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

Abstract

Pressure-swirl atomizers (PSAs) produce fine spray and are used in many industrial, chemical and agricultural applications of sprays in flowing environments. The study examines spray from a small low-pressure PSA exposed to low-turbulence cross-flowing air. The PSA spray was investigated experimentally using phase Doppler anemometry (PDA) and high-speed visualisation (HSV). The atomizer sprayed water into cross-flowing air at varying flow velocities. The tests were performed at a newly developed wind tunnel facility in the Spray laboratory at Brno University of Technology. PDA results contain information on the size and velocity of individual droplets in multiple positions of the developed spray (after the liquid break-up is completed). A high-speed camera (HSC) documented the complexity of the liquid discharge, the formation and break-up of the liquid film, and the spray morphology. The data is relevant to CFD engineers and scientists involved in modelling as they can highlight the crucial phenomena to be considered in numerical simulations of the disperse two-phase flow case. The case allows to study 1) liquid discharge and sheet formation, the primary break-up of the liquid sheet, 2) secondary break-up and spray formation and 3) the interaction of the sprayed liquid with surrounding air: gas–liquid mixing, droplet collisions, droplet clustering and droplet reposition.

Figure 1a: Spray image in cross flow from high-speed imaging
Figure 1b: Optical measurement using PDA (taken from ^[1])

References

↑ O. Cejpek, Design and realization of an aerodynamic tunnel for spraying nozzles [online]. Brno, 2020 [cit. 2023-04-18]. Available from: https://www.vutbr.cz/studenti/zav-prace/detail/124871. Master thesis. Brno university of Technology

Nomenclature

Symbol	Description
$A$	Cross-section
AT	Arrival time to the measurement volume
$Bo$	Bond number
$c$	Droplet concentration
$C_{D}$	Discharge coefficient
$D$	Mean droplet diameter
$d$	Diameter
$D_{10}$	Arithmetic mean diameter
$D_{20}$	Surface mean diameter
$D_{32}$	Sauter mean diameter
$F$	Force acting on a liquid element
$Fr$	Froude number
$G$	Gravitational acceleration
$K$	Nozzle dimension constant
$L$	Characteristic distance
$l_{b}$	Break-up distance
LDA1	Velocity in Z-direction
LDA4	Velocity in Y-direction
$n$	Wave number, number of samples
$Oh$	Ohnesorge number
$p$	Pressure
$Q$	Flow rate
$q$	Liquid-to-air momentum ratio
$r$	Radius
$Re$	Reynolds number
$S$	Swirl number
$Stk$	Stokes number
$SCA$	Spray cone angle
$t$	Time
TT	Transit time through the measurement volume
$Tu$	Turbulence intensity
$u$ , $v$	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
$X,Y,Z$	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
AC	Air core
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