Curved Non-Newtonian Liquid Jets With Surfactants

2009 ◽  
Vol 131 (9) ◽  
Author(s):  
Jamal Uddin ◽  
Stephen P. Decent
Keyword(s):  
Free Surface ◽  
Shear Thickening ◽  
Linear Instability ◽  
Liquid Jets ◽  
Liquid Jet ◽  
Long Wavelength ◽  
Droplet Sizes ◽  
Wavelength Approximation ◽  
Steady Solutions ◽  
Linear Instability Analysis

Applications of the breakup of a liquid jet into droplets are common in a variety of different industrial and engineering processes. One such process is industrial prilling, where small spherical pellets and beads are generated from the rupture of a liquid thread. In such a process, curved liquid jets produced by rotating a perforated cylindrical drum are utilized to control drop sizes and breakup lengths. In general, smaller droplets are observed as the rotation rate is increased. The addition of surfactants along the free surface of the liquid jet as it emerges from the orifice provides a possibility of further manipulating breakup lengths and droplet sizes. In this paper, we build on the work of Uddin et al. (2006, “The Instability of Shear Thinning and Shear Thickening Liquid Jets: Linear Theory,” ASME J. Fluids Eng., 128, pp. 968–975) and investigate the instability of a rotating liquid jet (having a power law rheology) with a layer of surfactants along its free surface. Using a long wavelength approximation we reduce the governing equations into a set of one-dimensional equations. We use an asymptotic theory to find steady solutions and then carry out a linear instability analysis on these solutions.

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.

scholarly journals Effects of Asymmetric Gas Distribution on the Instability of a Plane Power-Law Liquid Jet

Energies ◽  
2018 ◽  
Vol 11 (7) ◽  
pp. 1854 ◽  
Author(s):  
Jin-Peng Guo ◽  
Yi-Bo Wang ◽  
Fu-Qiang Bai ◽  
Fan Zhang ◽  
Qing Du
Keyword(s):  
Power Law ◽  
Liquid Velocity ◽  
Linear Instability ◽  
Liquid Jets ◽  
Liquid Jet ◽  
Critical Curves ◽  
Jet Breakup ◽  
Plane Jets ◽  
Gas Space ◽  
Aerodynamic Asymmetry

As a kind of non-Newtonian fluid with special rheological features, the study of the breakup of power-law liquid jets has drawn more interest due to its extensive engineering applications. This paper investigated the effect of gas media confinement and asymmetry on the instability of power-law plane jets by linear instability analysis. The gas asymmetric conditions mainly result from unequal gas media thickness and aerodynamic forces on both sides of a liquid jet. The results show a limited gas space will strengthen the interaction between gas and liquid and destabilize the power-law liquid jet. Power-law fluid is easier to disintegrate into droplets in asymmetric gas medium than that in the symmetric case. The aerodynamic asymmetry destabilizes para-sinuous mode, whereas stabilizes para-varicose mode. For a large Weber number, the aerodynamic asymmetry plays a more significant role on jet instability compared with boundary asymmetry. The para-sinuous mode is always responsible for the jet breakup in the asymmetric gas media. With a larger gas density or higher liquid velocity, the aerodynamic asymmetry could dramatically promote liquid disintegration. Finally, the influence of two asymmetry distributions on the unstable range was analyzed and the critical curves were obtained to distinguish unstable regimes and stable regimes.

The Instability of Shear Thinning and Shear Thickening Spiralling Liquid Jets: Linear Theory

2006 ◽  
Vol 128 (5) ◽  
pp. 968-975 ◽  
Author(s):  
J. Uddin ◽  
S. P. Decent ◽  
M. J. Simmons
Keyword(s):  
Asymptotic Methods ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Wave Mode ◽  
Linear Instability ◽  
Liquid Jets ◽  
Flow Index ◽  
Rotation Rates ◽  
Newtonian Liquids ◽  
Small Rotation

The linear instability of a power law liquid emerging as a jet from an orifice on the surface of a rotating container is investigated, with applications to industrial prilling. Asymptotic methods are used to examine the growth rate and wavenumber of the most unstable traveling wave mode for different flow index numbers. Comparison with Newtonian liquids show that for small rotation rates shear thinning liquids are most stable to disturbances. In contrast for higher rotation rates we find shear thickening liquids are more stable than shear thinning liquids. The influence of viscosity, surface tension, and rotation rate on the growth rates and most unstable wavenumbers associated with both types of liquids are also examined.

Impingement Heat Transfer of Free-Surface Liquid Jets

2002 ◽  
Author(s):  
Albert Y. Tong
Keyword(s):  
Heat Transfer ◽  
Free Surface ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Liquid Jets ◽  
Liquid Jet ◽  
Stagnation Region ◽  
Navier Stokes Equations ◽  
Impingement Heat Transfer

The problem of convective heat transfer of a circular liquid jet impinging onto a substrate is studied numerically. The objective of the study is to understand the hydrodynamics and heat transfer of the impingement process. The Navier-Stokes equations are solved using a finite-volume formulation. The free surface of the jet is tracked by the volume-of-fluid method. The energy equation is modeled by using an enthalpy-based formulation. Detailed flow fields as well as free surface contours and pressure distributions on the substrate have been obtained. Local Nusselt number variations along the solid surface have also been calculated. The effects of several key parameters on the hydrodynamics and heat transfer of an impinging liquid jet have been examined. It has been found that the jet-inlet velocity profile and jet elevation have a significant effect on the hydrodynamics and heat transfer, particularly in the stagnation region, of an impinging jet. The numerical results have been compared with experimental data obtained from the literature. The close agreement supports the validity of the numerical study.

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.

Unstable Asymmetric Modes of a Liquid Jet

1999 ◽  
Vol 121 (2) ◽  
pp. 379-383 ◽  
Author(s):  
S. X. Shi ◽  
D. G. Xi ◽  
J. R. Qin ◽  
N. Liu ◽  
G. C. Shu
Keyword(s):  
High Speed ◽  
Three Dimensional ◽  
Linear Instability ◽  
Liquid Jet ◽  
Physical Conditions ◽  
Inviscid Gas ◽  
Theoretical Predictions ◽  
Linear Instability Analysis ◽  
Rates Of Growth ◽  
Gas Medium

This paper reports the results of a linear instability analysis for a viscous liquid jet injecting into a quiescent inviscid gas medium with three-dimensional disturbances. A dispersion equation that accounts for the growth of asymmetric waves is derived, and the maximum rates of growth of various modes are calculated. The asymmetric breakup phenomenon of the jet and its structures at different modes is also studied by using a high-speed multi-frame holographic system. The theoretical predictions agree well with the experimental observations. The results of this study thus confirm the existence and even domination of unstable asymmetric modes under certain physical conditions in the breakup process.

Dynamics of liquid jets revisited

1993 ◽  
Vol 250 ◽  
pp. 635-650 ◽  
Author(s):  
R. M. S. M. Schulkes
Keyword(s):  
Evolution Equations ◽  
Numerical Solutions ◽  
Perturbation Expansion ◽  
Nonlinear Evolution Equations ◽  
Liquid Jets ◽  
Liquid Jet ◽  
One Dimensional ◽  
Long Wavelength ◽  
The One ◽  
Made In

In this paper we investigate the long-wavelength approximations of the equations governing the motion of an inviscid liquid jet. Using a formal perturbation expansion it will be shown that the one-dimensional equations presented by Lee (1974) are inconsistent. The inconsistency arises from the fact that terms which have been retained in the boundary conditions should have been rejected in view of the approximations made in the momentum equations. With the correct equations a number of anomalies between Lee's model and other models are eliminated. An explicit periodic solution to the nonlinear evolution equations we have derived is presented. However, it turns out that the wavenumbers for which this solution is valid lie outside the range in which the long-wavelength approximations are applicable. In addition we present numerical solutions to the nonlinear equations we have derived. In the unstable regime we find that, as disturbances grow, the characteristic axial lengthscales of the major features are typically of the order of the radius of the jet. This casts some doubt on the validity of the long-wavelength approximations in the study of nonlinear liquid jet dynamics.

scholarly journals Linear instability analysis of low-pressure turbine flows

2009 ◽  
Vol 628 ◽  
pp. 57-83 ◽  
Author(s):  
N. ABDESSEMED ◽  
S. J. SHERWIN ◽  
V. THEOFILIS
Keyword(s):  
Separation Bubble ◽  
Three Dimensional ◽  
Low Pressure ◽  
Linear Instability ◽  
Base Flow ◽  
Element Discretization ◽  
Long Wavelength ◽  
Low Pressure Turbine ◽  
Linear Instability Analysis ◽  
Value Decomposition

Three-dimensional linear BiGlobal instability of two-dimensional states over a periodic array of T-106/300 low-pressure turbine (LPT) blades is investigated for Reynolds numbers below 5000. The analyses are based on a high-order spectral/hpelement discretization using a hybrid mesh. Steady basic states are investigated by solution of the partial-derivative eigenvalue problem, while Floquet theory is used to analyse time-periodic flow set-up past the first bifurcation. The leading mode is associated with the wake and long-wavelength perturbations, while a second short-wavelength mode can be associated with the separation bubble at the trailing edge. The leading eigenvalues and Floquet multipliers of the LPT flow have been obtained in a range of spanwise wavenumbers. For the most general configuration all secondary modes were observed to be stable in the Reynolds number regime considered. When a single LPT blade with top to bottom periodicity is considered as a base flow, the imposed periodicity forces the wakes of adjacent blades to be synchronized. This enforced synchronization can produce a linear instability due to long-wavelength disturbances. However, relaxing the periodic restrictions is shown to remove this instability. A pseudo-spectrum analysis shows that the eigenvalues can become unstable due to the non-orthogonal properties of the eigenmodes. Three-dimensional direct numerical simulations confirm all perturbations identified herein. An optimum growth analysis based on singular-value decomposition identifies perturbations with energy growthsO(105).

Simulation of Laminar Liquid Jets in Gaseous Crossflow Before the Onset of Primary Breakup

2011 ◽  
Author(s):  
C.-L. Ng ◽  
K. A. Sallam
Keyword(s):  
Experimental Data ◽  
Fuel Injection ◽  
Liquid Jets ◽  
Liquid Jet ◽  
Jet Breakup ◽  
Primary Breakup ◽  
Density Ratios ◽  
First Time ◽  
Two Sides ◽  
Reduced Pressures

The deformation of laminar liquid jets in gaseous crossflow before the onset of primary breakup is studied motivated by its application to fuel injection in jet afterburners and agricultural sprays, among others. Three crossflow Weber numbers that represent three different liquid jet breakup regimes; column, bag, and shear breakup regimes, were studied at large liquid/gas density ratios and small Ohnesorge numbers. In each case the liquid jet was simulated from the jet exit and ended before the location where the experimental data indicated the onset of breakup. The results show that in column and bag breakup, the reduced pressures along the sides of the jet cause the liquid to move to the sides of the jet and enhance the jet deformation. In shear breakup, the flattened upwind surface pushes the liquid towards the two sides of the jet and causing the gaseous crossflow to separate near the edges of the liquid jet thus preventing further deformation before the onset of breakup. It was also found out that in shear breakup regime, the liquid phase velocity inside the liquid jet was large enough to cause onset of ligament formation along the jet side, which was not the case in the column and bag breakup regimes. In bag breakup, downwind surface waves were observed to grow along the sides of the liquid jet triggered a complimentary experimental study that confirmed the existence of those waves for the first time.

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