THE INFLUENCE OF UPSTREAM TURBULENCE ON THE STABILITY BOUNDARIES OF A FLEXIBLE TUBE IN A BUNDLE

1998 ◽  
Vol 12 (2) ◽  
pp. 153-169 ◽  
Author(s):  
O. ROMBERG ◽  
K. POPP
Keyword(s):  
Stability Boundaries ◽  
Flexible Tube ◽  
The Stability

Influence of Upstream Turbulence on the Fluidelastic Instability of a Tube Bundle With Various Flexible Tubes

2002 ◽  
Author(s):  
M. Rottmann ◽  
K. Popp
Keyword(s):  
Heat Exchanger ◽  
Wind Tunnel ◽  
Tube Bundle ◽  
Stability Boundaries ◽  
Realistic Condition ◽  
Flexible Tube ◽  
Stabilizing Effect ◽  
The Stability ◽  
Flexible Tubes ◽  
Upstream Flow

The stability boundaries of a single flexible tube in one of the first rows of a tube bundle can be highly dependent on the turbulence characteristics of the upstream flow, cf. (Rottmann & Popp, 2001). For certain bundle geometries increased turbulence yields a stabilization of a flexible tube in the critical row. If this stabilization also occurs on the more realistic condition of a fully flexible bundle it could be a useful effect with respect to applications. The flow rate in a heat exchanger could be increased or existing stability problems could easily be solved by inserting turbulence grids at the inlet instead of changing the entire tube bundle. Therefore, wind tunnel tests have been carried out with various flexible tubes in the tube bundle. The vibrations in the tube bundle have been carefully observed and measured by means of accelerometers. These investigations still show a significant stabilizing effect of increased upstream turbulence.

Symmetrizable Difference Dchemes

2005 ◽  
Vol 5 (1) ◽  
pp. 3-50 ◽  
Author(s):  
Alexei A. Gulin
Keyword(s):  
Initial Data ◽  
Difference Scheme ◽  
Difference Schemes ◽  
Time Dependent ◽  
Stability Boundaries ◽  
Typical Representative ◽  
Variable Weight ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Right

AbstractA review of the stability theory of symmetrizable time-dependent difference schemes is represented. The notion of the operator-difference scheme is introduced and general ideas about stability in the sense of the initial data and in the sense of the right hand side are formulated. Further, the so-called symmetrizable difference schemes are considered in detail for which we manage to formulate the unimprovable necessary and su±cient conditions of stability in the sense of the initial data. The schemes with variable weight multipliers are a typical representative of symmetrizable difference schemes. For such schemes a numerical algorithm is proposed and realized for constructing stability boundaries.

scholarly journals Quiescent Gap Solitons in Coupled Nonuniform Bragg Gratings with Cubic-Quintic Nonlinearity

2021 ◽  
Vol 11 (11) ◽  
pp. 4833
Author(s):  
Afroja Akter ◽  
Md. Jahedul Islam ◽  
Javid Atai
Keyword(s):  
Numerical Stability ◽  
Bragg Gratings ◽  
Stability Boundaries ◽  
Quintic Nonlinearity ◽  
Numerical Stability Analysis ◽  
Gap Solitons ◽  
The Stability ◽  
Dual Core

We study the stability characteristics of zero-velocity gap solitons in dual-core Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity. The model supports two disjointed families of gap solitons (Type 1 and Type 2). Additionally, asymmetric and symmetric solitons exist in both Type 1 and Type 2 families. A comprehensive numerical stability analysis is performed to analyze the stability of solitons. It is found that dispersive reflectivity improves the stability of both types of solitons. Nontrivial stability boundaries have been identified within the bandgap for each family of solitons. The effects and interplay of dispersive reflectivity and the coupling coefficient on the stability regions are also analyzed.

DRY TURBULENCE FROM A TIME-DELAYED CHUA'S CIRCUIT

1993 ◽  
Vol 03 (02) ◽  
pp. 645-668 ◽  
Author(s):  
A. N. SHARKOVSKY ◽  
YU. MAISTRENKO ◽  
PH. DEREGEL ◽  
L. O. CHUA
Keyword(s):  
Difference Equation ◽  
Stability Region ◽  
Nonlinear Difference Equation ◽  
Chua’S Circuit ◽  
Stability Boundaries ◽  
Chua's Circuit ◽  
Infinite Dimensional ◽  
Chaotic Region ◽  
The Stability ◽  
Left Portion

In this paper, we consider an infinite-dimensional extension of Chua's circuit (Fig. 1) obtained by replacing the left portion of the circuit composed of the capacitance C2 and the inductance L by a lossless transmission line as shown in Fig. 2. As we shall see, if the remaining capacitance C1 is equal to zero, the dynamics of this so-called time-delayed Chua's circuit can be reduced to that of a scalar nonlinear difference equation. After deriving the corresponding 1-D map, it will be possible to determine without any approximation the analytical equation of the stability boundaries of cycles of every period n. Since the stability region is nonempty for each n, this proves rigorously that the time-delayed Chua's circuit exhibits the "period-adding" phenomenon where every two consecutive cycles are separated by a chaotic region.

Influence of Gravity and Taper on the Vibration of a Standing Column

2012 ◽  
Vol 4 (04) ◽  
pp. 483-495 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Cross Section ◽  
Numerical Stability ◽  
Natural Vibration ◽  
Vibration Frequencies ◽  
Stability Criteria ◽  
Initial Value ◽  
Vertical Column ◽  
Stability Boundaries ◽  
Section Shape ◽  
The Stability

AbstractThe stability and natural vibration of a standing tapered vertical column under its own weight are studied. Exact stability criteria are found for the pointy column and numerical stability boundaries are determined for the blunt tipped column. For vibrations we use an accurate, efficient initial value numerical method for the first three frequencies. Four kinds of columns with linear taper are considered. Both the taper and the cross section shape of the column have large influences on the vibration frequencies. It is found that gravity decreases the frequency while the degree of taper may increase or decrease frequency. Vibrations may occur in two different planes.

A Method of Model Reduction

1986 ◽  
Vol 108 (4) ◽  
pp. 368-371 ◽  
Author(s):  
Jium-Ming Lin ◽  
Kuang-Wei Han
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Model Reduction ◽  
Control Systems ◽  
Response Curve ◽  
Nonlinear Control Systems ◽  
Frequency Response Curve ◽  
Stability Boundaries ◽  
Parameter Variations ◽  
The Stability

In this brief note, the effects of model reduction on the stability boundaries of control systems with parameter variations, and the limit-cycle characteristics of nonlinear control systems are investigated. In order to reduce these effects, a method of model reduction is used which can approximate the original transfer function at S=0, S=∞, and also match some selected points on the frequency response curve of the original transfer function. Examples are given, and comparisons with the methods given in current literature are made.

Stability of non-parabolic flow in a flexible tube

1999 ◽  
Vol 395 ◽  
pp. 211-236 ◽  
Author(s):  
V. SHANKAR ◽  
V. KUMARAN
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Asymptotic Analysis ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Flexible Tube ◽  
Developing Flow ◽  
Parabolic Flow ◽  
High Reynolds ◽  
The Stability

Flows with velocity profiles very different from the parabolic velocity profile can occur in the entrance region of a tube as well as in tubes with converging/diverging cross-sections. In this paper, asymptotic and numerical studies are undertaken to analyse the temporal stability of such ‘non-parabolic’ flows in a flexible tube in the limit of high Reynolds numbers. Two specific cases are considered: (i) developing flow in a flexible tube; (ii) flow in a slightly converging flexible tube. Though the mean velocity profile contains both axial and radial components, the flow is assumed to be locally parallel in the stability analysis. The fluid is Newtonian and incompressible, while the flexible wall is modelled as a viscoelastic solid. A high Reynolds number asymptotic analysis shows that the non-parabolic velocity profiles can become unstable in the inviscid limit. This inviscid instability is qualitatively different from that observed in previous studies on the stability of parabolic flow in a flexible tube, and from the instability of developing flow in a rigid tube. The results of the asymptotic analysis are extended numerically to the moderate Reynolds number regime. The numerical results reveal that the developing flow could be unstable at much lower Reynolds numbers than the parabolic flow, and hence this instability can be important in destabilizing the fluid flow through flexible tubes at moderate and high Reynolds number. For flow in a slightly converging tube, even small deviations from the parabolic profile are found to be sufficient for the present instability mechanism to be operative. The dominant non-parallel effects are incorporated using an asymptotic analysis, and this indicates that non-parallel effects do not significantly affect the neutral stability curves. The viscosity of the wall medium is found to have a stabilizing effect on this instability.

Modern design of belt conveyors in the context of stability boundaries and chaos

1992 ◽  
Vol 338 (1651) ◽  
pp. 491-502 ◽  
Keyword(s):  
Initial Conditions ◽  
Nonlinear Resonance ◽  
Stability Boundaries ◽  
Belt Speed ◽  
Bearing Life ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration ◽  
Belt Conveyors ◽  
The Stability ◽  
Two Parameters

Belt conveying of bulk materials has evolved to the point where the demands of the modern mine to increase capacity is limited by the ability of engineers to design dynamically stable conveyors. Belt speed and width are two parameters that may be varied in the design to provide the required material flow rate. For certain values of belt speed, width and tension, unstable transverse belt vibration has been observed. Large-amplitude vibration may be so severe that the life of the supporting idler bearings is reduced significantly due to dynamic loads. Monitoring idlers for bearing failure in modern conveyors with lengths up to 20 km is practically difficult since there may be as many as 20000 idler sets. Chaotic transverse belt vibrations occur for certain levels of excitation, further complicating the prediction of bearing life. Before conveyor installation, an estimate of the stability boundaries for resonance-free operation is an essential precursor to failure-free conveyor operation. Nonlinear resonance phenomena such as belt flap is sensitive to initial conditions. The effects of chaotic vibrations on the predictability of design stability is reviewed using some examples of forced vibrations.

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