Abstract
Atomization is the process of breaking down of bulk liquid into small droplets due to the action of several forces such as centrifugal, aerodynamic, viscous and surface tension forces. In twin-fluid atomizers, gases are injected at high velocities to further assist the disintegration process of the liquid sheet. Though the effect of viscosity is mostly ignored in instability studies due to high fluid velocity assumption, it may still have a stabilizing or destabilizing effect on the liquid sheet depending upon the flow conditions. The present study performs a linear instability analysis of viscous liquid sheet moving in-between two gas streams of nonzero equal velocities. The effect of gas velocity on maximum growth rate and critical wave number has been presented for a range of gas to liquid density ratios and liquid Weber numbers. While gas velocity has a major destabilizing effect on the liquid sheet, gas density and liquid Weber number mostly influence the critical wave number at low gas velocities.
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Abbreviations
- u l :
-
Liquid velocity (m/s)
- \( u_{1} \) :
-
Inviscid velocity component of liquid (dimensionless)
- \( u_{2} \) :
-
Viscous velocity component of liquid (dimensionless)
- \( u_{g} \) :
-
Gas velocity (m/s)
- U :
-
Gas to liquid velocity ratio (dimensionless)
- a :
-
Sheet thickness (m)
- t :
-
Time (s)
- k :
-
Wave number (dimensionless)
- Re:
-
Reynold’s number (dimensionless)
- We:
-
Weber number (dimensionless)
- p :
-
Pressure (dimensionless)
- \( \rho_{l} \) :
-
Liquid density (N/m2)
- μ :
-
Dynamic liquid viscosity (kg/m s)
- \( \rho_{g} \) :
-
Gas density (N/m2)
- \( \rho \) :
-
Gas to liquid density ratio (dimensionless)
- \( \varphi \) :
-
Velocity potential (dimensionless)
- ψ :
-
Stream function (dimensionless)
- Ï„ :
-
Normal stress (dimensionless)
- ω :
-
First-order complex root (dimensionless)
- β :
-
Growth rate (dimensionless)
- α :
-
Angular frequency (dimensionless)
- l :
-
Liquid flow
- g :
-
Gas flow
- 1:
-
Inviscid liquid velocity component
- 2:
-
Viscous liquid velocity component
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Dasgupta, D., Nath, S., Bhanja, D. (2020). Linear Instability Analysis of Viscous Planar Liquid Sheet Sandwiched Between Two Moving Gas Streams. In: Biswal, B., Sarkar, B., Mahanta, P. (eds) Advances in Mechanical Engineering. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-0124-1_5
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DOI: https://doi.org/10.1007/978-981-15-0124-1_5
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