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Fundamental Issues and Canonical Flows

# Investigation of the Linear Stability Problem of Electrified Jets, Inviscid Analysis

[+] Author and Article Information
Serkan Özgen, Oguz Uzol

Professor Department of Aerospace Engineering,  Middle East Technical University, 06800, Ankara, Turkey e-mail: sozgen@ae.metu.edu.trAssistant Professor Department of Aerospace Engineering,  Middle East Technical University, 06800, Ankara, Turkey e-mail: uzol@ae.metu.edu.tr

J. Fluids Eng 134(9), 091201 (Aug 21, 2012) (9 pages) doi:10.1115/1.4007157 History: Received February 15, 2012; Revised June 06, 2012; Published August 21, 2012; Online August 21, 2012

## Abstract

The instability characteristics of a liquid jet discharging from a nozzle into a stagnant gas are investigated using the linear stability theory. Starting with the equations of motion for incompressible, inviscid, axisymmetric flows in cylindrical coordinates, a dispersion relation is obtained, where the amplification factor of the disturbance is related to its wave number. The parameters of the problem are the laminar velocity profile shape parameter, surface tension, fluid densities, and electrical charge of the liquid jet. The dispersion relation is numerically solved as a function of the wave number. The growth of instabilities occurs in two modes, the Rayleigh and atomization modes. For $rWe<1$ (where $We$ represents the Weber number and $r$ represents the gas-to-liquid density ratio) corresponds to a Rayleigh or long wave instability, where atomization does not occur. On the contrary, for $rWe>>1$ the waves at the liquid-gas interface are shorter and when they reach a threshold amplitude the jet breaks down or atomizes. The surface tension stabilizes the flow in the atomization regime, while the density stratification and electric charges destabilize it. Additionally, a fully developed flow is more stable compared to an underdeveloped one. For the Rayleigh regime, both the surface tension and electric charges destabilize the flow.

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## Figures

Figure 1

Flow geometry

Figure 2

Velocity profiles used in the parametric study

Figure 3

Effect of the velocity profile parameter on the amplification rates of the atomization mode of instability (r=0.01,We=10,000,E1=0)

Figure 4

Effect of the Weber number on the amplification rates of the atomization mode of instability (r=0.01,We=10,000,E1=0)

Figure 5

Amplification rates of the Rayleigh and atomization modes of instability as a function of the Weber number (r=0.01,b=0.2,E1=0)

Figure 6

Effect of the density ratio on the amplification rates of the atomization mode of instability (We=10,000,b=0.2,E1=0)

Figure 7

Effect of the electrical charges on the amplification rates of the atomization mode (r=0.01,We=10,000,b=0.2)

Figure 8

Effect of electric charges on the amplification rates of the Rayleigh mode (r=0.01,We=1,b=0.2)

Figure 9

Critical values of the velocity profile parameter for the unconditional stability of the atomization mode (r=0.01)

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