Nonlinear Stability Analysis of a Two-Dimensional Model of an Elastic Tube Conveying a Compressible Flow

1979 ◽  
Vol 46 (1) ◽  
pp. 31-36 ◽  
Author(s):  
Y. Matsuzaki ◽  
Y.-C. Fung
Keyword(s):  
Fluid Dynamic ◽  
Elastic Tube ◽  
Two Dimensional ◽  
Nonlinear Stability Analysis ◽  
Internal Wall ◽  
Equilibrium Configurations ◽  
Dynamic Forces ◽  
Unsteady Fluid ◽  
The Stability ◽  
Small Disturbances

This paper examines the dynamic behavior of a two-dimensional channel whose upper and lower walls deform symmetrically with respect to the center line of the channel. Unsteady fluid dynamic forces acting on the internal wall are analytically evaluated on the basis of a linearized compressible potential flow theory. The effects of distributed springs outside the channel and an internal pressure on the stability characteristics are studied by considering small disturbances about flat and buckled equilibrium configurations of the wall. The analytic methods indicate that no flutter of the flat or buckled wall is predicted when the Mach number is small and the viscous damping coefficient is positive. Numerical results by the Runge-Kutta-Gill method suggest that nonlinear effect of flow should be taken into account to fully examine the dynamic characteristics of the channel conveying a flow.

Direct Measurement of Unsteady Fluid Dynamic Forces for a Hovering Dragonfly

AIAA Journal ◽  
2005 ◽  
Vol 43 (12) ◽  
pp. 2475-2480 ◽  
Author(s):  
Manabu Yamamoto ◽  
Koji Isogai
Keyword(s):  
Direct Measurement ◽  
Fluid Dynamic ◽  
Dynamic Forces ◽  
Unsteady Fluid

Flow-Induced Vibration of Tube Arrays With Various Pitch-to-Diameter Ratios

1982 ◽  
Vol 104 (3) ◽  
pp. 168-174 ◽  
Author(s):  
H. Tanaka ◽  
S. Takahara ◽  
K. Ohta
Keyword(s):  
Fluid Dynamic ◽  
Cross Flow ◽  
Diameter Ratio ◽  
Flow Induced Vibration ◽  
Threshold Velocity ◽  
Unsteady Forces ◽  
Practical Applications ◽  
Tube Arrays ◽  
Dynamic Forces ◽  
Unsteady Fluid

Tube arrays in cross flow start to vibrate abruptly when the flow reaches at a certain velocity. The threshold flow velocity depends upon the geometrical arrangement of tubes. It is very important for practical applications to understand the relations between the threshold velocity and pitch-to-diameter ratio of tube array. Unsteady fluid dynamic forces on a tube array with a pitch-to-diameter ratio of 2.0 were clarified experimentally and the characteristics of the threshold velocity were revealed by calculating the velocity with the unsteady forces. By comparing the threshold velocities of tube arrays of pitch-to-diameter ratio of 2.0 and 1.33, the characteristics of threshold velocity with respect to pitch-to-diameter ratio were clarified.

The Unsteady Potential Flow in an Axially Variable Annulus and Its Effect on the Dynamics of the Oscillating Rigid Center-Body

1985 ◽  
Vol 107 (3) ◽  
pp. 421-427 ◽  
Author(s):  
Dan Mateescu ◽  
Michael P. Paidoussis
Keyword(s):  
Potential Flow ◽  
Fluid Dynamic ◽  
Variable Cross Section ◽  
Analytical Investigation ◽  
Accurate Solution ◽  
Variable Cross ◽  
Approximation Solution ◽  
Dynamic Forces ◽  
The Stability ◽  
Center Body

This paper presents an analytical investigation of the unsteady potential flow in a narrow annular passage formed by a motionless rigid duct and an oscillating rigid center-body, both of axially variable cross section, in order to determine the fluid-dynamic forces exerted on the center-body. Based on this theory, a first-approximation solution as well as a more accurate solution are derived for the unsteady incompressible fluid flow. The stability of the center-body is investigated, in terms of the aerodynamic (or hydrodynamic) coefficients of damping, stiffness and inertia (virtual mass), as determined by this theory. The influence of various system parameters on stability is discussed.

On the behaviour of small disturbances in plane Couette flow with a temperature gradient

1965 ◽  
Vol 286 (1404) ◽  
pp. 117-128 ◽  
Keyword(s):  
Rayleigh Number ◽  
Couette Flow ◽  
Reynolds Numbers ◽  
Neutral Stability ◽  
Two Dimensional ◽  
Plane Couette Flow ◽  
Infinitesimal Disturbance ◽  
Prandtl Numbers ◽  
The Stability ◽  
Small Disturbances

The stability of plane Couette flow with a heated lower plate is considered with respect to a two-dimensional infinitesimal disturbance. The eigenvalues are found with the aid of a digital computer as the latent roots of a matrix. Neutral stability curves for various Prandtl numbers at Reynolds numbers up to 150 are obtained by a second method. It is found that the principle of the exchange of stabilities does not hold for this problem. With the aid of Squire’s transformation the conclusion is drawn that all fluids will become unstable at the same value of the Rayleigh number irrespective of whether shear is present or not.

The stability of an incompressible two-dimensional wake

1972 ◽  
Vol 51 (2) ◽  
pp. 233-272 ◽  
Author(s):  
G. E. Mattingly ◽  
W. O. Criminale
Keyword(s):  
Reference Frames ◽  
Two Dimensional ◽  
Mean Velocity ◽  
Spatial Reference ◽  
Spatial Reference Frames ◽  
The Mean ◽  
Temporal And Spatial ◽  
The Stability ◽  
Transverse Oscillations ◽  
Small Disturbances

The growth of small disturbances in a two-dimensional incompressible wake has been investigated theoretically and experimentally. The theoretical analysis is based upon inviscid stability theory wherein small disturbances are considered from both temporal and spatial reference frames. Through a combined stability analysis, in which small disturbances are permitted to amplify in both time and space, the relationship between the disturbance characteristics for the temporal and spatial reference frames is shown. In these analyses a quasi-uniform assumption is adopted to account for the continuously varying mean-velocity profiles that occur behind flat plates and thin airfoils. It is found that the most unstable disturbances in the wake produce transverse oscillations in the mean-velocity profile and correspond to growing waves that have a minimum group velocity.Experimentally, the downstream development of the wake of a thin airfoil and the wave characteristics of naturally amplifying small disturbances are investigated in a water tank. The disturbances that develop are found to produce transverse oscillations of the mean-velocity profile in agreement with the theoretical prediction. From the comparison of the experimental results with the predictions for the characteristics of the most unstable waves via the temporal and spatial analyses, it is concluded that the stability analysis for the wake is to be considered solely from the more realistic spatial viewpoint. Undoubtedly, this conclusion is also applicable to other highly unstable flows such as jets and free shear layers.In accordance with the disturbance vorticity distribution as determined from the spatial model, a description of the initial development of a vortex street is put forth that contrasts with the description given by Sato & Kuriki (1961).

THE STUDY OF THE UNSTEADY FLUID-DYNAMIC FORCES ACTING ON AN AUTO ROTATING ELLIPTIC CYLINDER

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1675-1678
Author(s):  
TAKAHIRO YASUDA ◽  
YASUNARI TAKANO
Keyword(s):  
Fluid Dynamic ◽  
Elliptic Cylinder ◽  
The Body ◽  
High Lift ◽  
Dynamic Forces ◽  
Zero Degree ◽  
Unsteady Fluid ◽  
Complex Velocity Potential ◽  
The One ◽  
Cylinder Rotation

When a thin flat pate is released in the still air, the plate may fall aslant and automatically set into a rotational motion. This phenomenon is called autorotation. In this state, the unsteady fluid-dynamic forces act on the plate due to the vortex shedding and the rotation of the body. In this study, we focused on the auto-rotating phenomenon of an elliptic cylinder and investigated the effect of the cylinder rotation on the unsteady fluid-dynamic forces by the comparison between the result of the complex velocity potential theory and the one of numerical simulation. It was found that the low drag occurring at -160 degree phase and the high lift at zero degree phase are caused by the cylinder rotation.

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