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Measurement data/results

Numerical data from the PDA measurements, together with image type data from HSC are available for this test case.

Measurement data from PDA

Measurement data exported directly from the PDA software are provided as a set of .txt files in PDA directory. These contain raw, unprocessed information exported from the PDA system. The data are arranged in directories, where each directory contains a single airflow velocity case with a number of files for all the measured positions (Figure 10). Each data file contains raw information from a single-point measurement. The first five rows give the experiment description. Here only the fourth row is important, which documents the measurement position. The following rows document individual droplets sampled; each droplet is reported on a separate line. The first column addresses the sample number (Row#), followed by its arrival time to the measurement volume (AT, [ms]), the transit time through the measurement volume (TT, [µs]), velocity in Z-direction (LDA1, [m/s]), velocity in Y-direction (LDA4, [m/s]), a phase shift between photomultipliers 1 and 2 (U12, [°]), a phase shift between photomultipliers 1 and 3 (U13, [°]), and droplet diameter (D, [µm]).
Of practical importance are the LDA1 and LDA4, which give information on the droplet velocity in 2D and can be used for the calculation of droplet velocity magnitude (in 2D) and its motion direction. The D allows the calculation of droplet surface and volume.
The data in rows can be analysed and filtered in different ways to produce the size and velocity histograms, calculate the mean velocity or mean diameters, droplet concentration or other statistical moments as described in ^[1]. The velocity of the smallest droplets allows for estimating the local air velocity ^[2].
The AT adds the temporal information, which is useful for the analysis of steadiness ^[3], ^[4] and mean and turbulent kinetic energies in the spray ^[5] or frequency spectra. The columns of U12 and U13 give system information from photomultipliers which are primarily used by the measurement system for the calculation of D, and following the relation between U12 and U13 allows for droplet size validation to be done during the measurement ^[6]. It has no direct data assimilation for common users but might be used by advanced users if more sophisticated processing is required.
These multiple files of raw data were processed into Excel spreadsheet processed_data.xlsx (in the same directory) to show the statistical data in each measurement position (columns A, B and C), number of droplets sampled (D), velocity validation (E), mean droplet velocity in Z-direction [m/s] (F), mean droplet velocity in Y-direction [m/s] (G), spherical validation (H), diameters $D_{10}$ (I), $D_{20}$ (J), $D_{32}$ (K), and relative diameter span factor, $RSF$ (L). The mean droplet velocity $v_{m}={\sum _{i=1}^{n}v_{i}/n}$ , and diameters were calculated according to Equation 4. The relative span factor

RSF={\frac {D_{v0.9}-D_{v0.1}}{D_{v0.5}}}

(15)

characterises the droplet size span with respect to the median diameter. The subscript v symbolizes the volumetric fraction and values $D_{v0.1}$ , $D_{v0.5}$ (mass mean diameter, $MMD$ ), and $D_{v0.9}$ represent a diameter below which volumetric fractions 0.1, 0.5 and 0.9 of the total droplet volume in measurement point occurs; see Figure2b.
The PDA results are processed to show the variation of mean droplet velocity $v_{m}$ and droplet diameter $D_{20}$ along the Y-axis for one selected X and Z position in Figure 14. Y-axis profiles of $D_{10}$ and $D_{32}$ are similarly shown in Figure 10 of ^[7]. That paper also reports 2D surface plots of $D_{10}$ or Y-axis profiles of droplet counts and droplet collision rates along the Y-axis for varying $q$ values in Figure 11, 12 and 13, respectively.

Figure 14a: Profiles of mean velocity along the Y-axis
Figure 14b: $D_{20}$ distribution measured in $Z/d_{o}$ = 36 and $X/d_{o}$ = 0 for different $q$ values

Image recordings with HSC

The two HSC recordings were made with two sizes of the region of interest, arranged in HS directory. The first one with a larger field of view resolved the spray trajectory and spray shape. Liquid structures starting from liquid discharge at the orifice and spanning to the developed spray can be observed here. The second one focused on the liquid sheet morphology in detail. These results are sorted out in directories named according to nozzle type_Pin_cross-flow velocity_camera mark (e.g. SIMPLEX_5bar_vel8.0_C001H001S0001 marks this simplex atomizer operated at an injection pressure $p_{in}=$ 5 bar and cross-flow velocity of 8 m/s). Each file contains 4000 high-speed images numbered from 1 to 4000. Images are saved in the TIFF format. Each directory contains a .cih file (which can be opened in a txt editor) documenting the HSC setup. E.g. camera frame rate at line 16, shutter speed at line 17 and image width, and height at lines 24 and 25, respectively.
The data from HSC were processed to estimate mean spray boundaries and their standard mean deviation for different Re and We cases in Figure 6 of ^[7] and illustrative Figure 12. Figure 15 of ^[7] documents the time sequence of the bag break-up.

References

↑ F. Lizal, J. Jedelsky, K. Morgan, K. Bauer, J. Llop, U. Cossio, S. Kassinos, S. Verbanck, J. Ruiz-Cabello, A. Santos, E. Koch, and C. Schnabel, European Journal of Pharmaceutical Sciences 113, 95 (2018)
↑ E. Rácz, M. Malý, J. Jedelský, and V. Józsa, International Journal of Multiphase Flow 157, 104260 (2022)
↑ C. F. Edwards and K. D. Marx, Atomization and Sprays 5 (4-5), 435 (1995)
↑ J. T. K. Luong and P. E. Sojka, Atomization and Sprays 9 (1), 87 (1999)
↑ J. Jedelsky, M. Maly, N. Pinto del Corral, G. Wigley, L. Janackova, and M. Jicha, International Journal of Heat and Mass Transfer 121, 788 (2018)
↑ H.-E. Albrecht, Laser doppler and phase doppler measurement techniques. (Springer, Berlin ; New York, 2003)
↑ ^7.0 ^7.1 ^7.2 O. Cejpek, M. Maly, J. Slama, M. M. Avulapati, and J. Jedelsky, Continuum Mechanics and Thermodynamics 34 (6), 1497 (2022)