To reach the requirements of carbon emission reduction, global energy consumption must be optimized. Optimizing the combustion of electrofuels (e-fuels, including butanol and other alcohols [1]) requires assessing the ability of an injector to produce spray systems that efficiently transit from liquid to gas. Thus, there is a need for detailed quantitative information on the droplet cloud. In particular, mean droplet sizes and size distributions are key parameters in optimizing these processes.

In order to determine these parameters, various optical measurement techniques exist. The most widely used for determining the droplet size distribution of a spray is the phase Doppler anemometry (PDA) technique, also called phase Doppler interferometry (PDI) [2,3]. This experimental measurement does not require calibration and allows the simultaneous determination of droplet size and velocity. However, the measurement volume of this method is limited to a few hundred microns which makes the technique time-consuming for the complete characterization of an entire spray. To reduce the time of experimental measurements while maintaining a high spatial resolution, techniques based on laser sheet imaging appear to be a solution. Thus, laser-induced fluorescence (LIF)/Mie [4] and Raman/Mie [5] methods have been developed to allow planar imaging of the Sauter mean diameter. Recently, planar rainbow refractometry has been developed for directly imaging the standard droplet diameter [6].

However, despite their advantages, these imaging methods are limited to the study of low concentrations of droplets in space. Indeed, the application to optically dense sprays is challenging due to the occurrence of a phenomenon known as multiple light scattering. By suppressing this unwanted intensity contribution, structured laser illumination planar imaging (SLIPI) [7] has allowed the implementation of the LIF/Mie droplet sizing in optically dense sprays [8]. Nevertheless, due to the necessity of adding fluorescent dyes to the liquid, LIF/Mie droplet sizing is limited to the study of non-evaporating sprays [9]. Furthermore, the addition of a dye in significant proportions can alter the physical properties of the fluid [10].

In order to measure the droplet size field without the addition of fluorescent dyes, while maintaining a good signal-to-noise ratio, the polarization ratio technique can be used. This technique has been introduced in the 1980s [11,12], where the behavior of the polarization ratio has been studied on isothermal sprays and burning conditions. It has also been applied to size droplets from various monodisperse streams [13,14]. The technique is based on collecting the perpendicular ($S$-$pol$) and parallel polarized ($P$-$pol$) light emitted via Lorenz–Mie scattering in laser sheet imaging. It allows obtaining an image whose intensity ratio is proportional to the statistical surface mean diameter ($D_{21}$). This is detailed as follows: the measurement is only applicable in the case of spherical droplets. According to Ref. [15], the scattered flux of light by a spherical particle $P(\theta,m,D)$ [W], measured within the solid angle $\Delta \Omega$ [sr$^{-1}]$ and from the scattering volume $\Delta V$ [m$^3]$, is linearly proportional to the incident light flux density $I_{i}$ [W m$^{-2}]$ through the scattering coefficient $\mu (\theta,m,D)$ [m$^{-1}$ sr$^{-1}]$:

The optical setup used is illustrated in Fig. 1 and consists in generating a structured laser sheet of approximately 12 cm in height. For this purpose, a continuous-wave laser beam of 532 nm (5 W maximum power) is used and converted into a laser sheet by the use of cylindrical lenses. The modulation of the light intensity is implemented by means of a diffractive optical element (DOE), acting like a light-efficient Ronchi grating. The spray used for this study is a hollow cone steady water spray, formed under atmospheric conditions. The scattering signal is recorded using a large telecentric objective (0.066X, 1 in. C-Mount TitanTL Telecentric Lens) placed at $\theta = 90^\circ$ and coupled to two sCMOS cameras (Andor, Zyla 5.5) resulting in a resolution of 0.29 mm per pixel. As shown by Ref. [20], the use of a telecentric lens allows us to remove the angular dependence of the scattered Mie signal in the field of view. In order to form the same image simultaneously on both cameras while using a single telecentric lens, a TwinCam system (CairnOptics) has been used. This system consists of an imaging relay that formed the image on a beam splitter cube and two additional imaging relays to form the image on both cameras. Polarization filters (of optical density six) have been placed in front of each camera to collect the desired polarization on each sensor. Also, in order to smooth out the ripples from the Lorenz–Mie scattered light, the images have been recorded using a long exposure time of 50 ms. Thus, several droplets are present on one pixel, resulting in a spatial average and smoothing of the intensity ripples. A zero-order, air-spaced $\lambda /2$ wave plate has been used to adjust the polarization axis of the incident beam. In order to use the polarization ratio method, the polarizer is oriented at $45^\circ$. The effect of the orientation of the incident polarization on the ratio is shown in Fig. S2 of Supplement 1. These simulated calculations also demonstrate numerically the feasibility of the technique in our experimental conditions. optical depth ($OD$) measurements of the spray are realized simultaneously, by using a third camera that records the fluorescence signal from a cell containing Eosin Y in water placed behind the spray (Fig. 1). A conventional lens (Nikkor ${\rm f} = 105$ mm) is used to obtain the same zoom level on the images.

 

Fig. 1. Scheme of the experimental setup for 3p-SLIPI polarization ratio measurement. A spatially modulated light sheet is generated by means of a diffractive optical element. The incident light is adjusted to a polarization angle of $45^\circ$ using a half wave plate. The scattering signal is collected using a telecentric lens (placed at $\theta = 90^\circ$), and the image corresponding to the parallel and perpendicular signal are formed on two cameras using a beam splitter cube and two polarizing filters. A third camera recording the signal transmission in a cuvette filled with a fluorescent dye is added to allow $OD$ measurement.

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To suppress the undesirable effects of multiple scattering and to maintain the spatial resolution offered by the detection setup, the three-phase SLIPI method (3p-SLIPI) has been implemented. The final image is generated by recording three modulated images where the phase of the sinusoidal modulation of the intensity is shifted by $2 \pi /3$. This is experimentally done by vertically displacing the DOE. The final image of light intensity $I_{SLIPI}$ is obtained using the following equation:

 

Fig. 2. SLIPI, $S$-$pol$, and $P$-$pol$ averaged images of the spray running at 50 bar are generated by recording three modulated sub-images. These modulated images are recorded with a phase shift of $120^\circ$, and only the first phase is depicted here in panel (a). (b) SLIPI images are then obtained using Eq. (6). For comparison, the images obtained with a conventional light sheet are added. The polarization ratio obtained using the conventional and SLIPI images are also illustrated in panel (c).

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In order to compare conventional and SLIPI results, the images are post-processed according to the same method: the images are thresholded above a value equal to five times the background value (intensity value outside of the spray region), and 200 images are averaged to generate the conventional and SLIPI images. Figure 2(c) presents the polarization ratio obtained with a conventional light sheet excitation and using 3p-SLIPI [Eq. (6)]. Firstly, a non-zero polarization ratio is observed in the upper part of the conventional image, in contrast to the SLIPI image. This part of the spray is not directly illuminated by the laser sheet but by multiple light scattering. As observed, this unwanted signal is well removed in the case of the SLIPI image. In addition, it can be observed that the spray symmetry is recovered using the 3p-SLIPI technique. At this point, according to Eq. (5) the ratio is proportional to the $D_{21}$. However, to obtain an absolute measurement, a calibration of the polarization ratio is necessary. This is performed using PDI (Artium instrument PDI-TK2) measurements at different vertical positions from the center of the spray to its edges ($Z_1=7$, $Z_2=9$, $Z_3=11$, and $Z4=13$ cm from the injector). Data are acquired every millimeter and are validated when 100 000 droplets are acquired for each measurement point. In order to obtain a geometrical correspondence between the PDI measurements and the polarization ratio, an image of the measurement volume is recorded on each camera. A value of the polarization ratio is assigned for each PDI measurement and is shown in Fig. 3. For the case of conventional illumination, it is observed that for an identical polarization ratio, different $D_{21}$ values are measured as a function of the height in the spray. Thus, the polarization ratio cannot be calibrated in the case of optically dense sprays when using conventional illumination. On the contrary, when using SLIPI, a single solution of the $D_{21}$ is found for the polarization ratio. A calibration curve is then determined by applying a second-order power law allowing to deduce the $D_{21}$ from the polarization ratio measurement.

 

Fig. 3. Calibration of the polarization ratio as a function of the $D_{21}$ when using (a) conventional illumination and (b) 3p-SLIPI at different distances from the nozzle indicated in Fig. 2. The fact that the relationship between polarization ratio and $D_{21}$ is not a bijective function when conventional illumination is used makes the calibration of the measurement impossible. However, when SLIPI is used, a unique solution for each $D_{21}$ is found showing the ability to calibrate the technique.

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After having calibrated the SLIPI polarization ratio, a 2D map of the absolute $D_{21}$ is obtained and presented in Fig. 4(a) (injection pressure of 50 bar). As observed, small droplets are located in the spray center while larger droplets are present on the spray edges. Measurements have been then made at two additional injection pressures (30 bar and 70 bar). $OD$ measurements have been carried out simultaneously and show the increase in spray density while increasing injection pressure [(Fig. 4(b)]. The $D_{21}$ measurements allow to observe the modification of the granulometry of the spray as a function of the injection pressure. Figure 4(c) presents the comparisons between 3p-SLIPI polarization ratio measurements and PDI measurement at a distance of 7 cm from the injector. As observed, whatever the injection pressure, the imaging data are in good agreement with those obtained by PDI. In conclusion, the SLIPI polarization ratio has been applied for the first time to the characterization of the $D_{21}$ on an entire spray having $OD$ ranging from 0.4 to 3. However, it is still possible to apply the technique to sprays with larger $OD$. However, the full characterization of the spray will require reconstruction of the image due to laser extinction along the spray. Mie intensity ripples are reduced when measurements are carried out in a polydisperse environment such as a spray. Additionally, the angular dependence of the Mie signal in the resulting image is suppressed by the use of a telecentric objective. In addition, the calibration of the polarization ratio is achievable when structured illumination is used but remains impossible with conventional light sheet imaging. In order to strengthen the calibration, comparisons with other measurement techniques such as shadowgraphy, digital inline holography [21], or planar rainbow refractometry [6] may be carried out in the future. The technique is applicable to evaporating sprays due to the fact that no dyes are added to the liquid. Instantaneous measurements may also be achievable if the polarization ratio technique is coupled with an ultra-short laser excitation (femtosecond laser) [18] or with the use of a non-fluorescent dye absorbing the laser light in the liquid.

 

Fig. 4. (a) 2D 3p-SLIPI maps of the $D_{21}$, obtained for three injection pressures 30, 50, and 70 bar. (b) $OD$ measurements as a function of the distance from the nozzle. (c) Sizing validated with PDI measurements made at a distance of 7 cm from the nozzle and compared with the 3p-SLIPI for the different investigated injection pressure. An $R^2$ value is added to the plot to assess the correspondence between PDI and imaging measurements.

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