The Effect of Finite Amplitude Disturbance Magnitude on Departures From Laminar Conditions in Impulsively Started and Steady Pipe Entrance Flows

2001 ◽  
Vol 124 (1) ◽  
pp. 235-240 ◽  
Author(s):  
E. A. Moss ◽  
A. H. Abbot
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shape Parameter ◽  
Critical Reynolds Number ◽  
Flow Instability ◽  
Finite Amplitude ◽  
Pipe Flows ◽  
Displacement Thickness ◽  
Layer Flow ◽  
The Stability

The aim of this study was to investigate first departures from laminar conditions in both impulsively started and steady pipe entrance flows. Wall shear stress measurements were conducted of transition in impulsively started pipe flows with large disturbances. These results were reconciled in a framework of displacement thickness Reynolds number and a velocity profile shape parameter, with existing measurements of pipe entrance flow instability, pipe-Poiseuille and boundary layer flow responses to large disturbances, and linear stability predictions. Limiting critical Reynolds number variations for each type of flow were thus inferred, corresponding to the small and gross disturbance limits respectively. Consequently, insights have been provided regarding the effect of disturbance levels on the stability of both steady and unsteady pipe flows.

The stability of laminar boundary layers at separation

1965 ◽  
Vol 23 (4) ◽  
pp. 737-747 ◽  
Author(s):  
T. H. Hughes ◽  
W. H. Reid
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Adverse Pressure Gradient ◽  
Neutral Curve ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Laminar Boundary Layers ◽  
The Stability ◽  
Limiting Case

The effect of an adverse pressure gradient on the stability of a laminar boundary layer is considered in the limiting case when the skin friction at the wall vanishes, i.e. when U′(0) = 0. Such flows are not absolutely unstable as might have been expected but have a minimum critical Reynolds number of the order of 25. General results are given for the asymptotic behaviour of both the upper and lower branches of the neutral curve and a complete neutral curve is obtained for Pohlhausen's simple fourth-degree polynomial profile at separation.

An experimental study of absolute instability of the rotating-disk boundary-layer flow

1996 ◽  
Vol 314 ◽  
pp. 373-405 ◽  
Author(s):  
R. J. Lingwood
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Wave Packet ◽  
Boundary Layer Flow ◽  
Critical Reynolds Number ◽  
Linear Stability Theory ◽  
Absolute Instability ◽  
Unstable Flow ◽  
Average Value ◽  
Layer Flow

In this paper, the results of experiments on unsteady disturbances in the boundary-layer flow over a disk rotating in otherwise still air are presented. The flow was perturbed impulsively at a point corresponding to a Reynolds numberRbelow the value at which transition from laminar to turbulent flow is observed. Among the frequencies excited are convectively unstable modes, which form a three-dimensional wave packet that initially convects away from the source. The wave packet consists of two families of travelling convectively unstable waves that propagate together as one packet. These two families are predicted by linear-stability theory: branch-2 modes dominate close to the source but, as the packet moves outwards into regions with higher Reynolds numbers, branch-1 modes grow preferentially and this behaviour was found in the experiment. However, the radial propagation of the trailing edge of the wave packet was observed to tend towards zero as it approaches the critical Reynolds number (about 510) for the onset of radial absolute instability. The wave packet remains convectively unstable in the circumferential direction up to this critical Reynolds number, but it is suggested that the accumulation of energy at a well-defined radius, due to the flow becoming radially absolutely unstable, causes the onset of laminar–turbulent transition. The onset of transition has been consistently observed by previous authors at an average value of 513, with only a small scatter around this value. Here, transition is also observed at about this average value, with and without artificial excitation of the boundary layer. This lack of sensitivity to the exact form of the disturbance environment is characteristic of an absolutely unstable flow, because absolute growth of disturbances can start from either noise or artificial sources to reach the same final state, which is determined by nonlinear effects.

The effect of external forcing on the stability of plane Poiseuille flow

1978 ◽  
Vol 359 (1699) ◽  
pp. 453-478 ◽  
Keyword(s):  
Reynolds Number ◽  
Poiseuille Flow ◽  
Critical Reynolds Number ◽  
Stable Solution ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Plane Poiseuille Flow ◽  
Critical Reynolds Numbers ◽  
Threshold Amplitude ◽  
The Stability

The stability of plane Poiseuille flow in a channel forced by a wavelike motion on one of the channel walls is investigated. The amplitude Є of this forcing is taken to be small. The most dangerous modes of forcing are identified and it is found in general the critical Reynolds number is changed by O (Є) 2 . However, we identify two particular modes of forcing which give rise to decrements of order Є 2/3 and Є in the critical Reynolds number. Some types of forcing are found to generate sub critical stable finite amplitude perturbations to plane Poiseuille flow. This contrasts with the unforced case where the only stable solution is the zero amplitude solution. The forcing also deforms the unstable subcritical limit cycle solution from its usual circular shape into a more complicated shape. This has an effect on the threshold amplitude ideas suggested by, for example, Meksyn & Stuart (1951). It is found that the phase of disturbances must also be considered when finding the amplitude dependent critical Reynolds numbers.

On the stability of attachment-line boundary layers. Part 2. The effect of leading-edge curvature

1997 ◽  
Vol 333 ◽  
pp. 125-137 ◽  
Author(s):  
RAY-SING LIN ◽  
MUJEEB R. MALIK
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Leading Edge ◽  
Mean Flow ◽  
Eigenvalue Approach ◽  
Curvature Effects ◽  
The Mean ◽  
The Stability ◽  
Attachment Line

The stability of the incompressible attachment-line boundary layer has been studied by Hall, Malik & Poll (1984) and more recently by Lin & Malik (1996). These studies, however, ignored the effect of leading-edge curvature. In this paper, we investigate this effect. The second-order boundary-layer theory is used to account for the curvature effects on the mean flow and then a two-dimensional eigenvalue approach is applied to solve the linear stability equations which fully account for the effects of non-parallelism and leading-edge curvature. The results show that the leading-edge curvature has a stabilizing influence on the attachment-line boundary layer and that the inclusion of curvature in both the mean-flow and stability equations contributes to this stabilizing effect. The effect of curvature can be characterized by the Reynolds number Ra (based on the leading-edge radius). For Ra = 104, the critical Reynolds number R (based on the attachment-line boundary-layer length scale, see §2.2) for the onset of instability is about 637; however, when Ra increases to about 106 the critical Reynolds number approaches the value obtained earlier without curvature effect.

The Stability of Pipe Entrance Flows Subjected to Axisymmetric Disturbances

1994 ◽  
Vol 116 (1) ◽  
pp. 61-65 ◽  
Author(s):  
D. F. da Silva ◽  
E. A. Moss
Keyword(s):  
Boundary Layer ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Axial Distance ◽  
Displacement Thickness ◽  
Critical Reynolds Numbers ◽  
Equilibrium Profile ◽  
Stability Data ◽  
The Stability ◽  
Theoretical Results

This paper reexamines an important unresolved problem in fluid mechanics—the discrepancy between measurements and predictions of stability in pipe entrance flows. Whereas measured critical Reynolds numbers are relatively insensitive to velocity profile shape in the streamwise direction, the theoretical results indicate a rapid increase, both as the equilibrium profile is approached, and toward the inlet. The current work uses the displacement thickness based Reynolds number as a rational basis on which to compare new stability predictions obtained by means of the Q-Z algorithm, with existing theoretical results. Although the present data are shown to be the only that are consistent with the classical parallel boundary layer limit towards the inlet, they still deviate increasingly with axial distance from the only available experimental results. By examining pipe inlet stability data in relation to boundary layer measurements and predictions, the work effectively questions the commonly held belief that streamwise variations of flow alone are responsible for these deviations, suggesting that the finite amplitude nature of the applied disturbances is the most likely cause.

Analysis of an Electromagnetic Boundary Layer Probe for Low Magnetic Reynolds Number Flows

1993 ◽  
Vol 115 (4) ◽  
pp. 726-731 ◽  
Author(s):  
L. S. Langston ◽  
R. G. Kasper
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layer Flow ◽  
Magnetic Reynolds Number ◽  
Field Size ◽  
Flow Meter ◽  
Displacement Thickness ◽  
Layer Flow ◽  
Reynolds Number Flows

Electromagnetic (EM) flow meters are used to measure volume flow rates of electrically conductive fluids (e.g., low magnetic Reynolds number flows of seawater, milk, etc.) in pipe flows. The possibility of using a modified form of EM flow meter to nonobtrusively measure boundary-layer flow characteristics is analytically investigated in this paper. The device, named an electromagnetic boundary layer (EBL) probe, would have a velocity integral-dependent voltage induced between parallel wall-mounted electrodes, as a conductive fluid flows over a dielectric wall and through the probe’s magnetic field. The Shercliff-Bevir integral equation, taken from EM flow meter theory and design, is used as the basis of the analytical model for predicting EBL probe voltage outputs, given a specified probe geometry and boundary layer flow conditions. Predictions are made of the effective range of the nonobtrusive EBL probe in terms of electrode dimensions, the magnetic field size and strength, and boundary layer velocity profile and thickness. The analysis gives expected voltage calibration curves and shows that an array of paired electrodes would be a beneficial feature for probe design. A key result is that the EBL probe becomes a displacement thickness meter, if operated under certain conditions. That is, the output voltage was found to be directly proportional to the boundary layer displacement thickness, δ1, for a given free stream velocity.

scholarly journals On the stability of the boundary layer at the bottom of propagating surface waves

2021 ◽  
Vol 928 ◽  
Author(s):  
Paolo Blondeaux ◽  
Jan Oscar Pralits ◽  
Giovanna Vittori
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Second Harmonic ◽  
Harmonic Component ◽  
Threshold Value ◽  
Finite Amplitude ◽  
Turbulent Regime ◽  
Laminar Regime ◽  
Steady Streaming ◽  
The Stability

This study contributes to an improved understanding of the stability of the boundary layer generated at the bottom of a propagating surface wave of small but finite amplitude such that both a second harmonic component and a steady streaming component, which are superimposed on the main oscillatory flow, assume significant values. A linear stability analysis of the laminar flow is made to determine the conditions leading to transition and turbulence appearance. The Reynolds number of the phenomenon is assumed to be large and a ‘momentary’ criterion of stability is used. The results show that, at a given location, the laminar regime becomes unstable when the flow close to the bottom reverses its direction from the onshore to the offshore direction and the Reynolds number exceeds a first critical value $R_{\delta ,c1}$ . However, close to the critical condition, the flow is expected to relaminarize during the other phases of the cycle. Only when the Reynolds number is increased does turbulence tend to appear also after the passage of the wave trough when the flow close to the bottom reverses from the offshore to the onshore direction. When the Reynolds number is further increased and becomes larger than a second ‘threshold’ value, the growth rate of the perturbations becomes positive over the entire wave period. The obtained results suggest the existence of four different flow regimes: the laminar regime, the disturbed laminar regime, the intermittently turbulent regime and the fully developed turbulent regime.

Effect of Reynolds number on drag reduction in turbulent boundary layer flow over liquid–gas interface

2020 ◽  
Vol 32 (12) ◽  
pp. 122111
Author(s):  
Hongyuan Li ◽  
SongSong Ji ◽  
Xiangkui Tan ◽  
Zexiang Li ◽  
Yaolei Xiang ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Drag Reduction ◽  
Boundary Layer Flow ◽  
Turbulent Boundary Layer Flow ◽  
Layer Flow
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