd = O(1012)) already at the nozzle exit plane, thus resulting in a very high optical thickness. Experimental evidence, however, indicates the presence of an intact liquid core on the spray axis (till roughly x/D = 7) associated with a rarefied droplet cloud on the spray boundaries. Figure 5(a) shows, in fact, very high emissivities on the jet axis (ε = 0.8), corresponding to the bulk liquid values. Hence, the actual optical thickness at x/D < 5 is smaller than the values adopted for these simulations, leading to lower inaccuracies in the actual measurements.

(a) (Fscat – Ftrans)/Ftrans (b) Fback /Fsact (c) Error in temperature data

Fig. 8. Exemplary result from the multiple scattering simulations based on the solver DISORT.


In order to analyse the modalities of the scattering process, figure 8b compares the forward and backward radiation fluxes at different axial distances along the jet for the fully scattering simulation. In agreement with scattering theory [5], the simulation confirms that for a highly polydisperse cloud most of the radiation is scattered in the forward direction. The backscattering flux, in fact, never exceeds 4% of the forward scattered radiation throughout the spray. As a result, for radiative heat transfer problem in droplet clouds, only the fraction of forward scattered radiation can be considered without compromising the accuracy of the results. By calculating the relative error (Fscat – Ftrans)/Ftrans at each axial distance x/D and applying polynomial decomposition to the Boltzmann law, it is possible to derive an expression for the relative temperature error. The result of this exercise is plotted in figure 8c, showing that the highest temperature error amounts at utmost 12% when scattering effects are completely neglected.

As a concluding remark, we would like to point out that multiple scattering effects are not an exclusive prerogative of infrared-based techniques. As a matter of fact, any optical technique (e.g. Raman, Mie scattering or fluorescence methods) will be affected by multiple scattering effects during the propagation of the optical signal through a particulate media. Thanks to the longer wavelength in the infrared range, the size parameter (α = 2 π rd / λ) is always smaller in thermal radiation problems compared to the visible range. Therefore for a prescribed droplet cloud, the multiple scattering effects will have a lower impact for thermal radiation problems compared to other optical methods.

4.3. Optical resolution effects

A third hampering factor is represented by the optical resolution of the imaging system. In the present experiments a magnification 1:7 is adopted, as the primary objective is to characterise the entire temperature field and to verify the feasibility of thermographic measurements in a superheated liquid spray. This implies that 1 pixel corresponds to an area of the spray of 100x100 µm. Hence, any temperature variation within the spray occurring within a distance of 100 µm will not be detected. Instead, the camera reading will result in an average temperature, whose inaccuracy increases the highest the actual temperature gradient. In order to quantify this error, we made the following theoretical exercise. We considered two different optical resolutions 100 and 15 µm, respectively. Note that these two resolutions are not chosen arbitrarily, but correspond to the actual magnifications attainable with currently available infrared macro-objectives. For each pixel size, we applied a negative temperature gradient from 0.01 till 0.1 K/µm, which corresponds to typical values encountered in the flashing experiments. As can be seen in figure 9, for temperature variations around 10K per millimetre, the difference in temperature reading between the two resolutions is below 1%. A drastic increase in inaccuracy, however, is noted for the low resolution configuration with increasing temperature gradient. For the 15 µm case, the inaccuracy does not exceed 1% up to temperature variations of 100K per millimetre. As an example, figure 9b-c show two radial temperature profiles and the associated inaccuracy, corresponding to axial distances x/D of 2 and 20, respectively. As can be seen, the measurements in the near nozzle region (x/D = O(1)) are mostly affected by the resolution of the imaging system, due to the rapid cooling of the jet through flash boiling. Therefore, only the data in the downstream region will be used to validate the DIT. For the upcoming test campaign, the macro-objective with a magnification 1:1 (15 µm) will be used. This will guarantee a high accuracy in the temperature measurements through the entire flow field.

(a) Effect of the spatial resolution (b) Exemplary temperature profiles (c) Error in the temperature data

Fig. 9. Temperature inaccuracy associated with a specific spatial resolution.

5. Validation

The validation of DIT measurements is not straightforward due to the absence of thermal data in sprays, which can be used as a reference. In order to overcome this limitation, we returned to the theory of submerged turbulent jets, [12,13] and compared our measurement data to theoretical predictions. The basic idea is that flashing effects can be characterised as deviations from the theoretical behaviour. As soon as the spray relaxes to equilibrium (i.e. no liquid boiling), the temperature axial and radial profiles should not exhibit any significant departure from the theoretical profiles. Compliance with this requisite provides an indirect validation of the DIT technique. For completeness, the main findings


from the theory of single-phase turbulent jets [12,13] are briefly summarised hereafter. The axial temperature distribution can be expressed as follows

€

Taxis −Tam

Tinj −Tam

=0.7

0.14x / D + 0.29 (11)

where Taxis, Tam and Tinj are the axial, ambient and injection temperatures, respectively. The radial temperature profiles exhibit a self-similar behaviour and can be efficiently reduced according to

€

T −Tmin

Taxis −Tmin

= 1− rr0.5

⎛

⎝ ⎜

⎞

⎠ ⎟

1.5⎡

⎣

⎢ ⎢

⎤

⎦

⎥ ⎥ (12)

where Tmin is the lowest temperature value along a radial profile, r/r0.5 is the non-dimensional radial coordinate and r0.5 is the lateral position at which the velocity is half the centerline value. The latter can be can be expressed as function of the half-thickness b at the corresponding cross section: r0.5 = 0.441 b. Figure 10a shows a comparison between the theoretical (Eq.11) and experimental axial temperature profiles, expressed in non-dimensional form. A great discrepancy is observed near the nozzle region (0.14 x/D < 1.5), where the experimental curve approaches the ambient temperature more rapidly due to the fast vaporisation rate associated with flashing effects. At x/D ≈ 20 (or 0.14 x/D ≈ 2.5) the experimental curve merges completely with the theoretical one, thus implying that the downstream cooling of the jet is mainly controlled by heat conduction. Correspondingly the radial temperature profiles become self-similar starting from x/D ≈ 20 in agreement with the theoretical predictions (Eq. 12), as shown in figure 10b. Finally, the absolute axial temperature tends to Tam = 22°C for x/D >> 1 when the jet is in thermal equilibrium with the surroundings. Recalling the inaccuracy analysis of section 4, this result is not surprising since neither scattering effects nor the optical resolution have any significant impact on the measurement accuracy in the downstream region of the jet. As a result, DIT is also capable to deliver correct quantitative data. For the near nozzle region where strong temperature gradients are expected, the DIT method severely underestimates the fluid temperature. The accuracy can be greatly improved by increasing the optical resolution from 100 to 15 µm/pixel. For the validation of the measurements in the flashing regime, a comparison with data obtained with the global rainbow technique is planned.

(a) Non-dimensional axial temperature (b) Non-dimensional radial profiles (c) Axial temperature profile

Fig. 10. Exemplary temperature measurement and comparison with theoretical predictions [12-13]. Test conditions: Tinj = 84°C, pam = 0.06 bar, pinj = 10 bar. Fluid: Ethanol.

6. Conclusions

A novel application of infrared thermography for mapping the temperature field in liquid sprays is presented. In order to assess the feasibility of quantitative data interpretation, a precise rationale is followed. First of all, the interdependency between emission and scattering of thermal radiation within a spray is highlighted, by employing classical results from the theory of light scattering. This interdependency is subsequently exploited for assessing the effect of multiple scattering on the acquired infrared signals, and hence on the temperature data.

Second, a methodology is presented to determine the local distribution of the spray emissivity, independently from the knowledge of the drop size distribution function and of fluid thermodynamic properties. The basic idea is to image the spray is imaged twice in front of a temperature-controlled background with a high emissivity. By varying the background temperature and applying image substraction, the spray emissivity distribution is derived as the fraction of recorded signal deprived of the transmitted contribution, which varies with the background temperature. It is shown that if the spray temperature distribution is intermediate between the background temperatures, the measurement inaccuracy is below 5K everywhere in the flow field.


Third the impact of multiple scattering effects and of spatial resolution on the measurement accuracy is also analysed. The most severe source of inaccuracy is related to the optical resolution of the imaging systems. For low spatial resolutions, cold and hot areas of the spray are averaged on the same pixel, thus leading to a significant underestimation of the actual temperature distribution. In a first approximation, the technique is validated by comparing the experimental temperature profiles with the theory of single-phase turbulent jets [12-13], showing a remarkable good agreement.

REFERENCES

[1] Yildiz, D., Rambaud, P., Beeck J. V., Buchlin J.-M., “Thermal characterization of a r134a two-phase flashing jet”, 6th National Congress on Theoretical and Applied Mechanics, Gent (Belgium), May 26-27, 2003.

[2] Laverriere, C., “Caracterisation des sprays de kerosene a haute temperature, par imagerie visible et infrarouge”, Master thesis, Ecole Polytechnique federale de Lausanne, 2008.

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Differential infrared thermography (DIT) in a flashing...

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