Viscous effects on Kelvin–Helmholtz instability in a channel

2011 ◽  
Vol 680 ◽  
pp. 398-416 ◽  
Author(s):  
H. KIM ◽  
J. C. PADRINO ◽  
D. D. JOSEPH
Keyword(s):  
Slug Flow ◽  
Kinematic Viscosity ◽  
Relative Velocity ◽  
Viscosity Ratio ◽  
Critical Value ◽  
Helmholtz Instability ◽  
Viscous Effects ◽  
Velocity Difference ◽  
Neutral Curves ◽  
Gas Fractions

The effects of viscosity on Kelvin–Helmholtz instability in a channel are studied using three different theories; a purely irrotational theory based on the dissipation method, an exact rotational theory and a hybrid irrotational–rotational theory. These new results are compared with previous results from a viscous irrotational theory. An analysis of the neutral state is conducted and its predictions are compared with experimental results related to the transition from a stratified-smooth to a stratified-wavy or slug flow. For values of the gas fraction greater than about 0.20, there is an interval of velocity differences for which the flow is unstable for an interval of wavenumbers between two cutoff wavenumbers, k− and k+. For unstable flows with a velocity difference above that interval or with gas fractions less than 0.20, k− = 0. The maximum critical relative velocity that determines the onset of instability can be found when the kinematic viscosity of the gas and liquid are the same. This critical value is surprisingly achieved when both fluids are inviscid. The neutral curves from the analyses of potential flow of viscous fluids and the hybrid method, the only theories that account for the viscosity of both fluids in this work, indicate that the critical velocity does not change with the viscosity ratio when the kinematic viscosity of the liquid is greater than a critical value. For smaller liquid viscosities, the critical relative velocity decreases.

Study on Kelvin–Helmholtz Instability With Heat and Mass Transfer

2014 ◽  
Vol 136 (12) ◽  
Author(s):  
Mukesh Kumar Awasthi
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Stability Criterion ◽  
Relative Velocity ◽  
Critical Value ◽  
Helmholtz Instability ◽  
Stabilizing Effect ◽  
Vapor Fraction ◽  
The Stability ◽  
Liquid And Vapor Phases

The effect of heat and mass transfer on the Kelvin–Helmholtz instability between liquid and vapor phases of a fluid has been studied using three different theories: a purely irrotational theory based on the dissipation method, a hybrid irrotational-rotational theory, and an inviscid potential flow theory. These new results are compared with previous results from viscous irrotational theory. The stability criterion is given in terms of the critical value of relative velocity. The system is shown to be unstable when the relative velocity is greater than the critical value of relative velocity; otherwise, it is stable. It is observed that heat and mass transfer has a destabilizing effect on the stability of the system while vapor fraction has a stabilizing effect.

Research Report 1: Experiments on the Hydrodynamic Stability of the Flow between Eccentric Rotating Cylinders

1966 ◽  
Vol 181 (2) ◽  
pp. 134-137
Author(s):  
P. Castle ◽  
F. R. Mobbs
Keyword(s):  
Circular Cylinder ◽  
Rotational Speed ◽  
Kinematic Viscosity ◽  
Outer Cylinder ◽  
Critical Value ◽  
Research Report ◽  
Taylor Vortices ◽  
Rotating Circular Cylinder ◽  
Toroidal Vortices ◽  
Square Cells

Since THE Early Work of Taylor (I)†, it has become well known that the Couette flow between an inner, rotating circular cylinder and a concentric, stationary outer cylinder becomes unstable at sufficiently high rotational speeds. The initial instability leads to the formation of a series of toroidal vortices, commonly referred to as Taylor vortices. The vortices occupy approximately square cells, and adjacent pairs are contra-rotating. When the gap d between the cylinders is small compared with the inner cylinder radius R1, the criterion for the onset on the instability is the Taylor number T = Ω1 R1 d3 / v2 where Ω1 is the rotational speed and v the kinematic viscosity of the fluid. A widely accepted critical value is Tc = 1708. Recently Coles (2) has shown the existence of a second instability consisting of travelling circumferential waves superimposed on the Taylor vortices.

Transient Two-Phase Flow Model for High Viscous Liquids Over Hilly Terrain

2014 ◽  
Author(s):  
Abraham Parra ◽  
Miguel Asuaje
Keyword(s):  
Slug Flow ◽  
Mechanical Design ◽  
Fluid Model ◽  
Process Equipment ◽  
Maximum Deviation ◽  
Multiphase Model ◽  
Viscous Effects ◽  
Hilly Terrain ◽  
Two Phase ◽  
Wide Range

This paper presents the detailed development of a multiphase model to predict the behavior of terrain-induced slugging, influenced by the viscous effects and hilly terrain. Currently, high viscosity heavy crude oil represents most of the available fossil resources. This crude flows inside long and expensive pipelines, usually over hilly terrain, causing the formation of slug flow. A very common flow pattern produces critical effects on pipelines in terms of modelling, mechanical stress, induced oscillations, fatigue, production losses, and other negative effects for the system. An accurate characterization of this pattern may give critical data for the mechanical design of piping systems and provide valuable information for the downstream process equipment selection. At present, most of the existing models to predict the behavior of slug flow neglect relevant parameters such as the effect of liquid viscosity and the effect of topographic terrain profile. The objective of this study is to present a mechanistic fluid model to determine the behavior of slug flow affected by the hilly terrain using viscous fluids. The model predicts the four stages of slug flow proposed by Schmidt et al. [1], and extends these stages to hilly terrain systems. The model is valid for a wide range of fluid viscosities and considers a range of pipe inclinations between 0° and 90°. Model validation with available literature and experimental data, shows a maximum deviation of 6%.

scholarly journals Numerical Simulation of the Motion of Inextensible Capsules in Shear Flow Under the Effect of the Natural State

2015 ◽  
Vol 18 (3) ◽  
pp. 787-807 ◽  
Author(s):  
Xiting Niu ◽  
Lingling Shi ◽  
Tsorng-Whay Pan ◽  
Roland Glowinski
Keyword(s):  
Shear Flow ◽  
Viscosity Ratio ◽  
Critical Value ◽  
Natural State ◽  
Small Range ◽  
Spring Model ◽  
Intermittent Behavior ◽  
Internal Fluid ◽  
Tumbling Motion ◽  
Full Disk

AbstractIn this paper, a computational model for the natural state of an inextensible capsule has been successfully combined with a spring model of the capsule membrane to simulate the motion of the capsule in two-dimensional shear flow. Besides the viscosity ratio of the internal fluid and external fluid of the capsule, the natural state also plays a role for having the transition between two well known motions, tumbling and tank-treading (TT) with the long axis oscillates about a fixed inclination angle (a swinging mode), when varying the shear rate. Between tumbling and tank-treading, the intermittent behavior has been obtained for the capsule with a biconcave rest shape. The estimated critical value of the swelling ratio for having the intermittent transition behavior is less than 0.7, i.e., the capsules with rest shape closer to a full disk do not have the intermittent behavior in shear flow. The intermittent dynamics of the capsule in the transition region is a mixture of tumbling and TT with a swinging mode. Just like the motion of TT with a swing mode, which can be viewed as a tank-treading with an incomplete tumbling, the membrane tank-treads backward and forward within a small range during the tumbling motion.

A resolution of the blow-off singularity for similarity flow on a flat plate

1974 ◽  
Vol 62 (1) ◽  
pp. 145-161 ◽  
Author(s):  
D. R. Kassoy
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Critical Value ◽  
Injection Rate ◽  
Uniform Flow ◽  
Boundary Layer Theory ◽  
Viscous Effects ◽  
Critical Rate ◽  
Flow Past ◽  
Classical Boundary

A study is made of uniform flow past a semi-infinite flat plate with a similarity injection distribution of boundary-layer magnitude. Attention is focused on a solution at exactly the critical injection rate for which classical boundary-layer theory predicts the blow-off singularity. Following a description of the more recent interaction analyses which also fail at the critical rate, a new theory is developed which leads to physically meaningful results. In particular, it is shown that the non-monotonic variation in wall shear with increasing injection rate near the critical value, noted by Klemp & Acrivos (1972), is real. A delicate interplay of weak pressure interactions and viscous effects is shown to be responsible for this surprising phenomenon.

Criteria for Recognition of Wheel Skid of Trains Based on Time Series Analysis

2013 ◽  
Vol 440 ◽  
pp. 237-242
Author(s):  
Jun Bin Peng ◽  
Xiao Yi Hu ◽  
Yong Jun Liu
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Characteristic Equation ◽  
Critical Value ◽  
Time Series Model ◽  
Data Series ◽  
Velocity Difference ◽  
Series Analysis ◽  
Greens Function ◽  
Order Determination

Current criteria to judge wheel skid of trains such as velocity difference often cannot recognize wheel skid timely and have no uniform critical value for different trains or railway lines. Aiming at the disadvantages, new criteria based on time series analysis are proposed. With appropriate method of order determination and parameter estimation, AR time series model is established for the data series of velocity difference. Then, Greens function and characteristic equation are constructed with the parameters of the model to determine wheel skid by the convergence state of Greens function or the value of characteristic equations roots. Simulation result shows that the two criteria based on time series model can recognize wheel skid earlier than velocity difference. Moreover, the roots of characteristic equation can also be used as a criterion with a uniform critical value under different application conditions.

On the occurrence of cellular motion in Bénard convection

1967 ◽  
Vol 30 (4) ◽  
pp. 651-661 ◽  
Author(s):  
E. Palm ◽  
T. Ellingsen ◽  
B. Gjevik
Keyword(s):  
Kinematic Viscosity ◽  
Silicone Oil ◽  
Fluid Layer ◽  
Critical Value ◽  
Free Boundaries ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Numbers ◽  
Effect Of Surface ◽  
Cellular Motion

The interval of Rayleigh numbers in Bénard convection corresponding to cellular motion is determined in the case of free-free boundaries, rigid-free boundaries and rigid-rigid boundaries, taking into account the variation of the kinematic viscosity with temperature. Neglecting the effect of surface tension, it is shown that this interval is largest for the rigid-rigid case. The most important feature from the obtained formula (6.1) is, however, that the interval is extremely dependent on the depth of the fluid layer. To obtain a cellular pattern it is therefore necessary to have very small fluid depths. For example, with Silicone oil and a fluid depth of 7 mm, cellular motion will, according to the theory, be observed for Rayleigh numbers larger than the critical value and less than 1·07 times the critical value. For a fluid depth of 5 mm, however, the formula (6.1) gives that cellular motion will be observed for Rayleigh numbers up to 1·54 times the critical value.

scholarly journals Влияние нелинейности закона намагничивания феррожидкости на неустойчивость Кельвина--Гельмгольца

2021 ◽  
Vol 91 (8) ◽  
pp. 1199
Author(s):  
В.М. Коровин
Keyword(s):  
Magnetic Field ◽  
Field Intensity ◽  
Relative Velocity ◽  
Gas Flow ◽  
Magnetic Field Intensity ◽  
Homogeneous Magnetic Field ◽  
Helmholtz Instability ◽  
Magnetization Saturation ◽  
The Magnetic Field ◽  
Stability Area

We study Kelvin-Helmholtz instability which develops when a homogenous gas flow is moving over a horizontal surface of a ferrofluid of given physical properties moving in the same direction, in presence of a homogeneous magnetic field parallel to this direction. Magnetic field intensity range includes the values that correspond to the interval where magnetization curve reaches magnetization saturation level. Stability area is constructed in the “magnetic field intensity – dimensionless relative velocity of fluids” parameter plane.

Effect of Gas/Liquid Shearing on the Viscoelastic Instability of a Planar Sheet

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Ming-Xi Tong ◽  
Li-Jun Yang ◽  
Qing-Fei Fu ◽  
Chao-Jie Mo
Keyword(s):  
Linear Instability ◽  
Viscoelastic Flows ◽  
Helmholtz Instability ◽  
Viscous Effects ◽  
Position Change ◽  
Instability Analysis ◽  
Viscoelastic Effects ◽  
Viscoelastic Instability ◽  
Linear Instability Analysis

The Kelvin–Helmholtz instability of viscoelastic flows was examined through a linear instability analysis. Due of the position change of viscoelastic effects, different unstable responses of liquid elastic effects and medium viscous effects were fully investigated. Finally, a comparison of gas/liquid shearing and inviscid aerodynamic effects on sheet instability is conducted.

Horizontal Slug Flow: A Comparison of Existing Theories

1990 ◽  
Vol 112 (1) ◽  
pp. 74-83 ◽  
Author(s):  
E. Kordyban
Keyword(s):  
Experimental Data ◽  
Slug Flow ◽  
Wave Motion ◽  
Phase Flow ◽  
Bernoulli Equation ◽  
Helmholtz Instability ◽  
Two Phase ◽  
Motion Equations ◽  
The Waves ◽  
Number Of Authors

Over the last twenty years a number of papers have appeared in literature concerning the transition to slug flow in horizontal two-phase flow. The theories proposed in these papers are described, and compared to each other and to results of experiments. It is found that most writers accept that the transition is due to Kelvin-Helmholtz instability of the waves, but if this is studied on the basis of wave motion equations, the transition is found to be dependent on wavelength which contradicts experimental data. A number of authors look at this instability by studying the Bernoulli equation, but this does not predict the wave height. Various approaches are taken by the authors to determine this quantity.

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