Latest revision as of 08:24, 17 August 2023

Pressure-swirl spray in a low-turbulence cross-flow

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 was for each direction calculated separately as $v_{Ym}={\sum _{i=1}^{n}v_{Yi}/n}$ , $v_{Zm}={\sum _{i=1}^{n}v_{Zi}/n}$ , and diameters were calculated according to Equation 4. The magnitude of mean droplet velocity $v_{m}$ was calculated from the $v_{Ym}$ and $v_{Zm}$ components. 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 the magnitude 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 (the Z positions are reported in the Figure relative to the exit orifice diameter value $d_{o}=$ 0.42 mm).

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. Figures 15 and 16 present the statistical PDA results of $v_{m}$ and $D_{20}$ in the form of contour plots. They are shown at $Z/d_{o}$ = 35.7 for varying $u_{cf}$ velocities (Figure 15) and at the three Z planes where the measurements were taken for (Figure 16).

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

Figure 15: Contour plots of $D_{20}$ (top) and $v_{m}$ (bottom) for different $u_{cf}$ at $Z/d_{o}$ = 36 (Z = 15 mm)

Figure 16: Contour plots of $D_{20}$ (top) and $v_{m}$ (bottom) for different Z planes at $u_{cf}$ = 32 m/s

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 17 shows instant spray images for different cross-flow velocities to illustrate the influence of the cross-flow. And Figure 15 of ^[7] documents the time sequence of the bag break-up.

Figure 17: Instant spray images for different cross-flow velocities, the configuration of HSC and view direction according to Figure 11

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)

Nomenclature

Symbol	Description
$A$	Cross-section
AT	Arrival time to the measurement volume
$Bo$	Bond number; $Bo=\Delta \rho gD^{2}/\sigma$
$c$	Droplet concentration
$C_{D}$	Discharge coefficient; $C_{D}=Q_{l}{\sqrt {\rho }}_{l}/(A_{o}{\sqrt {2p_{in}}})$
$D$	Mean droplet diameter
$d$	Diameter
$D_{10}$	Arithmetic mean diameter; $D_{10}={\sum _{i=1}^{n}d_{i}/n}$
$D_{20}$	Surface mean diameter; $D_{20}={\sqrt {\sum _{i=1}^{n}d_{i}^{2}/n}}$
$D_{32}$	Sauter mean diameter; $D_{32}={\sum _{i=1}^{n}d_{i}^{3}/\sum _{i=1}^{n}d_{i}^{2}}$
$F$	Force acting on a liquid element
$Fr$	Froude number; $Fr={\frac {u}{\sqrt {gL}}}$
$G$	Gravitational acceleration
$k$	Nozzle dimension constant; $k=A_{in}/4r_{c}r_{o}$
$L$	Characteristic distance or dimension
$l_{b}$	Break-up distance
LDA1	Velocity in Z-direction
LDA4	Velocity in Y-direction
$n$	Wave number, number of samples
$Oh$	Ohnesorge number; $Oh={\sqrt {We}}/\operatorname {Re}$
$p$	Pressure
$Q$	Volumetric flow rate
$q$	Liquid-to-air momentum ratio; $q={\frac {\rho _{l}u_{l}^{2}}{\rho _{g}u_{cf}^{2}}}$
$r$	Radius
$Re$	Reynolds number; $Re=\rho uL/\mu$
$S$	Swirl number; $S={\frac {wr_{c}}{u_{o}r_{o}}}$
$Stk$	Stokes number; $Stk=\rho _{l}{\bar {D}}_{p}^{2}\Delta {\bar {v}}/18\mu _{g}L$
$SCA$	Spray cone angle
$t$	Time
TT	Transit time through the measurement volume
$Tu$	Turbulence intensity; $Tu=v_{rms}/{\bar {v}}$
$u$ , $v$	Velocity
U12	Phase shift between photomultipliers 1 and 2
U13	Phase shift between photomultipliers 1 and 3
$w$	Swirl component of the velocity
$We$	Weber number; $We=\rho u^{2}L/\sigma$
$X,Y,Z$	Cartesian coordinates

Greek symbols
$\Delta v$	Difference between the gas and droplet velocity
$\eta _{n}$	Nozzle efficiency
$\mu$	Dynamic viscosity
$\rho$	Liquid density
$\sigma$	Surface tension

Indices
$a$	Aerodynamic
$ac$	Air core
$c$	Swirl chamber
$cf$	Cross-flow
$Cr$	Critical
$D$	Droplet
$g$	Gas
$i$	Index number of a droplet
$in$	Atomizer inlet (inlet ports)
$l$	Liquid
$m$	Inertia
$n$	Total number of droplets
$o$	Exit orifice
$p$	Pressure
$r$	Relative
$v0.1,v0.5,v0.9$	Volumetric fractions 0.1, 0.5 and 0.9 of the total droplet volume
$\mu$	Related to dynamic viscosity
$\sigma$	Related to surface tension
$\tau$	Liquid film thickness

Abbreviations
fps	Frames per second
GT	Gas turbine
HSC	High-speed camera
HSV	High-speed vizualization
LDA	Laser Doppler anemometry,
PDA	Phase Doppler anemometry
PSA	Pressure-swirl atomizer
RSF	Relative diameter span factor