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Interaction of pressure swirl spray with cross-flow

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Abstract

Sprays are exposed to ambient flow in most of their applications, which alters the spray behaviour. The understanding of spray performance in realistic conditions allows for nozzle improvements, process intensification, or emission reductions. The present paper investigates the pressure-swirl atomizer operating at three Reynolds numbers in the inlet ports (Re\(_{\mathrm{p}})\) 960, 1330 and 1880, subjected to low-turbulence cross-flow with aerodynamic Weber number (We) from 0 to 7.1. High-speed visualization and phase Doppler anemometry (PDA) captured the characteristic shape and trajectory of the spray, droplet dynamics, droplet collisions, and spatial droplet distributions. An empirical correlation for a mean spray trajectory prediction was developed for a wide range of flow parameters. An analytical model of the droplet trajectory was assembled and validated using PDA data. The model accurately predicts trajectories for droplets larger than 40 \(\upmu \)m. A mutual interaction of droplets was investigated. Elevated cross-flow velocity (v) increased the impact Weber number and the total droplet collision rate and enhanced the droplet mixing. A bag breakup regime was observed for the liquid to the air momentum ratio (q) lower than 300. The bag breakup modified the initial droplet velocity. The experiments imply the formation of a complicated vortex structure around the pressure swirl spray in cross-flow.

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Abbreviations

A :

Constant in the empirical equation

B :

Constant in the empirical equation

C :

Constant in the empirical equation

\(C_{\mathrm{d}}\) :

Drag coefficient of a liquid jet in cross-flow

\(C_{Ni,j}\) :

Droplet number concentration of i-th, j-th droplet group

\(d_{\mathrm{o}}\) :

Diameter of the discharge orifice

\(D_{\mathrm{p}}\) :

Hydraulic diameter of tangential inlet port

\(D_{i}\) :

Droplet diameter of i-th group

\(D_{j}\) :

Droplet diameter of j-th group

\(D_{10}\) :

Linear average value of all the drops in spray

\(D_{32}\) :

Sauter mean diameter

F :

Force on the liquid jet element

\(l_{0}\) :

Characteristic dimension

m :

Mass

\(m_{\mathrm{l}}\) :

Liquid flow rate trough exit orifice

Oh:

Ohnesorge number

\(P_{\mathrm{in}}\) :

Nozzle inlet pressure

q :

Liquid to air momentum ratio

\({\mathrm{Re}}_{\mathrm{o}}\) :

Reynolds number in exit orifice

\({\mathrm{Re}}_{\mathrm{p}}\) :

Reynolds number in tangential inlet ports

S :

Surface area of the liquid sheet

\(S_{o}\) :

Swirl number

t :

Time

\(t_{\mathrm{f}}\) :

Liquid film thickness

\(t_{Ti}\) :

Transition time of the i-the particle group through the measurement volume

\(t_{0}\) :

Characteristic time

u :

Velocity

\(u_{\mathrm{n}}\) :

Component of the cross-flow velocity normal to the liquid sheet surface

\(u_{\mathrm{p}}\) :

Liquid velocity at tangential inlet port

\(U_{\mathrm{rel}}\) :

Relative velocity between the droplet and cross-flow

v :

Cross-flow velocity

\(v_{\mathrm{rel}}\) :

Relative velocity of cross-flow velocity and liquid film velocity

\(v_{ai,j}\) :

Droplet axial velocity of i-th, j-th group

\(v_{i}\) :

Droplet velocity of i-th group

\(v_{j}\) :

Droplet velocity of j-th group

Vol:

Volume of measurement volume

\(v_{\mathrm{rel}}\) :

Relative velocity of colliding droplets

\(v_{ri,j}\) :

Droplet radial velocity of i-th, j-th group

We:

Aerodynamic Weber number

\({\mathrm{We}}_{aij}\) :

Collision Weber number in the axial direction for i-th and j-th droplet size group

\({\mathrm{We}}_{\mathrm{rel}}\) :

Relative Weber Number

\({\mathrm{We}}_{rij}\) :

Collision Weber number in the radial direction for i-th and j-th droplet size group

X :

Impact parameter

x :

Dimensionless impact parameter

\(x/d_{\mathrm{o}}\) :

Dimensionless horizontal distance from the nozzle tip

\(y/d_{\mathrm{o}}\) :

Dimensionless vertical distance from the nozzle tip

\(Z_{aij}\) :

Collision rate in the axial direction of i-th and j-th droplet size group

\(Z_{ij}\) :

Collision rate of i-th and j-th droplet size group

\(Z_{rij}\) :

Collision rate in the radial direction of i-th and j-th droplet size group

\(z/d_{\mathrm{o}}\) :

Dimensionless axial distance from the nozzle tip

\(\alpha \) :

Constant in the empirical equation 

\(\beta \) :

Constant in the empirical equation 

\(\gamma \) :

Constant in the empirical equation 

\(\varDelta \) :

Ratio of larger to smaller droplet

\(\delta \) :

Constant in the empirical equation 

\(\Delta t\) :

Measurement time duration

\(\varTheta \) :

Constant in the empirical equation 

\(\mu \) :

Liquid dynamic viscosity

\(\mu _{g}\) :

Air dynamic viscosity

\(\rho \) :

Liquid density

\(\rho _{\mathrm{AIR}}\) :

Density of air

\(\sigma \) :

Surface tension of water droplet in air

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Acknowledgements

The authors acknowledge the financial support from the Project No. LTAIN19044 funded from the program INTER EXCELLENCE (INTER–ACTION) by the Ministry of Education, Youth and Sports of the Czech Republic, Project No. GA18-15839S funded by the Czech Science Foundation and from No. FSI-S-20-6295 founded by Faculty of Mechanical Engineering, Brno University of Technology.

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Brno University of Technology, Technická 2896/2, 616 69, Brno, Czech Republic

    Ondrej Cejpek, Milan Maly & Jan Jedelsky

  2. Provyko s.r.o, 603 00, Brno, Czech Republic

    Jaroslav Slama

  3. Indian Institute of Technology Tirupati, Renigunta Road, Tirupati, 517 506, India

    Madan Mohan Avulapati

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  1. Ondrej Cejpek
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Cejpek, O., Maly, M., Slama, J. et al. Interaction of pressure swirl spray with cross-flow. Continuum Mech. Thermodyn. 34, 1497–1515 (2022). https://doi.org/10.1007/s00161-022-01142-3

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