Instability of Viscoelastic Annular Liquid Jets in a Radial Electric Field

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
Lu-jia Liu ◽  
Li-peng Lu
Keyword(s):  
Growth Rate ◽  
Electric Field ◽  
Weber Number ◽  
Radial Electric Field ◽  
Wave Number ◽  
Liquid Jets ◽  
Instability Analysis ◽  
Temporal Instability ◽  
Spatiotemporal Instability ◽  
The Absolute

Research on the instability of viscoelastic annular liquid jets in a radial electric field has been carried out. The analytical dimensionless dispersion relation between unstable growth rate and wave number is derived by linear stability analysis. The Oldroyd B model was used to describe the viscoelastic characteristics of the viscoelastic fluids. Considering that the para-sinuous mode has been found to be always dominant in the jet instability, the effects of various parameters on the instability of viscoelastic annular liquid jets are examined only in the para-sinuous mode. Nondimensionalized plots of the solutions exhibit the stabilizing or destabilizing influences of electric field effects and the physical properties of the liquid jets. Both temporal instability analysis and spatiotemporal instability analysis were conducted. The results show that the radial electric field has a dual impact on viscoelastic annular liquid jets in the temporal mode. Physical mechanisms for the instability are discussed in various possible limits. The effects of Weber number, elasticity number, and electrical Euler number for spatiotemporal instability analysis were checked. As the Weber number increases, the liquid jet is first in absolute instability and then in convective instability. However, the absolute value of the absolute growth rate at first decreases, and then increases with the increase of We, which is in accordance with temporal instability analysis. Comparisons of viscoelastic annular jets with viscoelastic planar liquid jets and cylindrical liquid jets were also carried out.

Linear Instability Analysis of an Annular Liquid Sheet With Inner and Outer Gas Flow

2009 ◽  
Author(s):  
Fathollah Ommi ◽  
Seid Askari Mahdavi ◽  
S. Mostafa Hosseinalipour ◽  
Ehsan Movahednejad
Keyword(s):  
Growth Rate ◽  
Dispersion Equation ◽  
Liquid Sheet ◽  
Linear Instability ◽  
Wave Number ◽  
Unstable Wave ◽  
Instability Analysis ◽  
Air Stream ◽  
Linear Instability Analysis ◽  
Air Streams

A linear instability analysis of an inviscid annular liquid sheet emanating from an atomizer subjected to inner and outer swirling air streams has been carried out. The dimensionless dispersion equation that governs the instability is derived. The dispersion equation solved by Numerical method to investigate the effects of the liquid-gas swirl orientation on the maximum growth rate and its corresponding unstable wave number that it produces the finest droplets. To understand the effect of air swirl orientation with respect to liquid swirl direction, four possible combinations with both swirling air streams with respect to the liquid swirl direction have been considered. Results show that at low liquid swirl Weber number a combination of co-inner air stream and counter-outer air stream has the largest most unstable wave number and shortest breakup length. The combination of inner and the outer air stream co-rotating with the liquid has the highest growth rate.

STUDY ON ELECTROHYDRODYNAMIC CAPILLARY INSTABILITY OF VISCOELASTIC FLUIDS WITH RADIAL ELECTRIC FIELD

2014 ◽  
Vol 06 (04) ◽  
pp. 1450037
Author(s):  
MUKESH KUMAR AWASTHI
Keyword(s):  
Dispersion Relation ◽  
Electric Field ◽  
Radial Electric Field ◽  
Critical Value ◽  
Linear Analysis ◽  
Wave Number ◽  
Dual Effect ◽  
Capillary Instability ◽  
Viscous Potential Flow ◽  
The Stability

We study the linear analysis of electrohydrodynamic capillary instability of the interface between a viscous fluid and viscoelastic fluid of Maxwell type, when the phases are enclosed between two horizontal cylindrical surfaces coaxial with the interface, and when fluids are subjected to the radial electric field. Here, we use an irrotational theory known as viscous potential flow (VPF) theory in which viscosity enters through normal stress balance but shearing stresses are assumed to be zero. A quadratic dispersion relation that accounts for the growth of axisymmetric waves is obtained and stability criterion is given in terms of a critical value of wave number as well as electric field. It is observed that the radial electric field has dual effect on the stability of the system.

Theoretical Analysis of Surface Waves on Liquid Jets in Crossflows with Deformation

2013 ◽  
Vol 681 ◽  
pp. 152-157
Author(s):  
Shao Lin Wang ◽  
Yong Huang ◽  
Fang Wang ◽  
Zhi Lin Liu
Keyword(s):  
Growth Rate ◽  
Theoretical Analysis ◽  
Surface Waves ◽  
Cross Section ◽  
Aerodynamic Force ◽  
Linear Instability ◽  
Wave Number ◽  
Liquid Jets ◽  
Liquid Jet ◽  
The Cross

Liquid jets in cross air flows are widely used and play an important role in propulsion systems, such as ramjet combustors. Surface waves on the liquid jets in gaseous crossflows have been observed in numerous experiments. Especially for lower gas Webber number, liquid jets breaks up due to the surface waves. However compared with injecting into gas coaxial flow, liquid jet will be deformed in crossflow due to the transverse aerodynamic force. Deformation of jet is investigated by analyzing stress force equilibrium of the cross-section. Though linear instability analysis, dispersion relation and growth rate of surface waves of liquid jet with deformation were derived. According to the present theoretical analysis, the cross-section shape can be deformed to stable ellipse only if the gas velocity was lower than 9m/s for 1mm diameter jet. The maximum growth rate of disturbances takes place at wave number 0.7 approximately, and it will decrease with increasing the jet diameter. The range of instable wave number will expand and the most instable wave number will grow for the deformed jets.

Saturation mechanism and generated viscosity in gravito-turbulent accretion disks

2020 ◽  
Vol 640 ◽  
pp. A53
Author(s):  
L. Löhnert ◽  
S. Krätschmer ◽  
A. G. Peeters
Keyword(s):  
Growth Rate ◽  
Numerical Simulations ◽  
Accretion Disks ◽  
Gravitational Instability ◽  
Turbulent Viscosity ◽  
Radial Distance ◽  
Maximum Growth ◽  
Wave Number ◽  
Radiative Cooling ◽  
Mixing Length

Here, we address the turbulent dynamics of the gravitational instability in accretion disks, retaining both radiative cooling and irradiation. Due to radiative cooling, the disk is unstable for all values of the Toomre parameter, and an accurate estimate of the maximum growth rate is derived analytically. A detailed study of the turbulent spectra shows a rapid decay with an azimuthal wave number stronger than ky−3, whereas the spectrum is more broad in the radial direction and shows a scaling in the range kx−3 to kx−2. The radial component of the radial velocity profile consists of a superposition of shocks of different heights, and is similar to that found in Burgers’ turbulence. Assuming saturation occurs through nonlinear wave steepening leading to shock formation, we developed a mixing-length model in which the typical length scale is related to the average radial distance between shocks. Furthermore, since the numerical simulations show that linear drive is necessary in order to sustain turbulence, we used the growth rate of the most unstable mode to estimate the typical timescale. The mixing-length model that was obtained agrees well with numerical simulations. The model gives an analytic expression for the turbulent viscosity as a function of the Toomre parameter and cooling time. It predicts that relevant values of α = 10−3 can be obtained in disks that have a Toomre parameter as high as Q ≈ 10.

scholarly journals Investigation of turbulence rotation and radial electric field in the island divertor and plasma edge at W7-X

2019 ◽  
Vol 61 (5) ◽  
pp. 054003 ◽  
Author(s):  
A Krämer-Flecken ◽  
X Han ◽  
T Windisch ◽  
J Cosfeld ◽  
P Drews ◽  
...  
Keyword(s):  
Electric Field ◽  
Radial Electric Field ◽  
Plasma Edge
Sign in / Sign up

Export Citation Format

Share Document