scholarly journals Numerical Study on Nonlinear Effects of Compression Waves Propagated in a Tube.

1992 ◽  
Vol 58 (546) ◽  
pp. 338-342 ◽  
Author(s):  
Kazuyuki KAGE ◽  
Shigetoshi KAWAGOE
Keyword(s):  
Numerical Study ◽  
Nonlinear Effects ◽  
Compression Waves

Numerical Study of Viscous Flows Inside Partially Filled Spinning and Coning Cylinders

1996 ◽  
Vol 118 (2) ◽  
pp. 335-340 ◽  
Author(s):  
Mohamed Selmi
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Center Of Mass ◽  
Steady Motion ◽  
Practical Interest ◽  
Nonlinear Effects ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Practical Applications ◽  
Analysis And Design

This paper is concerned with the solution of the 3-D-Navier-Stokes equations describing the steady motion of a viscous fluid inside a partially filled spinning and coning cylinder. The cylinder contains either a single fluid of volume less than that of the cylinder or a central rod and a single fluid of combined volume (volume of the rod plus volume of the fluid) equal to that of the cylinder. The cylinder rotates about its axis at the spin rate ω and rotates about an axis that passes through its center of mass at the coning rate Ω. In practical applications, as in the analysis and design of liquid-filled projectiles, the parameter ε = τ sin θ, where τ = Ω/ω and θ is the angle between spin axis and coning axis, is small. As a result, linearization of the Navier-Stokes equations with this parameter is possible. Here, the full and linearized Navier-Stokes equations are solved by a spectral collocation method to investigate the nonlinear effects on the moments caused by the motion of the fluid inside the cylinder. In this regard, it has been found that nonlinear effects are negligible for τ ≈ 0.1, which is of practical interest to the design of liquid-filled projectiles, and the solution of the linearized Navier-Stokes equations is adequate for such a case. However, as τ increases, nonlinear effects increase, and become significant as ε surpasses about 0.1. In such a case, the nonlinear problem must be solved. Complete details on how to solve such a problem is presented.

scholarly journals The transformation of an interfacial solitary wave of elevation at a bottom step

2009 ◽  
Vol 16 (1) ◽  
pp. 33-42 ◽  
Author(s):  
V. Maderich ◽  
T. Talipova ◽  
R. Grimshaw ◽  
E. Pelinovsky ◽  
B. H. Choi ◽  
...  
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Numerical Study ◽  
Nonlinear Effects ◽  
Ocean Model ◽  
Gardner Equation ◽  
Fully Nonlinear ◽  
Layer Flow ◽  
The One ◽  
Bottom Step

Abstract. In this paper we study the transformation of an internal solitary wave at a bottom step in the framework of two-layer flow, for the case when the interface lies close to the bottom, and so the solitary waves are elevation waves. The outcome is the formation of solitary waves and dispersive wave trains in both the reflected and transmitted fields. We use a two-pronged approach, based on numerical simulations of the fully nonlinear equations using a version of the Princeton Ocean Model on the one hand, and a theoretical and numerical study of the Gardner equation on the other hand. In the numerical experiments, the ratio of the initial wave amplitude to the layer thickness is varied up one-half, and nonlinear effects are then essential. In general, the characteristics of the generated solitary waves obtained in the fully nonlinear simulations are in reasonable agreement with the predictions of our theoretical model, which is based on matching linear shallow-water theory in the vicinity of a step with solutions of the Gardner equation for waves far from the step.

scholarly journals Numerical Study on the Characteristics of Boger Type Viscoelastic Fluid Flow in a Micro Cross-Slot under Sinusoidal Stimulation

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 64
Author(s):  
Chao Yuan ◽  
Hong-Na Zhang ◽  
Li-Xia Chen ◽  
Jun-Long Zhao ◽  
Xiao-Bin Li ◽  
...  
Keyword(s):  
Flow Pattern ◽  
Natural Frequency ◽  
Viscoelastic Fluid ◽  
Numerical Study ◽  
Nonlinear Effects ◽  
Weissenberg Number ◽  
Stimulation Frequency ◽  
External Stimulation ◽  
Inlet Velocity ◽  
The Cross

The cross-slot geometry plays an important role in the study of nonlinear effects of viscoelastic fluids. The flow of viscoelastic fluid in a micro cross-slot with a high channel aspect ratio (AR, the ratio of channel depth to width) can be divided into three types, which are symmetric flow, steady-state asymmetric flow and time-dependent flow under the inlet condition with a constant velocity. However, the flow pattern of a viscoelastic fluid in the cross-slot when a stimulation is applied at inlets has been rarely reported. In this paper, the response of cross-slot flow under an external sinusoidal stimulation is studied by numerical simulations of a two-dimensional model representing the geometry with a maximum limit of AR. For the cases under constant inlet velocity conditions, three different flow patterns occur successively with the increase of Weissenberg number (Wi). For the cases under sinusoidal varying inlet velocity conditions, when the stimulation frequency is far away from the natural frequency of a viscoelastic fluid, the frequency spectrum of velocity fluctuation field shows the characteristics of a fundamental frequency and several harmonics. However, the harmonic frequency disappears when the stimulation frequency is close to the natural frequency of the viscoelastic fluid. Besides, the flow pattern shows spatial symmetry and changes with time. In conclusion, the external stimulation has an effect on the flow pattern of viscoelastic fluid in the 2D micro cross-slot channel, and a resonance occurs when the stimulation frequency is close to the natural frequency of the fluid.

Nonlinear wave propagation in sandstone: A numerical study

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1935-1938 ◽  
Author(s):  
Ningya Cheng
Keyword(s):  
Seismic Waves ◽  
Numerical Study ◽  
Nonlinear Effects ◽  
Crystalline Rock ◽  
Harmonic Spectrum ◽  
Structural Defects ◽  
Single Frequency ◽  
Elastic Behavior ◽  
Nonlinear Wave Propagation ◽  
Frequency Wave

Elastic nonlinear effects in rocks are observed widely in laboratory experiments. For example, Toksöz et al. (1976) measured the pressure dependence of wave speed in the rocks. In crystalline rock and sandstone, Johnson et al. (1987) and Johnson and Shankland (1989) have demonstrated the nonlinear generation of elastic waves. The importance of nonlinear effects in seismic waves in the earth in regard to models of the source is given in Johnson and McCall (1994). The evolution of the harmonic spectrum of a single frequency wave propagated in Berea Sandstone was shown in Meegan et al. (1993). The structural defects contained in rock, such as microcracks and grain‐to‐grain contacts, give rise to this strong elastic nonlinearity (e.g., Gist, 1994). A new theoretical model is developed in McCall and Guyer (1994) to describe elastic behavior of hysteretic nonlinear materials, such as rock. In general, the third‐order elastic constants of the rocks have much larger values than ordered solids.

scholarly journals Accretion of Planetesimals within a Gaseous Ring

1980 ◽  
Vol 33 (3) ◽  
pp. 623 ◽  
Author(s):  
AJR Prentice
Keyword(s):  
Numerical Study ◽  
Nonlinear Effects ◽  
Equation Of Motion ◽  
The Sun ◽  
Gas Density ◽  
Planetary Embryo ◽  
Outer Atmosphere ◽  
Gravitational Influence ◽  
High Reynolds ◽  
Gas Drag

An analytical study is made of the accretion of planetesimals by a planetary embryo within the framework of a modem Laplacian theory for the formation of the planetary system. The equation of motion of the particle, which is initially comoving ahead of (or behind) the growing planet on the same circular Keplerian orbit about the Sun, is examined both in the presence and abseflce of a gaseous torus which is also centred on the same mean orbit. The gas density in the torus is taken to be uniform and the drag exerted on the particle is assumed to vary as the square of the relative velocity, corresponding to motion at high Reynolds number. It is found that the gas acts as a damper to the coriolis acceleration due to the Sun in the rotating frame of reference of the embryo, which tends to pull the particle off the mean circular orbit, thus preventing accretion. In the absence of the gaseous drag, less than 1 % of particles lying well inside the so-called sphere of gravitational influence of the embryo are accreted, whilst if the gas drag is included nearly all of these particles are captured. In all instances the accreting particles impart a spin angular momentum to the embryo which is prograde with the orbital motion. The actual spin rate decreases with increasing gas drag and is found to be lowest for the innermost planets Mercury and Venus, where the gas density is greatest. A more detailed numerical study is probably required to determine the rotational period of larger planets and planetary cores which possess an outer atmosphere, not included in the p$ent study, and where nonlinear effects in the particle's equation of motion cannot be ignored.' 'r.'

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