Refractive index measurements by Global rainbow refractometry for spherical and non spherical droplets

Transcription

1 Refractive index measurements by Global rainbow refractometry for spherical and non spherical droplets Sawitree Saengkaew 1, Gilles Godard 2, Jean-Bernard Blaisot 3, Gérard Gréhan 4 1 to 4 : UMR 6614/CORIA, CNRS/INSA et Université de Rouen, France, sawitree_s@coria.fr Abstract: To accurately study the heat up, the evaporation and the combustion of liquid droplets, experiments are often carried out with lines of mono dispersed droplets. The measurement of droplets temperature with a classical rainbow refractometer is limited at short distance from the orifice. This limitation is due to the fact that the droplets shapes are not spherical, especially in combustion conditions. This paper shows that by using a Global rainbow refractometer temperature measurement can be carried out on non spherical droplets. 1. Introduction In the combustion of liquid, the liquid fuel is often injected as a spray of tiny droplets and then evaporated. The accurate measurement of the properties of the droplets under evaporation (size, velocity, temperature, etc.,) is still a challenge. To obtain good engineering of stable spray combustor, it s essential to develop a complete understanding of fundamental phenomena of droplet that influence the combustion process. The experimental data are necessary in order to establish and validate models or correlation. These experimental data must be collected in sufficiently basic and realistic situations. Mono-dispersed lines of droplets are continuously fed, and all the droplets have the same trajectory, the same initial diameter and are equally spaced. Then, mono-dispersed lines of droplets are configurations for which the influence of different parameters (drop size, velocity, inter-droplets distance, etc.,) can be easily separated. To measure accurately the droplet characteristics optical techniques are needed. During the last decades, a large effort has been devoted to develop powerful optical techniques (as LDV, PDA, PIV, etc.,) which essentially give a geometrical description of the spray: the size distribution and velocity field. However, the access to the thermo chemical characteristics of droplets has not received much attention from the investigators, even though this property is one of the most important properties which control combustion efficiency. Among other techniques, rainbow refractometry which permits to measure the temperature of spherical particle is attractive. This robust and non intrusive technique can be applied in a large domain of temperature. Moreover, there is no need to add any dye in the liquid. By analyzing the rainbow signal, the droplet size and refractive index, therefore the temperature can be simultaneously extracted. Nevertheless, real implementations of rainbow refractometry must take into account for: 1. The main rainbow is characterized by low frequency signal created by interference between one times internally reflected rays. This is classically described by the Airy's theory. 2. A high frequency component, called ripple structure, is superimposed on the main rainbow. These high frequencies are essentially created by interference between one time internally reflected light and externally reflected light but other higher orders of interaction can contribute to the ripple. 3. The droplet shape can differ from the perfect sphere, inducing a modification of the relationship between rainbow angular location and refractive index value

2 Rainbow refractometry has been used to measure the heat up of line of mono dispersed droplets in various environments [1], including flames. However the technique can be applied only on a finite range of distance, especially under combustion, because the deformations of the droplet reduce dramatically the refractive index measurement accuracy. Alternatively, van Beeck et al [2] introduce the Global rainbow refractometry where a synthetic rainbow created by a large number of droplets, arbitrarily located and oriented in a section of spray, is recorded. Under such condition, the global rainbow technique is claimed to be relatively insensitive to droplets shape. The objective of this paper is to study the possibility to use the Global rainbow refractometry to extend the temperature measurement domain when working on lines of droplets. The paper is organized as follows. Section 2 describes the experimental setup. Section 3 compiles and discusses the results obtained for refractive index measurements. Section 4 compiles and discusses the results obtained for size distribution measurements. Section 5 is a conclusion. 2. The experimental setup 2.1 Droplets generation Droplets are generated by using a vibrating orifice. The nominal droplet diameter is a function of: the orifice diameter, the flow rate and the excitation frequency. The main part of the nozzle can be regulated in temperature, permitting to adjust the temperature of the droplets from 5 C to 80 C. The droplets are injected in a steady air at 23 C. The measurement point is located at 20 mm for the generator orifice. The orifice diameter is equal to 50 µm, the flow rate to 4.0 cc/min and the excitation frequencies used run from 13 khz to 19 khz. The droplet velocity is typically equal to 3 m/s. The experience consists, for a given temperature of the water to atomize, to create a line of droplets as spherical as possible, to characterize this line of droplets, and then to modify the excitation frequency to generate droplets with a degree of non sphericity. As the water physical properties are a function of the temperature, the excitation frequency to obtain spherical droplets changes slightly with the temperature. 2.2 PDA The Dual Mode PDA from DANTEC Company is used. The signal is processed by a BSA P80 processor. The laser source is an Argon-ion laser (Coherent Innova 300C), with a maximum power equal to 10 W. The focal length of the emitting unit is equal to 500 mm and the collecting unit focal length is equal to 310 mm. With such a configuration, the range of measurable diameters runs from 0 to 250 µm. 2.3 Shadow Imaging Figure 1: An example of a line of non spherical droplets. The shadow imaging setup is based on the use of white light pulses. The temporal duration of the light pulse is equal to 5 µs (stroboscope MVS-2611). The images, created by the use of a long distance microscope (Infinity K2/S), are recorded by a numerical camera (KAPPA 1050x1450 pixels). For the working conditions used in this paper, about 6-8 droplets will be visible on each - 2 -

3 image. Software has been developed which gives the possibility to extract diameter, sphericity, ellipticity, irregularity and uniformity of each droplet from images. These parameters are defined by using the notion of perfect disk. The perfect disk is the disk with the same barycentre and surface than the 2D image of the droplet under study. The parameters are defined as: Figure 2: Sphericity (Sp): the area of the non common surface divided by the area of the perfect disk. Figure 3: Ellipticity (ε): the ratio small length on long length. Figure 4: Irregularity (ϕ): ratio drop perimeter length on perfect disk perimeter length Figure 5: Uniformity (η): difference between the maximum and minimum distance to the barycentre For perfectly spherical droplets, these parameters have the following values: Sp = 0, ε=1, ϕ=1, η= Global rainbow setup and processing Figure 6 displays the global rainbow set up developed at Rouen (which is very close to VKI configuration). The setup characteristics are the following: The collecting focal length is equal to 50 mm A spatial filter with a diameter equal to 1 mm gives the possibility to select a control volume equal to typically 500 µm 3. A lens with a focal length equal to 100 mm conjugates the first lens image focal plan on detector surface The image is digitalized by using a CCD camera KAPPA 1050x1450 Pixels A PC records the image and carried out the image processing

4 The figure 7 is a typical example of a global rainbow recorded from a line of perfectly spherical droplets Figure 6: the Global rainbow setup developed at Rouen. Figure 7: a typical global rainbow recorded from a line of spherical droplets. 2.5 Devices connection The different measurement setups and cameras are ordered by a delay boxes (BNC 565) in order to impose that the same droplets are analyzed by the different techniques. Typically, the pulses delivered by the delay box have a frequency times smaller than the excitation frequency: Only about 6-8 droplets by second can be recorded by the shadow imaging setup. Thanks to this configuration, the PDA can be used to measure the velocity and size distribution continuously or by series of 6-8 particles corresponding to the shadow image possibility. For the PDA, the out put can be a classical size histogram or a direct one by one comparison with shadow image technique. 2.6 Rainbow signals When the droplets are viewed as spherical, the recorded rainbows look as the one displayed in Figure 7. Such rainbows are characterized by a high degree of symmetry relatively to the horizontal axis. When the droplets shape is modified by changing the excitation frequency, the rainbow behavior is more complex. When highly steady reproducible orientations are obtained, the - 4 -

5 recorded rainbows have lost their symmetry relatively to the horizontal axis. The two images displayed in figure 8 are typical of such situations. In these cases no measurements are possible. In figure 8.a, the rainbow topology is completely lost. In figure 8.b, the global topology is conserved; nevertheless this figure is characterized by phase jumps in the supernumerary bows organization. Such no symmetrical signals have been rejected in the processing procedure. (a) (b) Figure 8: Typical rainbow recorded for spheroid without random orientation. 3 Refractive index (temperature) measurements 3.1 Spherical droplets A first experiment has been carried out on a line of droplets as spherical as possible (excitation frequency equal to 19 khz). The water is injected with different temperature from 10 to 70 C (the temperature is measured with a thermocouple located inside the injector). The recorded rainbow signals for different temperature are presented in figure 9. These rainbows are very similar to the one displayed in figure 7 but when the liquid injection temperature increases a shift of the rainbows toward smaller scattering angles is visible. 300 Scattered intensity C 21 C 30 C 40 C 50 C 60 C 69 C Scattering angle Figure 9: Rainbows recorded from lines of spherical droplets. The parameter is the temperature of the water in the nozzle

6 To process these signals, three angular domains have been selected. The first one corresponds to only the first major bow (from 132 to 140 ), the second to the fifth first bows (From 132 to 147 ), the third one to all the recorded scattering diagram (from 132 to 149 ) Measured refractive index All peaks 5 peaks 1st peak Water injected temperature ( C) Figure 10: Measured refractive index versus injection temperature. Figure 10 displays the extracted refractive index value versus the temperature imposed inside the nozzle. As for each temperature a series of measurements has been carried out, the statistical behavior of the measurements is represented by a box plots. For each series of measurements at one fixed temperature, the outlying points are represented by black points while the whiskers above and below the box indicate the 90 th and 10 th percentiles. A first remark is the low dispersion of the measurements. A second remark is that the values of the refractive index decrease when the injection temperature increases, from at 12 C to at 69 C. However, the relation looks to be linear. Furthermore, it is evident that when the processing is limited to the major bow, the measured refractive index is systematically smaller (from about 0.001) than when a large section of the scattering diagram is used in the inversion process. These measured refractive indices can be transformed to temperature by using equation (1). Figure 11 displays the associated temperature versus the injected water temperature. N= T T 2 (1) The continuous line materializes the expected answer. A first remark is that, for injection temperature lower than 50 C, the best results are obtained when a large part of the scattering diagram is used to carry out the inversion processing. When the injection temperature is larger than 50 C, the measured droplet temperature underestimates the injection temperature, but this disagreement can be attributed to a faster cooling. From such results, it can be affirmed that, for spherical droplets, the temperature is extracted with an accuracy of few degrees (about typically 2 C)

7 80 70 Measured temperature all peak 5 peak 1st peak expected values Injected temperature Figure 11: Measurement on lines of spherical droplets: measured temperature versus imposed temperature. 3.2 Non spherical droplets A first experiment has been carried out for a water temperature at injection equal to 24 C and excitation frequencies equal to 16 khz and 13 khz respectively. Figure 12 is an example of non spherical droplets created at these frequencies. A first remark is that the droplets deformation increases as the frequency decreases. Figure 13 compares the recorded rainbow for the different excitation frequencies. In red, for a frequency equal to 19 khz corresponding to nearly perfect spheres, the ripple structure is clearly visible. For 16 khz, the major modification is the lost of the ripple structure while for 13 khz the supernumerary bows are nearly invisible, especially for the larger scattering angles. Nevertheless, the inversion of these three curves gives the same refractive index value, corresponding at the injection temperature 26±3 C, independently of the droplet shape. (a) (b) Figure 12: Example of non spherical droplets created for different excitation frequencies (a) 16 khz and (b)13 khz - 7 -

8 Hz Hz Hz Intensity Pixel Figure 13: Evolution of global rainbow shape with droplet sphericity Then, for an excitation frequency equal to 16 khz, the temperature of the water inside the injection nozzle has been changed from 25 to 65 C. The recorded rainbows are plotted in figure 14. A shift of the rainbow toward lower scattering angles is visible as the temperature increases. These rainbows have been processed. The extracted refractive index values are plotted in Figure 15 while the associated temperatures are plotted in figure Scattered intensity C 38 C 58 C 65 C Scattering angle Figure 14: Typical rainbow recorded from non spherical droplets. The parameter is the temperature of water at injection

9 Refractive index Water injected Temperature ( C) Figure 15: The measured refractive index versus the water temperature at injection. Figure 15 evidences the decreasing of the refractive index value with the increasing of the temperature, up to a water injection temperature equal to about 60 C. When the measured refractive index values are transformed to temperature (see Figure 16), it is clear that the measurements overestimate the expected values (excepted for water injected at 68 C) but the overestimation is relatively small (the largest difference is equal to 10 C for an injection temperature equal to 38 C). At this overestimation of 10 C, corresponds to an underestimation of the refractive index equal to about It can be noted that the difference between the expected refractive index value and the linear regression on the measured refractive index values is always smaller than 4 C. This small difference between the measured refractive index values and the expected refractive index values has to be commented. 1) It is well known since the paper of Moebius [4] that, for an ellipsoid, the rainbow location is angularly shifted. The shift depends on the ellipticity and the orientation of spheroids. Rainbows from spheroids can also be rigorously computed by using codes developed by Y.P. Han [5]. From such computations, the relationship between the maximum error on refractive index evaluation and the spheroid ellipticity can be evaluated. Figure 17 displays such a relationship computed for water. From Figure 17, an error of on the refractive index value is associated to an ellipticity between and 1.001, which is very small when compared to the ellipticity evaluated at about 0.70 (with a standard deviation of 0.1) by imaging. This prove the efficiency of the use of global rainbow configuration on lines of droplets 2) The water presents a small dependence of its refractive index value with temperature. For other products with a larger dependence of the refractive index with temperature, the accuracy of the measurement will be better. Let us say about 1-2 C for fuel

10 80 Measured temperature ( C) Water injection temperature ( C) Figure 16: the measured temperature versus the water temperature at injection. The continuous black line materializes the expected results while the continuous red line materializes the linear regression of the measured points. Figure 17: Shift on refractive index value versus spheroid ellipticity. 4 Size distributions From a global rainbow signal, a size distribution is extracted simultaneously with a refractive index value. The extracted size distributions corresponding to the global rainbows of figure 13 are displayed in figures 18a, 19a and 20a. The size distributions measured at the same time, on the same droplets, by the PDA device are presented in figures 18b, 19b and 20b. When the droplets are spherical, the extracted size distribution are essentially monodispersed (figure 18) from global rainbow technique as well as for PDA measurements. Furthermore, the two techniques are in agreement. When the droplets shape is slightly modified, the size distributions extracted by global rainbow technique and by PDA are not completely mono-dispersed. However, the average diameter is still representative of the real size and in agreement between the two techniques (mean diameter equal to 110 µm)

11 For particle far from the sphericity, the behavior of the size distribution is very different. From global rainbow technique, the extracted size distribution (in number) is completely dominated by very small particles while PDA measurements exhibit a very large size distribution with a mean diameter equal to about 140 µm Number of particle Number of particle Diameter (µm) Diameter (mm) (a) GRT (b) PDA Figure 18: the size distributions for an excitation frequency equal to 18 khz Number of particle Number of particle Diameter (mm) Diameter (mm) (a) GRT (b) PDA Figure 19: the size distributions for an excitation frequency equal to 16 khz Number of particle Number of particle Diameter (mm) Diameter (mm) (a) GRT (b) PDA Figure 20: the size distributions for an excitation frequency equal to 13 khz. 5 Conclusions The effect of droplet shape on the global rainbow measurements accuracy has been presented. For spherical droplets, the temperature is measured with an accuracy of about 2 C. The associated size distributions are in agreement with size distribution measured by PDA. For non spherical and unsteady droplets, the temperature is measured with a good accuracy (about 5 C) but the associated size distribution (in number) are strongly dominated by ghost small particles

12 6 Acknowledgments This work is supported by the CNRS-ONERA program ASTRA. References [1] G. Castanet, P. Lavielle, F. Lemoine, M. Lebouche, A. Atthasit, Y. Biscos and G. Lavergne, Energetic budget on an evaporating monodisperse droplet stream using combined optical methods evaluation of the convective heat transfer, Heat and Mass Transfer, 45, , [2] J. van Beeck, D. Giannoulis, L. Zimmer and M. Riethmuller, Global rainbow refractometry for droplet temperature measurement, Optics Letters, 24, , [3] S. Saengkaew, Development of novel global rainbow technique for characterizing spray generated by ultrasonic nozzle., PhD thesis, University of Chulalongkorn (Thailand) and Rouen (France), 2006 [4] W. Moebius, Zur theorie des regenbogen und experimentelien prufung, Annalen der Physik, IV, , 1911 [5] Y.P.Han, L. Méès, K.F. Ren, G. Gouesbet and G. Grehan, Scattering of light by spheroids: the far field case, Optics Communications, 1-9,