Microstructure suspended in three-dimensional flows

1993 ◽  
Vol 250 ◽  
pp. 143-167 ◽  
Author(s):  
Andrew J. Szeri ◽  
L. Gary Leal
Keyword(s):  
Three Dimensional ◽  
Dynamical Behaviour ◽  
Simple Criterion ◽  
Asymptotic Dependence ◽  
Carrier Fluid ◽  
Periodic Attractors ◽  
Model Equations ◽  
Time Periodic ◽  
Lagrangian Frame ◽  
Generic Behaviour

The dynamical behaviour of stretchable, orientable microstructure suspended in a general three-dimensional fluid flow is investigated. Model equations given by Olbricht, Rallison & Leal (1982) are examined in the case of microstructure travelling through arbitrarily complicated flows of the carrier fluid. As in the two-dimensional analysis of Szeri, Wiggins & Leal (1991), one must first treat the orientation dynamics problem; only then can the equation for stretch of the microstructure be analyzed rationally. In three-dimensional flows that are steady in the Lagrangian frame, attractors for the orientation dynamics are shown to be equilibria or limit cycles; this asymptotic behaviour was first deduced by Bretherton (1962). In three-dimensional flows that are time periodic in the Lagrangian frame (e.g. recirculating flows), the orientation dynamics may be characterized by periodic or quasi-periodic attractors. Thus, robust (generic) behaviour in these cases is always characterized by a single global attractor; there is no asymptotic dependence of orientation dynamics on the initial orientation. The type of asymptotic orientation dynamics – steady, periodic, or quasi-periodic - is signified by a simple criterion. Details of the relevant bifurcations, as well as history-dependent strong flow criteria are developed. Examples which illustrate the various types of behaviour are given.

scholarly journals Particle Accumulation Structures in a 5 cSt Silicone Oil Liquid Bridge: New Data for the Preparation of the JEREMI Experiment

2021 ◽  
Vol 33 (2) ◽  
Author(s):  
Paolo Capobianchi ◽  
Marcello Lappa
Keyword(s):  
Liquid Bridge ◽  
Silicone Oil ◽  
Fluid Dynamic ◽  
Solid Particles ◽  
Critical Threshold ◽  
Marangoni Flow ◽  
Disk Radius ◽  
Carrier Fluid ◽  
Aspect Ratios ◽  
Time Periodic

AbstractSystems of solid particles in suspension driven by a time-periodic flow tend to create structures in the carrier fluid that are reminiscent of highly regular geometrical items. Within such a line of inquiry, the present study provides numerical results in support of the space experiments JEREMI (Japanese and European Research Experiment on Marangoni flow Instabilities) planned for execution onboard the International Space Station. The problem is tackled by solving the unsteady non-linear governing equations for the same conditions that will be established in space (microgravity, 5 cSt silicone oil and different aspect ratios of the liquid bridge). The results reveal that for a fixed supporting disk radius, the dynamics are deeply influenced by the height of the liquid column. In addition to its expected link with the critical threshold for the onset of instability (which makes Marangoni flow time-periodic), this geometrical parameter can have a significant impact on the emerging waveform and therefore the topology of particle structures. While for shallow liquid bridges, pulsating flows are the preferred mode of convection, for tall floating columns the dominant outcome is represented by rotating fluid-dynamic disturbance. In the former situation, particles self-organize in circular sectors bounded internally by regions of particle depletion, whereas in the latter case, particles are forced to accumulate in a spiral-like structure. The properties of some of these particle attractors have rarely been observed in earlier studies concerned with fluids characterized by smaller values of the Prandtl number.

Numerical study of multi-dimensional hyperbolic telegraph equations arising in nuclear material science via an efficient local meshless method

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Imtiaz Ahmad ◽  
Aly R. Seadawy ◽  
Hijaz Ahmad ◽  
Phatiphat Thounthong ◽  
Fuzhang Wang
Keyword(s):  
Meshless Method ◽  
Material Science ◽  
Numerical Study ◽  
Research Work ◽  
Time Integration ◽  
Three Dimensional ◽  
Nuclear Material ◽  
Telegraph Equations ◽  
Model Equations ◽  
Derivatives Of

Abstract This research work is to study the numerical solution of three-dimensional second-order hyperbolic telegraph equations using an efficient local meshless method based on radial basis function (RBF). The model equations are used in nuclear material science and in the modeling of vibrations of structures. The explicit time integration technique is utilized to semi-discretize the model in the time direction whereas the space derivatives of the model are discretized by the proposed local meshless procedure based on multiquadric RBF. Numerical experiments are performed with the proposed numerical scheme for rectangular and non-rectangular computational domains. The proposed method solutions are converging quickly in comparison with the different existing numerical methods in the recent literature.

BIFURCATION SCENARIO OF A THREE-DIMENSIONAL VAN DER POL OSCILLATOR

1993 ◽  
Vol 03 (02) ◽  
pp. 399-404 ◽  
Author(s):  
T. SÜNNER ◽  
H. SAUERMANN
Keyword(s):  
Bifurcation Diagram ◽  
Bifurcation Analysis ◽  
Chaotic Behavior ◽  
Three Dimensional ◽  
Global Bifurcation ◽  
Dynamical Behaviour ◽  
Van Der Pol Oscillator ◽  
Two Dimensional ◽  
Van Der Pol ◽  
Dimensional Models

Nonlinear self-excited oscillations are usually investigated for two-dimensional models. We extend the simplest and best known of these models, the van der Pol oscillator, to a three-dimensional one and study its dynamical behaviour by methods of bifurcation analysis. We find cusps and other local codimension 2 bifurcations. A homoclinic (i.e. global) bifurcation plays an important role in the bifurcation diagram. Finally it is demonstrated that chaos sets in. Thus the system belongs to the few three-dimensional autonomous ones modelling physical situations which lead to chaotic behavior.

The development of asymmetry and period doubling for oscillatory flow in baffled channels

1996 ◽  
Vol 328 ◽  
pp. 19-48 ◽  
Author(s):  
E. P. L. Roberts ◽  
M. R. Mackley
Keyword(s):  
Reynolds Number ◽  
Oscillatory Flow ◽  
Three Dimensional ◽  
Period Doubling ◽  
Progressive Increase ◽  
Newtonian Flow ◽  
Chaotic Flow ◽  
Spatially Periodic ◽  
Dimensional Simulation ◽  
Time Periodic

We report experimental and numerical observations on the way initially symmetric and time-periodic fluid oscillations in baffled channels develop in complexity. Experiments are carried out in a spatially periodic baffled channel with a sinusoidal oscillatory flow. At modest Reynolds number the observed vortex structure is symmetric and time periodic. At higher values the flow progressively becomes three-dimensional, asymmetric and aperiodic. A two-dimensional simulation of incompressible Newtonian flow is able to follow the flow pattern at modest oscillatory Reynolds number. At higher values we report the development of both asymmetry and a period-doubling cascade leading to a chaotic flow regime. A bifurcation diagram is constructed that can describe the progressive increase in complexity of the flow.

Steady-State Formulation for Stress and Distortion of Welds

1994 ◽  
Vol 116 (4) ◽  
pp. 467-474 ◽  
Author(s):  
M. Gu ◽  
J. A. Goldak
Keyword(s):  
Thermal Stress ◽  
Steady State ◽  
Three Dimensional ◽  
Significant Gain ◽  
Free Boundaries ◽  
Flow Lines ◽  
Eulerian Formulation ◽  
Noticeable Reduction ◽  
Computing Speed ◽  
Lagrangian Frame

A steady state formulation has been developed for thermal stress analysis. It uses features from both the Lagrangian formulation and the Eulerian formulation. The mesh sits on an Eulerian frame but deforms as if in the Lagrangian frame. Therefore, it is suitable for steady state problems with free boundaries. History dependent parameters are integrated along flow lines. A significant gain in computing speed and/or spatial resolution over transient analyses has been achieved together with a noticeable reduction for memory requirements. Numerical results are given for a three-dimensional analysis of edge weld.

scholarly journals Concentration and velocity statistics of inertial particles in upward and downward pipe flow

2017 ◽  
Vol 822 ◽  
pp. 640-663 ◽  
Author(s):  
J. L. G. Oliveira ◽  
C. W. M. van der Geld ◽  
J. G. M. Kuerten
Keyword(s):  
Liquid Velocity ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Stokes Number ◽  
Terminal Velocity ◽  
Point Particle ◽  
Inertial Particles ◽  
Carrier Fluid ◽  
Velocity Statistics ◽  
The Difference

Three-dimensional particle tracking velocimetry is applied to particle-laden turbulent pipe flows at a Reynolds number of 10 300, based on the bulk velocity and the pipe diameter, for developed fluid flow and not fully developed flow of inertial particles, which favours assessment of the radial migration of the inertial particles. Inertial particles with Stokes number ranging from 0.35 to 1.11, based on the particle relaxation time and the radial-dependent Kolmogorov time scale, and a ratio of the root-mean-square fluid velocity to the terminal velocity of order 1 have been used. Core peaking of the concentration of inertial particles in up-flow and wall peaking in down-flow have been found. The difference in mean particle and Eulerian mean liquid velocity is found to decrease to approximately zero near the wall in both flow directions. Although the carrier fluid has all of the characteristics of the corresponding turbulent single-phase flow, the Reynolds stress of the inertial particles is different near the wall in up-flow. These findings are explained from the preferential location of the inertial particles with the aid of direct numerical simulations with the point-particle approach.

On the Parametrical Excitation of Nonlinearly Coupled Wave Equations

1995 ◽  
Author(s):  
A. H. P. van der Burgh ◽  
P. Kuznetsov ◽  
S. A. Vavilov
Keyword(s):  
Wave Equations ◽  
Operator Method ◽  
Dynamical Behaviour ◽  
Existence Theory ◽  
Rigorous Analysis ◽  
Coupled Wave Equations ◽  
Time Periodic Solutions ◽  
Transversal Vibrations ◽  
Time Periodic ◽  
Coupled Wave

Abstract In this paper a mathematical model for the study of the interaction of longitudinal and transversal vibrations in a stretched string is presented. The study implies an existence theory for time periodic transversal vibrations generated by a horizontal excitation of one of the end-points of the string. The conditions for the existence of this parametrically excited time periodic vibrations are evaluated in a practical application. The innovative character of the results obtained concern the application of an operator method to a system of nonlinearly coupled wave equations modeling the dynamical behaviour of a strectched string where unite elasticity is taken into account. It may be known that in the literature little attention has been paid to a rigorous analysis of time periodic solutions for systems of partial differential equations.

scholarly journals Analysis of Arc Processes in Multi-chamber Arrester for Lightning Protection at High-voltage Overhead Power Lines

2017 ◽  
Vol 4 (2) ◽  
pp. 124-128 ◽  
Author(s):  
Iu. V. Murashov ◽  
V. Ya. Frolov ◽  
D. Uhrlandt ◽  
S. Gortschakow ◽  
D. V. Ivanov ◽  
...  
Keyword(s):  
Discharge Chamber ◽  
Three Dimensional ◽  
Plasma Temperature ◽  
Power Lines ◽  
Lightning Protection ◽  
Computational Domain ◽  
Transient Model ◽  
Electromagnetic Processes ◽  
Model Equations ◽  
Overhead Power Lines

Nowadays multi-chamber arresters are widely distributed as devices of lightning protection of overhead power lines. A mathematical modelling of processes in the discharge chamber of multichamber arrester is necessary to carry out in order to improve its breaking capacity. A three-dimensional mathematical transient model of thermal, gas-dynamic and electromagnetic processes taking place in the discharge chamber of multi-chamber arrester is presented in the article. Basic assumptions, model equations, a computational domain and the boundary conditions are described. Plasma turbulence is taken into account. The results of the calculation i.e. distributions of plasma temperature and overpressure in the discharge chamber at different time points are shown. The analysis of the results was carried out. It is shown that the presence of cavities in the electrodes design promotes electric arc extinction in the discharge chamber of multi-chamber arrester.

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