Temporal stability of Jeffery–Hamel flow

1994 ◽  
Vol 268 ◽  
pp. 71-88 ◽  
Author(s):  
Mahmoud Hamadiche ◽  
Julian Scott ◽  
Denis Jeandel
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Temporal Stability ◽  
Reynolds Numbers ◽  
Critical Value ◽  
Volume Flux ◽  
Short Channel ◽  
Oscillatory Solutions ◽  
Half Angle ◽  
Critical Reynolds Numbers

In this study of the temporal stability of Jeffery–Hamel flow, the critical Reynolds number based on the volume flux, Rc, and that based on the axial velocity, Rec, are computed. It is found that both critical Reynolds numbers decrease very rapidly when the half-angle of the channel, α, increases, such that the quantity αRc remains very nearly constant and αRecis a nearly linear function of α. For a short channel there can be more than one value of the critical Reynolds number. A fully nonlinear analysis, for Re close to the critical value, indicates that the loss of stability is supercritical. The resulting asymmetric oscillatory solutions show staggered arrays of vortices positioned along the channel.

On the force fluctuations acting on a circular cylinder in crossflow from subcritical up to transcritical Reynolds numbers

1983 ◽  
Vol 133 ◽  
pp. 265-285 ◽  
Author(s):  
Günter Schewe
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Dynamic Range ◽  
Reynolds Numbers ◽  
Band Spectrum ◽  
Transitional Region ◽  
Force Measurements ◽  
Unsteady Forces ◽  
Number Range ◽  
Critical Reynolds Numbers

Force measurements were conducted in a pressurized wind tunnel from subcritical up to transcritical Reynolds numbers 2.3 × 104[les ]Re[les ] 7.1 × 106without changing the experimental arrangement. The steady and unsteady forces were measured by means of a piezobalance, which features a high natural frequency, low interferences and a large dynamic range. In the critical Reynolds-number range, two discontinuous transitions were observed, which can be interpreted as bifurcations at two critical Reynolds numbers. In both cases, these transitions are accompanied by critical fluctuations, symmetry breaking (the occurrence of a steady lift) and hysteresis. In addition, both transitions were coupled with a drop of theCDvalue and a jump of the Strouhal number. Similar phenomena were observed in the upper transitional region between the super- and the transcritical Reynolds-number ranges. The transcritical range begins at aboutRe≈ 5 × 106, where a narrow-band spectrum is formed withSr(Re= 7.1 × 106) = 0.29.

The Stability of Water Flow Over Heated and Cooled Flat Plates

1968 ◽  
Vol 90 (1) ◽  
pp. 109-114 ◽  
Author(s):  
Ahmed R. Wazzan ◽  
T. Okamura ◽  
A. M. O. Smith
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Stream Temperature ◽  
Heated Wall ◽  
Flat Plates ◽  
Critical Reynolds Numbers ◽  
The Stability ◽  
Sommerfeld Equation

The theory of two-dimensional instability of laminar flow of water over solid surfaces is extended to include the effects of heat transfer. The equation that governs the stability of these flows to Tollmien-Schlichting disturbances is the Orr-Sommerfeld equation “modified” to include the effect of viscosity variation with temperature. Numerical solutions to this equation at high Reynolds numbers are obtained using a new method of integration. The method makes use of the Gram-Schmidt orthogonalization technique to obtain linearly independent solutions upon numerically integrating the “modified Orr-Sommerfeld” equation using single precision arithmetic. The method leads to satisfactory answers for Reynolds numbers as high as Rδ* = 100,000. The analysis is applied to the case of flow over both heated and cooled flat plates. The results indicate that heating and cooling of the wall have a large influence on the stability of boundary-layer flow in water. At a free-stream temperature of 60 deg F and wall temperatures of 60, 90, 120, 135, 150, 200, and 300deg F, the critical Reynolds numbers Rδ* are 520, 7200, 15200, 15600, 14800, 10250, and 4600, respectively. At a free-stream temperature of 200F and wall temperature of 60 deg F (cooled case), the critical Reynolds number is 151. Therefore, it is evident that a heated wall has a stabilizing effect, whereas a cooled wall has a destabilizing effect. These stability calculations show that heating increases the critical Reynolds number to a maximum value (Rδ* max = 15,700 at a temperature of TW = 130 deg F) but that further heating decreases the critical Reynolds number. In order to determine the influence of the viscosity derivatives upon the results, the critical Reynolds number for the heated case of T∞ = 40 and TW = 130 deg F was determined using (a) the Orr-Sommerfeld equation and (b) the present governing equation. The resulting critical Reynolds numbers are Rδ* = 140,000 and 16,200, respectively. Therefore, it is concluded that the terms pertaining to the first and second derivatives of the viscosity have a considerable destabilizing influence.

On the stability of flow in an elliptic pipe which is nearly circular

1978 ◽  
Vol 87 (2) ◽  
pp. 233-241 ◽  
Author(s):  
A. Davey
Keyword(s):  
Reynolds Number ◽  
Linear Stability ◽  
Cross Section ◽  
Poiseuille Flow ◽  
Critical Reynolds Number ◽  
Major Axis ◽  
Reynolds Numbers ◽  
Minor Axis ◽  
Critical Reynolds Numbers ◽  
The Stability

The linear stability of Poiseuille flow in an elliptic pipe which is nearly circular is examined by regarding the flow as a perturbation of Poiseuille flow in a circular pipe. We show that the temporal damping rates of non-axisymmetric infinitesimal disturbances which are concentrated near the wall of the pipe are decreased by the ellipticity. In particular we estimate that if the length of the minor axis of the cross-section of the pipe is less than about 96 ½% of that of the major axis then the flow will be unstable and a critical Reynolds number will exist. Also we calculate estimates of the ellipticities which will produce critical Reynolds numbers ranging from 1000 upwards.

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.

scholarly journals Interfacial Electrokinetic Effect on the Microchannel Flow Linear Stability

2004 ◽  
Vol 126 (1) ◽  
pp. 10-13 ◽  
Author(s):  
Sedat Tardu
Keyword(s):  
Reynolds Number ◽  
Hydrodynamic Stability ◽  
Poiseuille Flow ◽  
Critical Reynolds Number ◽  
Reynolds Numbers ◽  
Microchannel Flow ◽  
Electrokinetic Effect ◽  
Electrostatic Double Layer ◽  
Microchannel Flows ◽  
Critical Reynolds Numbers

The electrostatic double layer (EDL) effect on the linear hydrodynamic stability of microchannel flows is investigated. It is shown that the EDL destabilizes the Poiseuille flow considerably. The critical Reynolds number decreases by a factor five when the non-dimensional Debye-Huckel parameter κ is around ten. Thus, the transition may be quite rapid for microchannels of a couple of microns heights in particular when the liquid contains a very small number of ions. The EDL effect disappears quickly for κ⩾150 corresponding typically to channels of heights 400 μm or larger. These results may explain why significantly low critical Reynolds numbers have been encountered in some experiments dealing with microchannel flows.

Spar VIM Model Tests at Supercritical Reynolds Numbers

2007 ◽  
Author(s):  
Tim Finnigan ◽  
Dominique Roddier
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Reynolds Numbers ◽  
Model Tests ◽  
Energy Technology ◽  
Testing Procedures ◽  
The Past ◽  
Critical Reynolds Numbers ◽  
Truss Spar ◽  
Number Of Publications

There have been a number of publications on spar Vortex-Induced-Motions (VIM) model testing procedures and results over the past few years. All tests allowing full 6 DOF response to date have been done under sub-critical Reynolds Number conditions. Tests under super-Critical Reynolds Number conditions have only been done with a fully submerged 1 DOF rig. Early in 2006, Chevron Energy Technology Company (CETC) completed a series of model tests to investigate the effect of Reynolds Number and hull appurtenances on spar vortex induced motions (VIM) for a vertically moored 6DOF truss spar hull model with strakes. Tests were done at both sub- and super-critical Reynolds Numbers, with matching Froude Numbers. In order to assess the importance of appurtenances (chains, pipes and anodes) and current heading on strake effectiveness, tests were done with several sets of appurtenances, and at various headings and reduced velocities. This paper addresses the challenges of performing spar VIM model tests at Super Critical Reynolds Numbers, and how they were resolved without the restrictions noted in earlier publications. Certain aspects of the effect of appurtenances and current heading on strake effectiveness and VIM response are discussed.

Bifurcations of Flow Through Plane Symmetric Channel Contraction

2002 ◽  
Vol 124 (2) ◽  
pp. 444-451 ◽  
Author(s):  
T. P. Chiang ◽  
Tony W. H. Sheu
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Reynolds Numbers ◽  
Incompressible Fluid Flow ◽  
Channel Geometry ◽  
Plane Symmetric ◽  
Symmetric Channel ◽  
Contraction Ratio ◽  
Critical Reynolds Numbers ◽  
Flow Through

Computational investigations have been performed into the behavior of an incompressible fluid flow in the vicinity of a plane symmetric channel contraction. Our aim is to determine the critical Reynolds number, above which the flow becomes asymmetric with respect to the channel geometry using the bifurcation diagram. Three channels, which are characterized by the contraction ratio, are studied and the critical Reynolds numbers are determined as 3075, 1355, and 1100 for channels with contraction ratios of 2, 4, and 8, respectively. The cause and mechanism explaining the transition from symmetric to asymmetric states in the symmetric contraction channel are also provided.

Bifurcation Characteristics of Flows in Rectangular Sudden Expansion Channels

2005 ◽  
Author(s):  
Francine Battaglia ◽  
George Papadopoulos
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Expansion Ratio ◽  
Sudden Expansion ◽  
Two Dimensional ◽  
Effective Expansion ◽  
Three Dimensional Simulations

The effect of three-dimensionality on low Reynolds number flows past a symmetric sudden expansion in a channel was investigated. The geometric expansion ratio of in the current study was 2:1 and the aspect ratio was 6:1. Both experimental velocity measurements and two- and three-dimensional simulations for the flow along the centerplane of the rectangular duct are presented for Reynolds numbers in the range of 150 to 600. Comparison of the two-dimensional simulations with the experiments revealed that the simulations fail to capture completely the total expansion effect on the flow, which couples both geometric and hydrodynamic effects. To properly do so requires the definition of an effective expansion ratio, which is the ratio of the downstream and upstream hydraulic diameters and is therefore a function of both the expansion and aspect ratios. When the two-dimensional geometry was consistent with the effective expansion ratio, the new results agreed well with the three-dimensional simulations and the experiments. Furthermore, in the range of Reynolds numbers investigated, the laminar flow through the expansion underwent a symmetry-breaking bifurcation. The critical Reynolds number evaluated from the experiments and the simulations was compared to other values reported in the literature. Overall, side-wall proximity was found to enhance flow stability, helping to sustain laminar flow symmetry to higher Reynolds numbers in comparison to nominally two-dimensional double-expansion geometries. Lastly, and most importantly, when the logarithm of the critical Reynolds number from all these studies was plotted against the reciprocal of the effective expansion ratio, a linear trend emerged that uniquely captured the bifurcation dynamics of all symmetric double-sided planar expansions.

Loss Characteristics of Orifices and Nozzles

1978 ◽  
Vol 100 (3) ◽  
pp. 299-307 ◽  
Author(s):  
S. H. Alvi ◽  
K. Sridharan ◽  
N. S. Lakshmana Rao
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Flow Regime ◽  
Discharge Coefficient ◽  
Critical Reynolds Number ◽  
Reynolds Numbers ◽  
Center Line ◽  
Laminar Regime ◽  
Variation Of Parameters ◽  
Turbulent Flow Regime

Loss characteristics of sharp-edged orifices, quadrant-edged orifices for varying edge radii, and nozzles are studied for Reynolds numbers less than 10,000 for β ratios from 0.2 to 0.8. The results may be reliably extrapolated to higher Reynolds numbers. Presentation of losses as a percentage of meter pressure differential shows that the flow can be identified into fully laminar regime, critical Reynolds number regime, relaminarization regime, and turbulent flow regime. An integrated picture of variation of parameters such as discharge coefficient, loss coefficient, settling length, pressure recovery length, and center line velocity confirms this classification.

Computerized Model of Transition in Circular Pipe Flows: Part 1 — Experimental Definition of the Problem

1999 ◽  
Author(s):  
Hidesada Kanda
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Critical Reynolds Number ◽  
Natural Disturbance ◽  
Reynolds Numbers ◽  
Entrance Region ◽  
Circular Pipe ◽  
Experimental Investigations ◽  
Circular Pipes ◽  
Definition Of

Abstract A conceptual model was constructed for the problem of determining in circular pipes the conditions under which the transition from laminar to turbulent flow occurs, so that it becomes possible to calculate the minimum critical Reynolds number. Up until now this problem has been investigated by stability theory with disturbances at the pipe inlet. However, the minimum critical Reynolds number has not yet been obtained theoretically. Hence, the author took up the problem directly from many previous experimental investigations and found that (i) plots of the transition length versus the Reynolds number show that the transition occurs in the entrance region under the condition of a natural disturbance, and (ii) plots of the critical Reynolds number versus the ratio of bellmouth diameter to the pipe diamter show that with larger shapes of bellmouths, laminar flow will persist to higher Reynolds numbers. The problem is thus defined clearly as: Under the condition of an ordinary disturbance, the transition from laminar to turbulent flow occurs in the entrance region of a straight circular pipe, then the Reynolds number takes a minimum value of about 2000.

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