The trajectory and stability of a spiralling liquid jet. Part 1. Inviscid theory

2002 ◽  
Vol 459 ◽  
pp. 43-65 ◽  
Author(s):  
I. M. WALLWORK ◽  
S. P. DECENT ◽  
A. C. KING ◽  
R. M. S. M. SCHULKES
Keyword(s):  
Weber Number ◽  
Multiple Scales ◽  
Asymptotic Methods ◽  
Travelling Wave ◽  
Liquid Jet ◽  
Inviscid Liquid ◽  
Breakup Length ◽  
The Stability ◽  
Good Agreement ◽  
Wave Modes

We examine a spiralling slender inviscid liquid jet which emerges from a rapidly rotating orifice. The trajectory of this jet is determined using asymptotic methods, and the stability using a multiple scales approach. It is found that the trajectory of the jet becomes more tightly coiled as the Weber number is decreased. Unstable travelling wave modes are found to grow along the jet. The breakup length of the jet is calculated, showing good agreement with experiments.

scholarly journals Breakup of the Water Sheet Formed by Two Liquid Impinging Jets

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Yakang Xia ◽  
Lyes Khezzar ◽  
Shrinivas Bojanampati ◽  
Arman Molki
Keyword(s):  
Weber Number ◽  
Reynolds Numbers ◽  
Impinging Jets ◽  
Liquid Jets ◽  
Liquid Jet ◽  
Impingement Angle ◽  
Number Range ◽  
Breakup Length ◽  
Sheet Breakup ◽  
Visualization Experiments

Flow visualization experiments are carried out to study the flow regimes and breakup length of the water sheet generated by two impinging liquid jets from an atomizer made of two identical tubes 0.686 mm in diameter. These experiments cover liquid jet Reynolds numbers based on the pipe diameter in the range of 1541 to 5394. The effects of the jet velocities and impingement angle between the two jets on the breakup performance are studied. Four spray patterns are recognized, which are presheet formation, smooth sheet, ruffled sheet, and open-rim sheet regimes. Water sheet breakup length is found to be consistent with previous experimental and theoretical results in the lower Weber number (based on water jet diameter and velocity) range. In the relatively high Weber number range, the breakup length tends to a constant value with increasing Weber number, and some discrepancies between experimental and theoretical predictions do exist. Measured water sheet area increases with increasing liquid jet Reynolds numbers and impingement angle within the range of the current study.

scholarly journals Stability analysis and breakup length calculations for steady planar liquid jets

2010 ◽  
Vol 668 ◽  
pp. 384-411 ◽  
Author(s):  
M. R. TURNER ◽  
J. J. HEALEY ◽  
S. S. SAZHIN ◽  
R. PIAZZESI
Keyword(s):  
Stability Analysis ◽  
Velocity Profile ◽  
Shear Layer ◽  
Fluid Velocity ◽  
Finite Thickness ◽  
Liquid Jet ◽  
Absolute Instability ◽  
Breakup Length ◽  
The Stability ◽  
Thickness Shear

This study uses spatio-temporal stability analysis to investigate the convective and absolute instability properties of a steady unconfined planar liquid jet. The approach uses a piecewise linear velocity profile with a finite-thickness shear layer at the edge of the jet. This study investigates how properties such as the thickness of the shear layer and the value of the fluid velocity at the interface within the shear layer affect the stability properties of the jet. It is found that the presence of a finite-thickness shear layer can lead to an absolute instability for a range of density ratios, not seen when a simpler plug flow velocity profile is considered. It is also found that the inclusion of surface tension has a stabilizing effect on the convective instability but a destabilizing effect on the absolute instability. The stability results are used to obtain estimates for the breakup length of a planar liquid jet as the jet velocity varies. It is found that reducing the shear layer thickness within the jet causes the breakup length to decrease, while increasing the fluid velocity at the fluid interface within the shear layer causes the breakup length to increase. Combining these two effects into a profile, which evolves realistically with velocity, gives results in which the breakup length increases for small velocities and decreases for larger velocities. This behaviour agrees qualitatively with existing experiments on the breakup length of axisymmetric jets.

Transverse Vibrations of a Centrally Clamped Rotating Circular Disk

1999 ◽  
Author(s):  
Ali H. Nayfeh ◽  
Adel Jilani ◽  
Piergiuseppe Manzione
Keyword(s):  
Multiple Scales ◽  
Primary Resonance ◽  
Circular Disk ◽  
Qualitative Behavior ◽  
Equilibrium Solutions ◽  
Transverse Loads ◽  
Transverse Vibrations ◽  
Critical Rotational Speed ◽  
The Stability ◽  
Good Agreement

Abstract The transverse vibrations of a circular disk of uniform thickness rotating about its axis with constant angular velocity are analyzed. The results specialized to the linear case of disks clamped at the center and free at the periphery are in good agreement with those reported in the literature. The natural frequencies of spinning hard and floppy disks are obtained for various nodal diameters and nodal circles. Primary resonance is shown to occur at the critical rotational speed at which, in the linear analysis, the spinning disk is unable to support arbitrary spatially fixed transverse loads. Using the method of multiple scales, we determine a set of four nonlinear ordinary-differential equations governing the modulation of the amplitudes and phases of two interacting modes. The symmetry of the system and the loading conditions are reflected in the symmetry of the modulation equations. They are reduced to an equivalent set of two first-order equations whose equilibrium solutions are determined analytically. The stability characteristics of these solutions is studied; the qualitative behavior of the response is independent of the mode being considered.

Breakup phenomena in coaxial airblast atomizers

1995 ◽  
Vol 451 (1941) ◽  
pp. 189-229 ◽  
Keyword(s):  
Nozzle Exit ◽  
Weber Number ◽  
Slip Velocity ◽  
Air Flow ◽  
Density Ratio ◽  
Liquid Jet ◽  
High Speed Photography ◽  
Breakup Length ◽  
Air Jet ◽  
Energy Ratios

The breakup of a liquid jet with length-to-diameter ratio of 22 surrounded by a coaxial flow of air has been examined by a combination of high-speed photography and phase-Doppler velocimetry. The air-to-liquid momentum and kinetic energy ratios, the Reynolds number of the coaxial water and air jet flows and the exit-plane Weber number have been varied over extensive ranges and the results examined in terms of the breakup length, frequency, droplet size distributions and velocity characteristics. The photographs reveal the deterministic nature of the liquid flow at Reynolds numbers which are sufficient to guarantee turbulent flow, with the formation of a wave-like structure for a short distance followed by the formation of a liquid cluster and subsequent breakup into ligaments and droplets, with the entire process repeated in a periodic manner. Attempts are made to relate the breakup length and the frequency of the process to the air-to-liquid momentum and energy ratios, the exit Weber number and the slip velocity between the two streams at the nozzle exit. The results confirm that the ratio of the frequencies of the wave-like structures and breakup decreased with the slip velocity between the two streams and asymptotically approached a value of around one for values higher than 150 m s -1 . The photographs indicate that the droplet sizes in the sprays are due mainly to disintegration of liquid clusters produced after the initial breakup of the liquid jet and the phase Doppler measurements confirm that most of the liquid remained close to the centreline, where the mean diameter reached a maximum and the slip velocity between the droplets and the air flow was low. An atomization model based on the value of the local Weber number on the centreline of the sprays is used to explain the size characteristics of the sprays. The atomization process was affected by the air-to-liquid momentum ratio at the nozzle exit, the annular width of the coaxial atomizer, the liquid-to-air density ratio, the surface tension and the kinematic viscosity and density of the air. The rate of spread of the sprays close to the nozzle reduced with increase of the air and liquid flowrates and was affected by the initial breakup of the liquid jet and the amplitude of the wave-like structure of the liquid jet during breakup rather than by the air flow turbulence.

scholarly journals The strato-rotational instability of Taylor–Couette and Keplerian flows

2010 ◽  
Vol 660 ◽  
pp. 147-161 ◽  
Author(s):  
S. LE DIZÈS ◽  
X. RIEDINGER
Keyword(s):  
Potential Flow ◽  
Asymptotic Methods ◽  
Outer Boundary ◽  
Local Analysis ◽  
Rotational Instability ◽  
Flow Parameters ◽  
Radiative Instability ◽  
Taylor Couette ◽  
The Stability ◽  
Good Agreement

The linear inviscid stability of two families of centrifugally stable rotating flows in a stably stratified fluid of constant Brunt–Väisälä frequency N is analysed by using numerical and asymptotic methods. Both Taylor–Couette and Keplerian angular velocity profiles ΩTC = (1 − μ)/r2 + μ and ΩK = (1 − λ)/r2 + λ/r3/2 are considered between r = 1 (inner boundary) and r = d > 1 (outer boundary, or without boundary if d = ∞). The stability properties are obtained for flow parameters λ and μ ranging from 0 to +∞, and different values of d and N. The effect of the gap size is analysed first. By considering the potential flow (λ = μ = 0), we show how the instability associated with a mechanism of resonance for finite-gap changes into a radiative instability when d → ∞. Numerical results are compared with large axial wavenumber results and a very good agreement is obtained. For infinite gap (d = ∞), we show that the most unstable modes are obtained for large values of the azimuthal wavenumber for all λ and μ. We demonstrate that their properties can be captured by performing a local analysis near the inner cylinder in the limit of both large azimuthal and axial wavenumbers. The effect of the stratification is also analysed. We show that decreasing N is stabilizing. An asymptotic analysis for small N is also performed and shown to capture the properties of the most unstable mode of the potential flow in this limit.

Experiments on the capillary instability of a liquid jet

1966 ◽  
Vol 290 (1423) ◽  
pp. 547-556 ◽  
Keyword(s):  
Growth Rate ◽  
Dispersion Curve ◽  
Direct Measurement ◽  
Liquid Jet ◽  
Audio Frequency ◽  
Water Solutions ◽  
Glycerine Water ◽  
The Stability ◽  
Vertical Jet ◽  
Good Agreement

The stability of a vertical jet of water has been examined by imposing audio frequency disturbances. Flash photographs allow a direct measurement of the growth rate of the disturbances and the complete dispersion curve has been investigated. The effects of viscosity on the stability have been examined with glycerine-water solutions and have been found to be in good agreement with Chandrasekhar’s calculations.

scholarly journals Contact patch memory of tyres leading to lateral vibrations of four-wheeled vehicles

2013 ◽  
Vol 371 (1993) ◽  
pp. 20120427 ◽  
Author(s):  
Dénes Takács ◽  
Gábor Stépán
Keyword(s):  
Large Scale ◽  
Multiple Scales ◽  
Travelling Wave ◽  
Small Scale ◽  
Global Dynamics ◽  
Contact Patch ◽  
Lateral Vibrations ◽  
Wide Range ◽  
The Stability ◽  
Wheeled Vehicles

It has been shown recently that the shimmy motion of towed wheels can be predicted in a wide range of parameters by means of the so-called memory effect of tyres. This delay effect is related to the existence of a travelling-wave-like motion of the tyre points in contact with the ground relative to the wheel. This study shows that the dynamics within the small-scale contact patch can have an essential effect on the global dynamics of a four-wheeled automobile on a large scale. The stability charts identify narrow parameter regions of increased fuel consumption and tyre noise with the help of the delay models that are effective tools in dynamical problems through multiple scales.

scholarly journals Experimental and theoretical progress in pipe flow transition

2008 ◽  
Vol 366 (1876) ◽  
pp. 2671-2684 ◽  
Author(s):  
A.P Willis ◽  
J Peixinho ◽  
R.R Kerswell ◽  
T Mullin
Keyword(s):  
Pipe Flow ◽  
Quantitative Agreement ◽  
Travelling Wave ◽  
Turbulent Pipe Flow ◽  
Transition To Turbulence ◽  
Reynolds Number Flow ◽  
Threshold Amplitude ◽  
Number Flow ◽  
The Stability ◽  
Laminar State

There have been many investigations of the stability of Hagen–Poiseuille flow in the 125 years since Osborne Reynolds' famous experiments on the transition to turbulence in a pipe, and yet the pipe problem remains the focus of attention of much research. Here, we discuss recent results from experimental and numerical investigations obtained in this new century. Progress has been made on three fundamental issues: the threshold amplitude of disturbances required to trigger a transition to turbulence from the laminar state; the threshold Reynolds number flow below which a disturbance decays from turbulence to the laminar state, with quantitative agreement between experimental and numerical results; and understanding the relevance of recently discovered families of unstable travelling wave solutions to transitional and turbulent pipe flow.

OPTIMAL VELOCITY MODEL WITH RELATIVE VELOCITY

2006 ◽  
Vol 17 (01) ◽  
pp. 65-73 ◽  
Author(s):  
SHIRO SAWADA
Keyword(s):  
Nonlinear Analysis ◽  
Relative Velocity ◽  
Velocity Model ◽  
Fundamental Diagram ◽  
Optimal Velocity ◽  
Traffic Jam ◽  
Optimal Velocity Model ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Good Agreement

The optimal velocity model which depends not only on the headway but also on the relative velocity is analyzed in detail. We investigate the effect of considering the relative velocity based on the linear and nonlinear analysis of the model. The linear stability analysis shows that the improvement in the stability of the traffic flow is obtained by taking into account the relative velocity. From the nonlinear analysis, the relative velocity dependence of the propagating kink solution for traffic jam is obtained. The relation between the headway and the velocity and the fundamental diagram are examined by numerical simulation. We find that the results by the linear and nonlinear analysis of the model are in good agreement with the numerical results.

TRAVELLING WAVES AND OSCILLATIONS IN SAL’NIKOV’S COMBUSTION REACTION IN A COMPRESSIBLE GAS

2015 ◽  
Vol 56 (3) ◽  
pp. 233-247 ◽  
Author(s):  
RHYS A. PAUL ◽  
LAWRENCE K. FORBES
Keyword(s):  
Asymptotic Solution ◽  
Multiple Scales ◽  
Travelling Waves ◽  
Method Of Lines ◽  
Travelling Wave ◽  
Reaction Scheme ◽  
Compressible Viscous Gas ◽  
The Method Of Lines ◽  
Temperature Waves ◽  
Parameter Values

We consider a two-step Sal’nikov reaction scheme occurring within a compressible viscous gas. The first step of the reaction may be either endothermic or exothermic, while the second step is strictly exothermic. Energy may also be lost from the system due to Newtonian cooling. An asymptotic solution for temperature perturbations of small amplitude is presented using the methods of strained coordinates and multiple scales, and a travelling wave solution with a sech-squared profile is derived. The method of lines is then used to approximate the full system with a set of ordinary differential equations, which are integrated numerically to track accurately the evolution of the reaction front. This numerical method is used to verify the asymptotic solution and investigate behaviours under different conditions. Using this method, temperature waves progressing as pulsatile fronts are detected at appropriate parameter values.

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