scholarly journals Weakly nonlinear instability of a viscous liquid jet

2017 ◽  
Author(s):  
Günter Brenn ◽  
Marie-Charlotte Renoult ◽  
Innocent Mutabazi
Keyword(s):  
Viscous Liquid ◽  
Initial Perturbation ◽  
Wave Number ◽  
Liquid Jet ◽  
Drop Formation ◽  
Liquid Viscosity ◽  
Nonlinear Stability Analysis ◽  
Numerical Work ◽  
Weakly Nonlinear ◽  
Small Wave Number

Aweakly nonlinear stability analysis of an axisymmetric viscous liquid jet is performed. The calculation is based ona small-amplitude perturbation method and restricted to second order. Contrary to the inviscid jet and the planar viscous sheet cases studied by Yuen in 1968 [1] and Yang et al. in 2013 [2], respectively, a part of the solution results from a polynomial approximation of Bessel functions. Results on interface shapes for a small wave number and initial perturbation amplitude, four different Ohnesorge numbers, taking into account the approximate part or not, are used to predict the influence of liquid viscosity on satellite drop formation and evaluate the influence of the approximation. It is observed that the liquid viscosity has a retarding effect on satellite drop formation, in agreement with previous experimental and numerical work. In addition, it is found that the approximate terms can be reasonably ignored, providing a simpler viscous weakly nonlinear model for the description of the first nonlinearity growth in liquid jets.The present work replaces the ILASS 2016 paper [3] by the authors on the same subject.DOI: http://dx.doi.org/10.4995/ILASS2017.2017.4711

Weakly nonlinear instability of a Newtonian liquid jet

2018 ◽  
Vol 856 ◽  
pp. 169-201 ◽  
Author(s):  
Marie-Charlotte Renoult ◽  
Günter Brenn ◽  
Gregor Plohl ◽  
Innocent Mutabazi
Keyword(s):  
Initial Perturbation ◽  
Newtonian Liquid ◽  
Liquid Jet ◽  
Drop Formation ◽  
Liquid Viscosity ◽  
Ohnesorge Number ◽  
Nonlinear Stability Analysis ◽  
Planar Case ◽  
Volume Conservation ◽  
Weakly Nonlinear

A weakly nonlinear stability analysis of an axisymmetric Newtonian liquid jet is presented. The calculation is based on a small-amplitude perturbation method and performed to second order in the perturbation parameter. The obtained solution includes terms derived from a polynomial approximation of a viscous contribution containing products of Bessel functions with different arguments. The use of such an approximation is not needed in the inviscid case and the planar case, since the equations of those problems can be solved in an exact form. The developed model depends on three dimensionless parameters: the initial perturbation amplitude, the perturbation wavenumber and the liquid Ohnesorge number, the latter being the dimensionless liquid viscosity. The influence of the approximate terms was shown to be relatively small for a large range of Ohnesorge numbers so that they can be ignored. This simplification provides a jet model as simple to use as the previous ones, but taking into account the liquid viscosity and the cylindrical geometry. The jet model is used to reveal the effect of both the wavenumber and the Ohnesorge number on the formation of satellite drops, which is known as a nonlinear effect. Results are found in good agreement with direct numerical simulations and forced liquid jet experiments for wavenumbers lower than a threshold value. Satellite drop formation is retarded with increasing Ohnesorge number and wavenumber, as expected by the damping and size effects of viscosity. The threshold number corresponds to the maximum wavenumber for which satellite drop formation is predicted before jet breakup, and for which volume conservation is satisfied within a certain amount. The volume conservation criterion is imposed to ensure that the conclusions inferred by our model are safe.

A non-linear model for the atomization of a swirling viscous liquid jet

2008 ◽  
Vol 222 (11) ◽  
pp. 2137-2145
Author(s):  
E A Ibrahim ◽  
T L Williams
Keyword(s):  
Viscous Liquid ◽  
Numerical Solutions ◽  
Mathematical Formulation ◽  
Wave Number ◽  
Liquid Jet ◽  
Jet Instability ◽  
Viscous Forces ◽  
Swirl Injectors ◽  
Satellite Drops ◽  
Surface Disturbances

The instability and consequent atomization of a swirling viscous liquid jet emanated into gaseous surroundings and subjected to periodical surface disturbances is modelled and investigated. The theoretical analysis is based on a simplified mathematical formulation of the continuity and momentum equations in their conservative forms. Numerical solutions of the governing equations along with appropriate initial and boundary conditions are obtained through a robust finite-difference scheme. The computations yield real-time evolution of the interfacial profile and subsequent breakup characteristics of the liquid jet. It is found that the jet disintegrates into main and satellite drops, under all the conditions considered in the present study. The swirl enhances the instability of the jet and causes radial stretching of the main drops, whereas the satellite drops exhibit axial elongation. Increasing viscosity hinders jet instability and leads to main and satellite drop deformations that are similar to those produced by the swirl. The sizes of both main and satellite drops are diminished at higher disturbance wave numbers. A greater swirl strength induces a higher dominant wave number, and hence a reduced size of resultant main and satellite drops. Larger satellite drops and smaller main drops are produced as viscous forces are increased. The present model could be used as a guide for designing swirl injectors.

NONLINEAR SIMULATION OF A HIGH-SPEED, VISCOUS LIQUID JET

1998 ◽  
Vol 8 (2) ◽  
pp. 155-178 ◽  
Author(s):  
J. H. Hilbing ◽  
Stephen D. Heister
Keyword(s):  
Viscous Liquid ◽  
High Speed ◽  
Liquid Jet ◽  
Nonlinear Simulation

scholarly journals Stability of a Viscous Liquid Jet in a Coaxial Twisting Compressible Airflow

Processes ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 918
Author(s):  
Li-Mei Guo ◽  
Ming Lü ◽  
Zhi Ning
Keyword(s):  
Viscous Liquid ◽  
Axial Velocity ◽  
Liquid Velocity ◽  
Velocity Ratio ◽  
Dominant Mode ◽  
Liquid Jet ◽  
Axisymmetric Mode ◽  
Jet Instability ◽  
Jet Stability ◽  
Jet Breakup

Based on the linear stability analysis, a mathematical model for the stability of a viscous liquid jet in a coaxial twisting compressible airflow has been developed. It takes into account the twist and compressibility of the surrounding airflow, the viscosity of the liquid jet, and the cavitation bubbles within the liquid jet. Then, the effects of aerodynamics caused by the gas–liquid velocity difference on the jet stability are analyzed. The results show that under the airflow ejecting effect, the jet instability decreases first and then increases with the increase of the airflow axial velocity. When the gas–liquid velocity ratio A = 1, the jet is the most stable. When the gas–liquid velocity ratio A > 2, this is meaningful for the jet breakup compared with A = 0 (no air axial velocity). When the surrounding airflow swirls, the airflow rotation strength E will change the jet dominant mode. E has a stabilizing effect on the liquid jet under the axisymmetric mode, while E is conducive to jet instability under the asymmetry mode. The maximum disturbance growth rate of the liquid jet also decreases first and then increases with the increase of E. The liquid jet is the most stable when E = 0.65, and the jet starts to become more easier to breakup when E = 0.8425 compared with E = 0 (no swirling air). When the surrounding airflow twists (air moves in both axial and circumferential directions), given the axial velocity to change the circumferential velocity of the surrounding airflow, it is not conducive to the jet breakup, regardless of the axisymmetric disturbance or asymmetry disturbance.

Linear Instability Analysis of an Annular Swirling Viscous Liquid Jet

2011 ◽  
Vol 66-68 ◽  
pp. 1556-1561 ◽  
Author(s):  
Kai Yan ◽  
Ming Lv ◽  
Zhi Ning ◽  
Yun Chao Song
Keyword(s):  
Viscous Liquid ◽  
Liquid Velocity ◽  
Aerodynamic Force ◽  
Numerical Procedure ◽  
Liquid Sheet ◽  
Linear Instability ◽  
Viscous Force ◽  
Liquid Jet ◽  
Instability Analysis ◽  
Linear Instability Analysis

A three-dimensional linear instability analysis was carried out for an annular swirling viscous liquid jet with solid vortex swirl velocity profile. An analytical form of dispersion relation was derived and then solved by a direct numerical procedure. A parametric study was performed to explore the instability mechanisms that affect the maximum spatial growth rate. It is observed that the liquid swirl enhances the breakup of liquid sheet. The surface tension stabilizes the jet in the low velocity regime. The aerodynamic force intensifies the developing of disturbance and makes the jet unstable. Liquid viscous force holds back the growing of disturbance and the makes the jet stable, especially in high liquid velocity regime.

Nonaxisymmetric evanescent waves in a viscous liquid jet

1994 ◽  
Vol 6 (7) ◽  
pp. 2545-2547 ◽  
Author(s):  
S. P. Lin ◽  
R. Webb
Keyword(s):  
Viscous Liquid ◽  
Evanescent Waves ◽  
Liquid Jet

The large-scale structure of homogeneous turbulence

1967 ◽  
Vol 27 (3) ◽  
pp. 581-593 ◽  
Author(s):  
P. G. Saffman
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
Homogeneous Turbulence ◽  
Wave Number ◽  
Initial Instant ◽  
Force System ◽  
Correlation Tensor ◽  
Number Magnitude ◽  
Small Wave Number ◽  
Conservation Of Momentum

A field of homogeneous turbulence generated at an initial instant by a distribution of random impulsive forces is considered. The statistical properties of the forces are assumed to be such that the integral moments of the cumulants of the force system all exist. The motion generated has the property that at the initial instant\[ E(\kappa) = C\kappa^2 + o(\kappa^2), \]whereE(k) is the energy spectrum function,kis the wave-number magnitude, andCis a positive number which is not in general zero. The corresponding forms of the velocity covariance spectral tensor and correlation tensor are determined. It is found that the terms in the velocity covarianceRij(r) areO(r−3) for large values of the separation magnituder.An argument based on the conservation of momentum is used to show thatCis a dynamical invariant and that the forms of the velocity covariance at large separation and the spectral tensor at small wave number are likewise invariant. For isotropic turbulence, the Loitsianski integral diverges but the integral\[ \int_0^{\infty} r^2R(r)dr = \frac{1}{2}\pi C \]exists and is invariant.

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