Stability of Nonparallel Developing Flow in a Pipe to Nonaxisymmetric Disturbances

1983 ◽  
Vol 50 (1) ◽  
pp. 210-214 ◽  
Author(s):  
V. K. Garg
Keyword(s):  
Experimental Data ◽  
Critical Reynolds Number ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Main Flow ◽  
Wave Number ◽  
Developing Flow ◽  
Azimuthal Wave Number ◽  
Flow Velocity Profile ◽  
Axisymmetric Disturbances

Linear spatial stability of the nonparallel developing flow in a rigid circular pipe has been studied at several axial locations for nonaxisymmetric disturbances. The main flow velocity profile is obtained by Hornbeck’s finite-difference method assuming uniform flow at entry to the pipe. The method of multiple scales is used to account for all the nonparallel effects. It is found that the nonparallel developing flow is most unstable to nonaxisymmetric disturbances with azimuthal wave number n equal to unity. Axisymmetric disturbances are, however, more unstable than nonaxisymmetric disturbances with n ≥ 2 except in the near-entry region. The results show that the parallel flow theory overpredicts the critical Reynolds number by as much as 136.5 percent in the near entry region for the n = 1 disturbance. The present results compare well with the available experimental data.

Stability of Nonparallel Developing Flow in an Annulus to Asymmetric Disturbances

1982 ◽  
Vol 49 (2) ◽  
pp. 436-439
Author(s):  
V. K. Garg
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Flow Theory ◽  
Diameter Ratio ◽  
Parallel Flow ◽  
Wave Number ◽  
Spatial Stability ◽  
Concentric Annulus ◽  
Developing Flow ◽  
Azimuthal Wave Number

Linear spatial stability of the nonparallel developing flow in a concentric annulus shows that the asymmetric disturbance with an azimuthal wave number equal to unity is more unstable than the axisymmetric disturbance at all axial locations. Also, in the near entry region, the critical Reynolds number corresponding to the parallel flow theory is as much as three times that due to the nonparallel theory for some values of the annular diameter ratio.

The method of multiple scales and non-linear dispersive waves

1971 ◽  
Vol 48 (3) ◽  
pp. 463-475 ◽  
Author(s):  
Ali Hasan Nayfeh ◽  
Sayed D. Hassan
Keyword(s):  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Electron Plasma ◽  
Wave Number ◽  
Hot Electron ◽  
Dispersive Waves ◽  
Physical Systems ◽  
Non Linear ◽  
Temporal And Spatial ◽  
Number Case

The method of multiple scales is used to analyze three non-linear physical systems which support dispersive waves. These systems are (i) waves on the interface between a liquid layer and a subsonic gas flowing parallel to the undisturbed interface, (ii) waves on the surface of a circular jet of liquid, and (iii) waves in a hot electron plasma. It is found that the partial differential equations that govern the temporal and spatial variations of the wave-numbers, amplitudes, and phases have the same form for all of these systems. The results show that the non-linear motion affects only the phase. For the constant wave-number case, the general solution for the amplitude and the phase can be obtained.

Kelvin--Helmholtz instability of a horizontal interface between a finite subsonic gas and a finite magnetic liquid

1998 ◽  
Vol 76 (5) ◽  
pp. 361-374 ◽  
Author(s):  
K Zakaria
Keyword(s):  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Solid Surfaces ◽  
Wave Number ◽  
Magnetic Liquid ◽  
Helmholtz Instability ◽  
Perturbed System ◽  
Progressive Waves ◽  
The Stability ◽  
Horizontal Interface

The nonlinear Kelvin-Helmholtz instability of a horizontal interface between a magnetic inviscid incompressible liquid and an inviscid laminar subsonic gas is investigated. The gas and the liquid are assumed to have finite thicknesses. The applied magnetic field is parallel to the solid surfaces of the considered system. The method of multiple scales is used to obtain two nonlinear Schrodinger equations describing the behaviour of the perturbed system. The stability of the progressive waves is discussed theoretically. The nonlinear cutoff wave number is obtained, where the stability conditions of the standing waves are obtained. A numerical example is applied to discuss the stability diagrams.PACS Nos.: 51.60 and 47.20

Stability of developing flow in a pipe: non-axisymmetric disturbances

1981 ◽  
Vol 110 ◽  
pp. 209-216 ◽  
Author(s):  
Vijay K. Garg
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Critical Reynolds Number ◽  
Temporal Stability ◽  
Developing Flow ◽  
The Stability ◽  
Axisymmetric Disturbances ◽  
Stability Results ◽  
Boundary Layer Edge ◽  
Critical Wavenumber

Spatial stability results for the developing flow in a rigid circular pipe are presented for the velocity profile obtained by the Hornbeck (1963) method and compared with the available temporal stability results for the velocity profile obtained by Sparrow, Lin & Lundgren (1964). The disturbance is taken to be non-axisymmetric, and Gram–Schmidt orthonormalization is used to remove the parasitic errors during numerical integration.It is found that the stability characteristics are very sensitive to the velocity field in the inlet region. At all axial locations investigated the critical frequency and critical wavenumber for the Hornbeck profile are larger than the corresponding values for the Sparrow profile while the critical Reynolds number is smaller. The minimum critical Reynolds number for the Hornbeck profile is only 13250 and occurs at $\overline{X} = 0.0032$ compared with 19780 at $\overline{X} = 0.0049$ for the Sparrow profile. The maximum difference between the two velocity profiles occurs near the boundary-layer edge but is within 5%. Results for the Hornbeck profile are found to be closer to the experimental data of Sarpkaya (1975).

Stability of Poiseuille Flow in Elastic Tubes

1977 ◽  
Vol 44 (1) ◽  
pp. 18-24 ◽  
Author(s):  
W. Midvidy ◽  
W. T. Rouleau
Keyword(s):  
Reynolds Number ◽  
Poiseuille Flow ◽  
Critical Reynolds Number ◽  
Tube Wall ◽  
The Other ◽  
Wave Number ◽  
Rotatory Inertia ◽  
Elastic Tubes ◽  
Temporal And Spatial ◽  
Axisymmetric Disturbances

This paper presents a theoretical analysis of the temporal and spatial stability of Poiseuille flow in elastic tubes to infinitesimal axisymmetric disturbances. A cylindrical shell model which includes the effects of transverse shear and rotatory inertia is employed for the tube wall. The characteristic equation of the system is solved numerically and two sets of modes are obtained; one set has eigenvalues that are independent of the properties and dimensions of the tube wall, while the other set has eigenvalues that depend on the tube parameters. One mode of the “tube-dependent” set is shown to have a critical Reynolds number that depends on the elastic properties and dimensions of the tube and either wave number or frequency of the disturbance.

scholarly journals Experimental Study on Coherent Structures by Particles Suspended in Half-Zone Thermocapillary Liquid Bridges: Review

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 105
Author(s):  
Ichiro Ueno
Keyword(s):  
Coherent Structures ◽  
Three Dimensional ◽  
Wave Number ◽  
Flow Structures ◽  
Liquid Bridges ◽  
Thermocapillary Effect ◽  
Particle Accumulation ◽  
Azimuthal Wave Number ◽  
Experimental Approaches ◽  
Particle Behaviour

Coherent structures by the particles suspended in the half-zone thermocapillary liquid bridges via experimental approaches are introduced. General knowledge on the particle accumulation structures (PAS) is described, and then the spatial–temporal behaviours of the particles forming the PAS are illustrated with the results of the two- and three-dimensional particle tracking. Variations of the coherent structures as functions of the intensity of the thermocapillary effect and the particle size are introduced by focusing on the PAS of the azimuthal wave number m=3. Correlation between the particle behaviour and the ordered flow structures known as the Kolmogorov–Arnold—Moser tori is discussed. Recent works on the PAS of m=1 are briefly introduced.

On the modulation of water waves on shear flows

1976 ◽  
Vol 347 (1651) ◽  
pp. 537-546 ◽  
Keyword(s):  
Water Waves ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Vries Equation ◽  
Harmonic Wave ◽  
Short Wave ◽  
Long Wave ◽  
Stokes Waves ◽  
The Stability ◽  
Wave Limit

The method of multiple scales is used to examine the slow modulation of a harmonic wave moving over the surface of a two dimensional channel. The flow is assumed inviscid and incompressible, but the basic flow takes the form of an arbitrary shear. The appropriate nonlinear Schrödinger equation is derived with coefficients that depend, in a complicated way, on the shear. It is shown that this equation agrees with previous work for the case of no shear; it also agrees in the long wave limit with the appropriate short wave limit of the Korteweg-de Vries equation, the shear being arbitrary. Finally, it is remarked that the stability of Stokes waves over any shear can be examined by using the results derived here.

Difference in Critical Reynolds Number Between Hagen-Poiseuille and Plane Poiseuille Flows

2001 ◽  
Author(s):  
Hidesada Kanda
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Poiseuille Flow ◽  
Average Velocity ◽  
Critical Reynolds Number ◽  
Inlet Section ◽  
Parallel Plates ◽  
Plane Poiseuille Flow ◽  
Contraction Ratio ◽  
Significant Difference

Abstract For plane Poiseuille flow, results of previous investigations were studied, focusing on experimental data on the critical Reynolds number, the entrance length, and the transition length. Consequently, concerning the natural transition, it was confirmed from the experimental data that (i) the transition occurs in the entrance region, (ii) the critical Reynolds number increases as the contraction ratio in the inlet section increases, and (iii) the minimum critical Reynolds number is obtained when the contraction ratio is the smallest or one, and there is no-shaped entrance or straight parallel plates. Its value exists in the neighborhood of 1300, based on the channel height and the average velocity. Although, for Hagen-Poiseuille flow, the minimum critical Reynolds number is approximately 2000, based on the pipe diameter and the average velocity, there seems to be no significant difference in the transition from laminar to turbulent flow between Hagen-Poiseuille flow and plane Poiseuille flow.

scholarly journals Dynamic analysis of a parametrically excited golden Muga silk embedded pneumatic artificial muscle

2018 ◽  
Vol 211 ◽  
pp. 02008 ◽  
Author(s):  
Bhaben Kalita ◽  
S. K. Dwivedy
Keyword(s):  
Dynamic Analysis ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Quadratic Function ◽  
Artificial Muscle ◽  
Equation Of Motion ◽  
Time Response ◽  
Phase Portraits ◽  
Pneumatic Artificial Muscle ◽  
Pneumatic Muscle

In this work a novel pneumatic artificial muscle is fabricated using golden muga silk and silicon rubber. It is assumed that the muscle force is a quadratic function of pressure. Here a single degree of freedom system is considered where a mass is supported by a spring-damper-and pneumatically actuated muscle. While the spring-mass damper is a passive system, the addition of pneumatic muscle makes the system active. The dynamic analysis of this system is carried out by developing the equation of motion which contains multi-frequency excitations with both forced and parametric excitations. Using method of multiple scales the reduced equations are developed for simple and principal parametric resonance conditions. The time response obtained using method of multiple scales have been compared with those obtained by solving the original equation of motion numerically. Using both time response and phase portraits, variation of few systems parameters have been carried out. This work may find application in developing wearable device and robotic device for rehabilitation purpose.

scholarly journals Intermediate-<I>m</I> ULF waves generated by substorm injection: a case study

2010 ◽  
Vol 28 (8) ◽  
pp. 1499-1509 ◽  
Author(s):  
T. K. Yeoman ◽  
D. Yu. Klimushkin ◽  
P. N. Mager
Keyword(s):  
Phase Variation ◽  
Wave Activity ◽  
Wave Number ◽  
Ulf Wave ◽  
Azimuthal Wave ◽  
Azimuthal Wave Number ◽  
Source Particle ◽  
Phase Propagation ◽  
Field Lines

Abstract. A case study of SuperDARN observations of Pc5 Alfvén ULF wave activity generated in the immediate aftermath of a modest-intensity substorm expansion phase onset is presented. Observations from the Hankasalmi radar reveal that the wave had a period of 580 s and was characterized by an intermediate azimuthal wave number (m=13), with an eastwards phase propagation. It had a significant poloidal component and a rapid equatorward phase propagation (~62° per degree of latitude). The total equatorward phase variation over the wave signatures visible in the radar field-of-view exceeded the 180° associated with field line resonances. The wave activity is interpreted as being stimulated by recently-injected energetic particles. Specifically the wave is thought to arise from an eastward drifting cloud of energetic electrons in a similar fashion to recent theoretical suggestions (Mager and Klimushkin, 2008; Zolotukhina et al., 2008; Mager et al., 2009). The azimuthal wave number m is determined by the wave eigenfrequency and the drift velocity of the source particle population. To create such an intermediate-m wave, the injected particles must have rather high energies for a given L-shell, in comparison to previous observations of wave events with equatorward polarization. The wave period is somewhat longer than previous observations of equatorward-propagating events. This may well be a consequence of the wave occurring very shortly after the substorm expansion, on stretched near-midnight field lines characterised by longer eigenfrequencies than those involved in previous observations.

Sign in / Sign up

Export Citation Format

Share Document