On a sphere performing linear and torsional oscillations in a viscous fluid

1988 ◽  
Vol 66 (7) ◽  
pp. 576-579
Author(s):  
G. T. Karahalios ◽  
C. Sfetsos
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Secondary Flow ◽  
Small Amplitude ◽  
Equations Of Motion ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Time Varying ◽  
Torsional Oscillations

A sphere executes small-amplitude linear and torsional oscillations in a fluid at rest. The equations of motion of the fluid are solved by the method of successive approximations. Outside the boundary layer, a steady secondary flow is induced in addition to the time-varying motion.

Method of successive approximations for the Riemann problem with a small-amplitude discontinuity

2011 ◽  
Vol 83 (2) ◽  
pp. 143-148
Author(s):  
P. E. Karabut ◽  
V. V. Ostapenko
Keyword(s):  
Riemann Problem ◽  
Small Amplitude ◽  
Successive Approximations ◽  
Method Of Successive Approximations

The flow induced by torsional oscillations of infinite planes

1969 ◽  
Vol 37 (2) ◽  
pp. 337-347 ◽  
Author(s):  
A. F. Jones ◽  
S. Rosenblat
Keyword(s):  
Viscous Fluid ◽  
Boundary Layers ◽  
High Frequency ◽  
Small Amplitude ◽  
Second Order ◽  
Torsional Oscillations ◽  
Common Axis ◽  
High Frequency Oscillations

A viscous fluid is confined between two parallel, infinite planes which perform torsional oscillations of small amplitude about a common axis. The resulting flow is studied for the case of high-frequency oscillations, when boundary layers form adjacent to moving surfaces. Particular analysis is made of the second-order, steady, radial-axial streaming. It is shown that in certain circumstances viscosity may be effective throughout the domain of flow, while in others there is a region in which viscosity is negligible.

Cavity Flow in a Boundary Layer

2010 ◽  
Author(s):  
Bum-Sang Yoon ◽  
Yuriy A. Semenov
Keyword(s):  
Boundary Layer ◽  
Numerical Procedure ◽  
Cavity Flow ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Finite Width ◽  
Layer Width ◽  
Variable Theory ◽  
Discrete Vortex ◽  
Vortex Lines

A numerical-and-analytical method for solving cavity flows in a vortex incidence flow is proposed. The continuous vorticity arbitrary displayed in the flow field is replaced by discrete vortex lines coinciding with stream lines. The flow between these lines is assumed to be vortex free. The problems of the flow in channels formed by stream/vortex lines and the problem of the cavity flow in a jet of a finite width connected to each other by the derived interaction conditions are solved by using complex variable theory. The numerical procedure is based on the method of successive approximations and adopted to investigate the effect of the velocity gradient in a boundary layer on parameters of the cavity flow. The presented calculations show that, at some fixed cavity length, the cavity number and drag coefficient decreases with the increase of the boundary layer width.

Parametric Excitation Under Multiple Excitation Parameters: Asymmetric Plates Under a Rotating Spring

1991 ◽  
Author(s):  
I. Y. Shen ◽  
C. D. Mote
Keyword(s):  
Dynamic Systems ◽  
Equations Of Motion ◽  
System Stability ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Matrix Eigenvalue Problem ◽  
Secondary Resonances ◽  
Nonlinear Matrix ◽  
Perturbation Parameters ◽  
Floquet Theorem

Abstract A perturbation method is developed to predict stability of parametrically excited dynamic systems containing multiple perturbation parameters. This method, based on the Floquet theorem and the method of successive approximations, results in a nonlinear matrix eigenvalue problem whose eigenvalues are used to predict the system stability. The method is applied to a classical circular plate, containing elastic or viscoelastic inclusions, excited by a linear transverse spring rotating at constant speed. Primary and secondary resonances are predicted. The transition to instability predicted by the perturbation analysis agrees with predictions obtained by numerical integration of the equations of motion.

Flow Near the Stagnation Point of a Body Which Undergoes a Sudden Change in a Steady Stream

1973 ◽  
Vol 40 (1) ◽  
pp. 37-42 ◽  
Author(s):  
K. Nanbu
Keyword(s):  
Stagnation Point ◽  
Equations Of Motion ◽  
Sudden Change ◽  
Order Theory ◽  
Small Time ◽  
The Body ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
First Order Theory ◽  
Time Solution

Unsteady laminar boundary layers near the stagnation point of a body which undergoes a sudden change in a steady stream are analyzed by the method of successive approximations. It is shown that the second approximation which includes the effect of nonlinear convective terms of the equations of motion improves remarkably the first-order theory by the earlier investigators. Also, it seems that when the body is started with velocity increasing gradually with increasing time, the small-time solution obtained thus connects smoothly with the existing large-time solution.

scholarly journals Curvilinear Squeeze Film Bearing Lubricated with a Dehaven Fluid or with Similar Fluids

2017 ◽  
Vol 22 (3) ◽  
pp. 697-715
Author(s):  
A. Walicka ◽  
P. Jurczak ◽  
J. Falicki
Keyword(s):  
Reynolds Equation ◽  
Equations Of Motion ◽  
Unified Model ◽  
Squeeze Film ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Shear Stresses ◽  
Strain Rates ◽  
Load Carrying Capacity ◽  
Load Carrying

AbstractIn the paper, the model of a DeHaven fluid and some other models of non-Newtonian fluids, in which the shear strain rates are known functions of the powers of shear stresses, are considered. It was demonstrated that these models for small values of material constants can be presented in a form similar to the form of a DeHaven fluid. This common form, called a unified model of the DeHaven fluid, was used to consider a curvilinear squeeze film bearing. The equations of motion of the unified model, given in a specific coordinate system are used to derive the Reynolds equation. The solution to the Reynolds equation is obtained by a method of successive approximations. As a result one obtains formulae expressing the pressure distribution and load-carrying capacity. The numerical examples of flows of the unified DeHaven fluid in gaps of two simple squeeze film bearings are presented.

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