Analysis of LIF and Mie signals from single micrometric droplets for instantaneous droplet sizing in sprays

Planar droplet sizing (PDS) is a technique relying on the assumption that laserinduced fluorescence (LIF) and Mie scattering optical signals from spherical droplets depend on their volume and surface area, respectively. In this article, we verify the validity of this assumption by experimentally analyzing the light intensity of the LIF and Mie optical signals from micrometric droplets as a function of their diameter. The size of the droplets is controlled using a new flow-focusing monodisperse droplet generator capable of producing droplets of the desired size in the range of 21 μm to 60 μm. Ethanol droplets doped with eosin dye and excited at 532 nm are considered in this study, and the individual droplets were imaged simultaneously at microscopic and macroscopic scale. The effects of laser power, dye concentration, and temperature variation are systematically studied as a function of LIF/Mie ratio in the whole range of droplet sizes. Finally, a calibration curve at tracer concentration of 0.5 vol% is deduced and used to extract the droplet Sauter mean diameter (SMD) from instantaneous images of a transient ethanol spray. This droplet size mapping is done using structured laser illumination planar imaging (SLIPI), in order to suppress the artifacts induced by multiple light scattering. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Another numerical study by Frackowiak et al. [10] confirmed this behavior as for a low absorbing mixture the LIF-signal obeyed the d 3 law, while for highly absorbing mixtures a d 2 relation was more favorable. Charalampous et al. [12] numerically investigated the d 3 and d 2 dependencies as a function of collection angle, dye concentration, and real part of the refractive index. It was concluded that for LIF the d 3 dependency was adhered to for the lowest dye (Rhodamine 6G) concentration of 0.001g/L and real refractive index variation had a very little effect. For Mie-scattering, it was found that the d 2 function depends strongly on the real refractive index, scattering angle, and dye concentration. The relation was best respected for lowest dye concentration, and scattering detection at 60° collection angle, for all droplet refractive indices. Therefore, the selection of LIF tracer and its concentration are essential to the accuracy of the LIF/Mie ratio technique. In addition, the influence of temperature and laser fluence on tracer LIF spectrum must be also characterized [15]. The effect of laser fluence on the LIF/Mie ratio is must be known for considering laser fluctuations (both shot-to-shot and spatial variations). Furthermore, the temperature of the droplets is often not known exactly. It may change during evaporation (due to heating of the droplets in the hot gas or due to cooling induced by the evaporation enthalpy). Thus, also the dye concentration will change during droplet evaporation.
In the past, tracers such as TMPD [16], naphthalene [17], Rhodamine [18,19], fluorescein [20], 3-pentanone [21,22], and triethylamine [23] have been used both in liquid and in vapor phases. Recently, the eosin dye has been found as a suitable dye tracer for LIF imaging in ethanol sprays [24][25][26]. In this work, it was also used because of its high quantum yield of ~ 0.68 in ethanol at 500 nm excitation [27]. Moreover, the quantum efficiency of the modern sCMOS image sensor is usually the highest (~ 60%) within the LIF emission spectrum of the eosin in ethanol solution (maximum at 550 nm).
To calibrate the LIF/Mie ratio, Phase Doppler Anemometry (PDA) was largely used in the past [6,[28][29][30][31][32][33][34]. However, PDA instruments measure temporally varying spray drop sizes at a single point, which is convenient for time-averaged measurements. Using a monodispersed droplet generator instead allows extracting the single-shot LIF/Mie ratio [35]. This second approach is more adequate for the calibration of instantaneous images. However, despite many reported investigations on LIF/Mie ratio calibration using monodisperse droplet generators, a thorough experimental study on d 3 dependence of LIF, and d 2 dependence of Mie is still missing for d ≤ 50 µm (which is relevant for engine sprays) along with varying influencing parameters such as droplet diameter, dye concentration, laser power, and droplet temperature etc. For example, Park et al. performed microscopic calibration of LIF/Mie ratio with 20 images averaged for each droplet of fluorescing unleaded gasoline produced in 50-300 µm size range [36]. Le Gal et al. reported macroscopic calibration of LIF/Mie ratio from the individual droplets of self-fluorescent 'mineral spirit' produced in the sizes range of 50-180 µm [2]. These droplet size ranges are not satisfactory for most cases of atomizing sprays, especially those used in for combustion applications.
In this article, we report simultaneous microscopic and macroscopic LIF/Mie measurements from a novel flow-focusing monodisperse droplet generator, for accurate calibration of instantaneous droplet sizing measurement. The experimental investigation is performed as follows: (i) Using the microscopic/macroscopic setup, the LIF and Mie signals are recorded simultaneously from each individual droplet of dye-doped ethanol to respectively evaluate their d 3 and d 2 dependence for 21 µm ≤ d ≤ 60 µm. (ii) The dependence of the LIF/Mie ratio on laser energy, dye concentration and the temperature is thoroughly investigated, in particular also to assess possible errors in the results due to variations or uncertainties in the process parameters. (iii) The derived calibration curve is used for sizing droplets in an ethanol DISI spray on a single-shot basis. This needs single droplet calibration data as PDA only provides averaged information in a limited SMD-range. To face measurement errors introduced by multiple light scattering while generating instantaneous spray images, the two-phase SLIPI (2p-SLIPI) approach [24,26]  allowing for the best possible signal to noise ratios at constant laser power. All optical components such as optical filters, ND filters, and beam splitters are characterized by a spectrometer (Perkin Elmer, UV/VIS Spectrometer, type Lambda 40). The macroscopic objective system is equipped with a 135 mm objective (Pentagon 2.8/135). The pixel resolution achieved in this case is 0.15 pixels/µm. This setup is fixed just opposite to the microscopic imaging system to perform simultaneous macroscopic evaluations synchronized with the microscopic detection. It is also equipped with the identical optical filters, beam splitter used in the microscopic objective system.

Monodisperse droplet generator
The monodisperse droplet generator is made by MSP Corp (Type 1530) and is reported to generate droplet of size ranging between 15 and 150 µm for methanol and water using the flow focusing concept [37]. This enables a rough adjustment of the average droplet size without any modification of the droplet generator. In this device, the droplet size is changed by fuel mass flow and piezo frequency in contrast to the orifice droplet generators. The flow focusing air and the fuel are kept at 298 K to enable constant conditions during the measurements at an ambient pressure of 0.1 MPa. The temperatures of the whole setup are monitored by integrated thermocouples (type K). The downstream distance between the droplet generator orifice and droplet measurement plane is between 3 and 7 mm depending on the droplet size.

CVC-chamber
The constant volume combustion (CVC) chamber is used to investigate DISI-sprays under engine-like conditions. It is operated with dry air at 0.2 MPa pressure and 298 K temperature, which represents a high load engine operating point. The ambient temperature in the CVC and the fuel temperature are set to 298K. The injector is heated by an integrated fluid-based heating circulator. The temperature of the nozzle tip is monitored with a highly sensitive micro sheathed thermocouple (0.25 mm diameter, type K). It is assumed that the fuel adopts the injector temperature due to the long residence time of the fuel in the injector (the injection duration is relatively short (1800 μs) for an injection repetition rate of 0.5 Hz. The chosen temperature range is also relevant for cold and warm start conditions of the engine sprays. The injection pressure is set to 16 MPa. A 5-hole DISI-injector (Bosch GmbH, Germany) is utilized, where one jet is centrally separated from others allowing unrestricted optical access. The physical parameters of the fuel ethanol are listed in Table 1. It should be noted that the dye concentration within the droplet could change due to evaporation. However, the studied conditions at moderate ambient temperatures lead to low evaporation rates. Thus, a strong variation of the dye concentration can be excluded. The temperature dependence of the LIFsignal is negligible at the investigated conditions. A detailed uncertainty analysis in the measurement due to changes in the dye concentration and temperature dependence of LIF can be found in [34]. For a wide temperature range, the LIF/Mie-ratio dependency will be addressed in the subsequent sections.  The LIF signal shows a volumetric trend and in our experiments, it is not very sensitive to the variation of the detection angle. The fitting curve roughly follows the d 3 dependence predicted by the literature [6][7][8][9][10][11][12]14]. It can be described by the following equation (power law) at standard conditions: 3 The Mie-signal fitting curve shows a good agreement with the d 2 dependence according to the literature. Nevertheless, an exponent greater than two is also reported by Le Gal et al. [2] due to MDRs. The corresponding LIF/Mie ratio follows the function: The fitting curve in this study roughly exhibits the d-dependence according to the hypothesis of LIF/Mie droplet sizing approach [2,6]. In Table 2, the respective average pre-factors, exponents and standard deviations of the three fitting curves (LIF, Mie, LIF/Mie) are summarized for the reference conditions (293 K, 0.5 vol % eosin). Here, the uncertainty for the pre-factor "A" is given by the geometric standard deviation, i.e. the 1-σ interval is from [A*σ; A/σ]. For the exponent b, the uncertainty is the arithmetic standard deviation, i.e. the 1- The average values and standard deviation were calculated from five individual calibration curves. The standard errors of the exponents show a lower variation for the LIF signal fit in comparison to the Mie signal fit. This behavior is caused by the detection angle dependence of the Mie signal in contrast to the LIF signal, which results in a wider signal distribution (see also discussion in section 6). In Fig. 4 the LIF/Mie ratio fitting curve is illustrated for the reference conditions with the corresponding experimental data. The uncertainty of the calibration data based on the standard deviation is plotted as well. Here the 1-σ uncertainties are depicted, resulting in the range of 5.5% for a droplet size of 30 µm. Furthermore, histograms of the LIF/Mie ratio distribution at certain droplet sizes (± 1 µm) are given in Fig. 5. The histograms of certain experimental data showed a log-normal behavior (see section 3.1).

Compari
For the macro the droplet g calibration an light sheet wa generator. Fig  recorded with Figure 7 shows the resulting LIF/Mie ratio intensity curves as a function of droplet diameter for both micro and macro detections. The corresponding curve fitting parameters are given in Table 3. In both cases, the ratio curves show an approximately linear dependence on droplet diameter. There are some deviations between the two detections, which could be due to the lower spatial resolution in case of macroscopic imaging and opposite light collection angle. Nevertheless, the effects of the decreased resolution of the macroscopic detection, and the detection angle dependence of the Mie signal are found negligible for the ratio calibration in the existing setup. The macroscopic measurements are more realistic for the planar droplet sizing in sprays, therefore, results from the macroscopic investigations are only discussed further in this article. The macroscopic calibration curve for ethanol with 0.5 vol% eosin at 0.1 MPa, 293 K and 100% laser power is used as a reference in the following investigations. Fig. 7. The micro and macro (reference marked red) LIF/Mie ratio plotted as a function of droplet diameter. The deviations between the two detections is due to loss of resolution in macroscopic system and opposite collection angle.

Effects of laser energy/fluence
The effects of laser energy variation are investigated at constant dye concentration (0.5 vol %) and temperature (293 K) for the macroscopic LIF/Mie ratio. Three output laser powers of 75%, 100% and 125% corresponding to laser fluences of 39.8 mJ/cm 2 , 53.0 mJ/cm 2 and 66.3 mJ/cm 2 are investigated. The laser power variations are listed in Table 4.

Single-sh
For the calibr resolve a sing in Fig. 1) is fi Fig. 1) needs LIF/Mie ratio variation in L 10. Effects of liq ed red) at constan erature of 333 K tions, the dye rema ases but Mie sig oration is negligibl increase.
fic parameters e 5. In general l fit in compar nsity in LIF co section 6).

Discussio
In this section are discussed and it is very follow a pot conditions of experiments, different. Thi angular smoo intensity osci droplet size f aperture of 5. The specific p The simulation was performed using a Matlab-algorithm based on the one presented by Bohren and Huffmann [46]. For the curve fitting the same routines as for the experimental data are used. In principle, the Mie-scattering calculation still shows the above-mentioned strong intensity fluctuations. However, the highly angle dependent Mie-signal gets smoothened by the averaging over the detection angle of the camera. In general, the fitting curves of the calculated and the experimental data show a good agreement. For a 30 µm droplet, the deviation is in the range of 8%. Thus, this smoothing effect confirms the chosen postprocessing algorithm according to section 3.1 based on a fitting to a potential function. Furthermore, Hofeldt et al. [44] also concluded that the integration over a continuous distribution in wavelength or diameter space will smoothen the scattered light intensities of the individual particles. Similar conclusions are also reported by Charalampous et al. [12]. Another experimental technique to reduce intensity oscillations within the Mie-scattering is the usage of femtosecond lasers as reported in [47] which also relies on the above mentioned effects.

Summary and conclusion
Monodisperse droplets of ethanol doped with eosin as a LIF tracer were studied with a long range microscope system. The droplets were produced using the flow-focusing mechanism, which results in droplets with high sphericity and a diameter ranging between 21 and 60 µm (although much larger droplets can be generated), which is relevant for engine spray conditions. The experimental data of the individual LIF, Mie signals and LIF/Mie ratio is fitted according to the power-law function I = a · d b . The Mie-scattering of individual droplets is highly sensitive to the angle of detection and the droplet size and does actually not follow a potential trend. A calculation of the Mie scattering intensity showed strong intensity oscillations of the Mie-signal with droplet size. However, the chosen detection angle smoothens the signal oscillations and allows the usage of a potential fitting procedure. Thus dye eosin with 0.5 vol % in ethanol showed a good agreement with the d 3 -and d 2dependence relation of the LIF-and Mie-signals, respectively. These microscopic measurements were simultaneously performed in combination with another macroscopic objective, and for the comparison between the two detection schemes a total number of 33,510 droplets were evaluated for the reference experiment.
The macroscopic investigations of the droplet generator can be summarized as follows: (i) There is very minor influence of laser power variation (at constant dye concentration and liquid temperature) on the LIF/Mie ratio. (ii) The variation of the dye concentration (at constant laser power and liquid temperature) showed a strong dependence of the LIF signal and a weak effect on Mie-signal on the amount of dye within the droplets leading to strong dependence on LIF/Mie ratio. Thus, for reliable droplet sizing with the current investigation, a constant dye concentration is required (i.e. evaporation and dye enrichment in the droplet should be reduced). (iii) The LIF/Mie ratio increases with an increase in fuel temperature. The larger variation in the ratio is observed at 333 K in comparison to temperatures at 253 K and 293 K. The investigated maximum temperature of 333 K is extremely high for the utilized fuel. This leads to an increase of the dye concentration within the droplets due to evaporation of ethanol. This is because the dye used is a solid and remains in the droplet. Accordingly, the technique is not applicable for high temperature environments and high evaporation rates. If the requirement and conditions such as constant dye concentration, and almost iso-thermal fuel temperatures are respected, the macroscopic LIF/Mie ratio of the droplet generator can be directly used to calibrate SLIPI-LIF/Mie ratio in other technical and IC engine sprays. In this case, the 1-σ uncertainty of the calibration data was determined to be 5.5% for droplet sizes of 30 µm.
The results from the spray measurement are as follows: (i) Instantaneous 2D mapping of droplet SMD field is extracted with the investigated method. (ii) Droplet SMD for the probed DISI spray varies between 5 to 50 µm at 293 K liquid temperature. The droplet SMD at the radial positions in spray edges are in the range of 5 µm to 40 µm. The droplets at the spray front are in the range 25-50 and higher, which is mainly due coalescence mechanisms. It is important to mention that the use of different fuels might affect the LIF/Mie ratio. For example, previous study of using butanol and ethanol as base fuels showed strong deviations of the LIF/Mie ratio calibration curves based on PDA calibration [34]. Therefore, effects of the fuel on LIF/Mie ratio will be part of future studies using droplet generator experiments that will be addressed in a subsequent publication.
Finally, the LIF/Mie ratio calibration setup in combination with SLIPI-based droplet sizing can measure droplet SMD in much faster and more reliable manner than in comparison to conventional PDS and PDA measurements. The setup can be used for layer-wise 2D and averaged 3D mapping of SMD in engine sprays and the other technical sprays employed for industrial applications.