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.

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.

Paper 5. Directional Stability and Control of a Vessel in Restricted Waters

1972 ◽  
Vol 14 (7) ◽  
pp. 29-33 ◽  
Author(s):  
M. Fujino
Keyword(s):  
Hydrodynamic Force ◽  
Equations Of Motion ◽  
Narrow Channel ◽  
Order Theory ◽  
Stability Criteria ◽  
First Order ◽  
Stability And Control ◽  
First Order Theory ◽  
And Control ◽  
Improve Stability

By way of introduction the paper discusses conflicting observations of stability behaviour of ships in restricted waters. The equations of motion of a ship in a narrow channel are given, leading to stability criteria; differences from the deep water case are highlighted. More qualitatively, the theory also illustrates the asymmetric hydrodynamic force. Criteria are outlined for an automatic control system to improve stability. However, the first-order theory is shown to provide an inadequate description of all experimental results.

On the theory of hypersonic flow past plane and axially symmetric bluff bodies

1956 ◽  
Vol 1 (4) ◽  
pp. 366-387 ◽  
Author(s):  
N. C. Freeman
Keyword(s):  
Hypersonic Flow ◽  
The Body ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Radius Of Curvature ◽  
Bluff Bodies ◽  
Axially Symmetric ◽  
Nose Radius ◽  
Flow Past ◽  
Past Plane

The ‘Newtonian-plus-centrifugal’ approximate solution (Busemann (1933) and Ivey (1948)) for hypersonic flow past plane and axially symmetric bluff bodies in gases with the ratio of the specific heats λ constant and equal to unity is rederived using ‘boundary layer’ techniques together with the von Mises variables x and ψ. A method of successive approximations then gives a closer approximation to this solution for ε (λ − 1)/(λ + 1) small and the free-strea Mach number infinite. Formulae for the streamlines, shock shape and pressure distribution are determined to this approximation. These formulae are valid for any plane or axially symmetric shape, giving the ‘stand-off’ distance of the shock wave from the body as ½εlog(4|3ε) and ε times the nose radius of curvature for plane and axially-symmetric flows respectively. Particular results are computed for a number of special shapes. For certain shapes, the theory has a singular point where the first approximation to the pressure vanishes (θ = 60° for a sphere). Actually, the theory is not applicable where the pressure becomes too small. The corresponding theory for gases of general thermodynamic properties is deduced, the approximation being valid provided the total energy of the gas is large compared with the energy contained in the translational modes of the gas molecules.

scholarly journals Impulsive Motion Inside a Cylindrical Cavity

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 192
Author(s):  
Yuriy Savchenko ◽  
Georgiy Savchenko ◽  
Yuriy A. Semenov
Keyword(s):  
Cylindrical Cavity ◽  
Experimental Studies ◽  
Added Mass ◽  
Axisymmetric Body ◽  
The Body ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Main Concern ◽  
Free Boundaries ◽  
Hodograph Method

Experimental studies of supercavitating models moving at speeds in the range from 400 m/s to 1000 m/s revealed a regime of bouncing motion, in which the rear part of an axisymmetric body periodically bounces against the free boundaries of the supercavity. The impulsive force generated by the impacts is the main concern in this paper. The analysis is performed in the approximation of two-dimensional potential flow of an ideal and incompressible liquid with negligible surface tension effects. The primary interest of the study is to determine the added mass taking into account the shape of the cavity. The theoretical study is based on the integral hodograph method, which makes it possible to obtain analytic expressions for the flow potential and for the complex velocity in an auxiliary parameter plane and obtain a parametric solution to the problem. The problem is reduced to a system of two integro-differential equations in two unknowns: the velocity magnitude on the cavity boundary and the slope of the velocity angle to the body. The equations are solved numerically using the method of successive approximations. The obtained results show that the added mass of an arc impacting a cylindrical cavity depends heavily on the arc angle. As the angle tends to zero or the radius of the cavity tends to infinity, the obtained solution predicts the added mass corresponding to a plate impacting a flat free surface.

Thermal boundary-layer theory near the stagnation point in three-dimensional fluctuating flow

1970 ◽  
Vol 43 (3) ◽  
pp. 465-476 ◽  
Author(s):  
S. Ghoshal ◽  
A. Ghoshal
Keyword(s):  
Skin Friction ◽  
Stagnation Point ◽  
Critical Frequency ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
The Body ◽  
Phase Advance ◽  
Mean Flow ◽  
The Mean ◽  
Oncoming Stream

The equations of motion and energy governing a three-dimensional fluctuating flow of an incompressible fluid in the vicinity of a stagnation point on a regular surface have been integrated analytically. The velocity of the oncoming flow relative to the body oscillates in magnitude but not in direction.It has also been shown that the analysis of Lighthill for the two-dimensional fluctuating flow may be extended to the three-dimensional flow (both chordwise and spanwise), namely for each point on the body there is a critical frequency ω0 such that for frequencies ω > ω0 the oscillations are to a close approximation ordinary ‘shear waves’, unaffected by the mean flow; the phase advance in the skin friction is then 45°. For frequencies ω < ω0 the oscillations may be closely approximated by the sum of two parts: one quasi-steady part and the other proportional to the acceleration of the oncoming stream. The phase advance in the skin friction is then tan−1 (ω/ω0).

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.

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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