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

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The Stability of Water Flow Over Heated and Cooled Flat Plates

Journal of Heat Transfer ◽

10.1115/1.3597439 ◽

1968 ◽

Vol 90 (1) ◽

pp. 109-114 ◽

Cited By ~ 52

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.

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

Journal of Fluid Mechanics ◽

10.1017/s0022112078001561 ◽

1978 ◽

Vol 87 (2) ◽

pp. 233-241 ◽

Cited By ~ 6

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.

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

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1978.0051 ◽

1978 ◽

Vol 359 (1699) ◽

pp. 453-478 ◽

Cited By ~ 3

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.

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Interfacial Electrokinetic Effect on the Microchannel Flow Linear Stability

Journal of Fluids Engineering ◽

10.1115/1.1637927 ◽

2004 ◽

Vol 126 (1) ◽

pp. 10-13 ◽

Cited By ~ 7

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.

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Temporal stability of Jeffery–Hamel flow

Journal of Fluid Mechanics ◽

10.1017/s0022112094001266 ◽

1994 ◽

Vol 268 ◽

pp. 71-88 ◽

Cited By ~ 38

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.

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Vortex shedding from spheres

Journal of Fluid Mechanics ◽

10.1017/s0022112074000644 ◽

1974 ◽

Vol 62 (2) ◽

pp. 209-221 ◽

Cited By ~ 312

Author(s):

Elmar Achenbach

Keyword(s):

Reynolds Number ◽

Vortex Shedding ◽

Critical Reynolds Number ◽

Measurement Techniques ◽

Reynolds Numbers ◽

Wake Flow ◽

Present Measurement ◽

Number Range ◽

Low Reynolds Numbers ◽

The Relationship

Vortex shedding from spheres has been studied in the Reynolds number range 400 < Re < 5 × 106. At low Reynolds numbers, i.e. up to Re = 3 × 103, the values of the Strouhal number as a function of Reynolds number measured by Möller (1938) have been confirmed using water flow. The lower critical Reynolds number, first reported by Cometta (1957), was found to be Re = 6 × 103. Here a discontinuity in the relationship between the Strouhal and Reynolds numbers is obvious. From Re = 6 × 103 to Re = 3 × 105 strong periodic fluctuations in the wake flow were observed. Beyond the upper critical Reynolds number (Re = 3.7 × 105) periodic vortex shedding could not be detected by the present measurement techniques.The hot-wire measurements indicate that the signals recorded simultaneously at different positions on the 75° circle (normal to the flow) show a phase shift. Thus it appears that the vortex separation point rotates around the sphere. An attempt is made to interpret this experimental evidence.

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Spar VIM Model Tests at Supercritical Reynolds Numbers

Volume 3: Pipeline and Riser Technology; CFD and VIV ◽

10.1115/omae2007-29160 ◽

2007 ◽

Cited By ~ 7

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.

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Bifurcations of Flow Through Plane Symmetric Channel Contraction

Journal of Fluids Engineering ◽

10.1115/1.1467643 ◽

2002 ◽

Vol 124 (2) ◽

pp. 444-451 ◽

Cited By ~ 8

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.

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Heat Transfer for High Aspect Ratio Rectangular Channels in a Stationary Serpentine Passage With Turbulated and Smooth Surfaces

Volume 3A: Heat Transfer ◽

10.1115/gt2013-94924 ◽

2013 ◽

Author(s):

Matthew A. Smith ◽

Randall M. Mathison ◽

Michael G. Dunn

Keyword(s):

Heat Transfer ◽

Reynolds Number ◽

Aspect Ratio ◽

Flow Behavior ◽

Reynolds Numbers ◽

Hydraulic Diameter ◽

Internal Cooling ◽

Number Range ◽

Aspect Ratios ◽

Parallel Configuration

Heat transfer distributions are presented for a stationary three passage serpentine internal cooling channel for a range of engine representative Reynolds numbers. The spacing between the sidewalls of the serpentine passage is fixed and the aspect ratio (AR) is adjusted to 1:1, 1:2, and 1:6 by changing the distance between the top and bottom walls. Data are presented for aspect ratios of 1:1 and 1:6 for smooth passage walls and for aspect ratios of 1:1, 1:2, and 1:6 for passages with two surfaces turbulated. For the turbulated cases, turbulators skewed 45° to the flow are installed on the top and bottom walls. The square turbulators are arranged in an offset parallel configuration with a fixed rib pitch-to-height ratio (P/e) of 10 and a rib height-to-hydraulic diameter ratio (e/Dh) range of 0.100 to 0.058 for AR 1:1 to 1:6, respectively. The experiments span a Reynolds number range of 4,000 to 130,000 based on the passage hydraulic diameter. While this experiment utilizes a basic layout similar to previous research, it is the first to run an aspect ratio as large as 1:6, and it also pushes the Reynolds number to higher values than were previously available for the 1:2 aspect ratio. The results demonstrate that while the normalized Nusselt number for the AR 1:2 configuration changes linearly with Reynolds number up to 130,000, there is a significant change in flow behavior between Re = 25,000 and Re = 50,000 for the aspect ratio 1:6 case. This suggests that while it may be possible to interpolate between points for different flow conditions, each geometric configuration must be investigated independently. The results show the highest heat transfer and the greatest heat transfer enhancement are obtained with the AR 1:6 configuration due to greater secondary flow development for both the smooth and turbulated cases. This enhancement was particularly notable for the AR 1:6 case for Reynolds numbers at or above 50,000.

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