Experimental Determination of the Critical Reynolds Number for Pulsating Poiseuille Flow

1966 ◽  
Vol 88 (3) ◽  
pp. 589-598 ◽  
Author(s):  
Turgut Sarpkaya
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Poiseuille Flow ◽  
Critical Reynolds Number ◽  
Pulsating Flow ◽  
Mean Velocity ◽  
Cross Sectional ◽  
Pressure Transducers ◽  
Mean Pressure ◽  
The Stability

The stability of fully developed Poiseuille flow pulsating under a harmonically and a nonharmonically varying pressure gradient was studied experimentally. The characteristics of turbulent plugs were determined for both steady and pulsating flow by means of pressure transducers. It was found that (a) for oscillating, stable Poiseuille flow, the phase angles determined experimentally agree well with those determined theoretically; (b) for the same mean pressure gradient, pulsating flow is more stable than the corresponding steady Poiseuille flow; (c) in pulsating flow, the presence of one or more inflection points is necessary but not sufficient for instability; and (d) the curves of the critical Reynolds number versus the relative amplitude of the periodic component of the cross-sectional mean velocity reach their maximum when at least one inflection ring continues to exist a time period 53 percent of the period of oscillation.

The stability of the flow of an elastic-viscous liquid in a curves channel

1963 ◽  
Vol 274 (1358) ◽  
pp. 371-385 ◽  
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Viscous Liquid ◽  
Critical Reynolds Number ◽  
Curved Channel ◽  
Main Effect ◽  
The Stability

Consideration is given to the stability of the flow of an idealized elastico-viscous liquid in a narrow curved channel, the motion being due to a pressure gradient acting around the channel. It is shown that the main effect of the elasticity of the liquid is to lower the value of the critical Reynolds number at which instability occurs.

Steady Flow Structures and Pressure Drops in Wavy-Walled Tubes

1987 ◽  
Vol 109 (3) ◽  
pp. 255-261 ◽  
Author(s):  
M. E. Ralph
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Creeping Flow ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Pressure Drops ◽  
Mean Pressure ◽  
Reynolds Number Flows

Solutions of the Navier-Stokes equations for steady axisymmetric flows in tubes with sinusoidal walls were obtained numerically, for Reynolds numbers (based on the tube radius and mean velocity at a constriction) up to 500, and for varying depth and wavelength of the wall perturbations. Results for the highest Reynolds numbers showed features suggestive of the boundary layer theory of Smith [23]. In the other Reynolds number limit, it has been found that creeping flow solutions can exhibit flow reversal if the perturbation depth is large enough. Experimentally measured pressure drops for a particular tube geometry were in agreement with computed predictions up to a Reynolds number of about 300, where transitional effects began to disturb the experiments. The dimensionless mean pressure gradient was found to decrease with increasing Reynolds number, although the rate of decrease was less rapid than in a straight-walled tube. Numerical results showed that the mean pressure gradient decreases as both the perturbation wavelength and depth increase, with the higher Reynolds number flows tending to be more influenced by the wavelength and the lower Reynolds number flows more affected by the depth.

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.

scholarly journals Study of the instability of the Poiseuille flow using a thermodynamic formalism

2015 ◽  
Vol 112 (31) ◽  
pp. 9518-9523 ◽  
Author(s):  
Jianchun Wang ◽  
Qianxiao Li ◽  
Weinan E
Keyword(s):  
Reynolds Number ◽  
Poiseuille Flow ◽  
Critical Reynolds Number ◽  
Thermodynamic Formalism ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Action Function ◽  
Continuous Transition ◽  
Wide Range ◽  
The Stability

The stability of the plane Poiseuille flow is analyzed using a thermodynamic formalism by considering the deterministic Navier–Stokes equation with Gaussian random initial data. A unique critical Reynolds number, Rec≈2,332, at which the probability of observing puffs in the solution changes from 0 to 1, is numerically demonstrated to exist in the thermodynamic limit and is found to be independent of the noise amplitude. Using the puff density as the macrostate variable, the free energy of such a system is computed and analyzed. The puff density approaches zero as the critical Reynolds number is approached from above, signaling a continuous transition despite the fact that the bifurcation is subcritical for a finite-sized system. An action function is found for the probability of observing puffs in a small subregion of the flow, and this action function depends only on the Reynolds number. The strategy used here should be applicable to a wide range of other problems exhibiting subcritical instabilities.

An experimental investigation of the stability of plane Poiseuille flow

1975 ◽  
Vol 72 (4) ◽  
pp. 731-751 ◽  
Author(s):  
M. Nishioka ◽  
S. Iid A ◽  
Y. Ichikawa
Keyword(s):  
Reynolds Number ◽  
Poiseuille Flow ◽  
Critical Reynolds Number ◽  
Rectangular Cross Section ◽  
Reynolds Numbers ◽  
Plane Poiseuille Flow ◽  
Background Turbulence ◽  
Sinusoidal Disturbance ◽  
The Stability ◽  
Long Channel

Stability experiments were made on plane Poiseuille flow generated in a long channel of a rectangular cross-section with a width-to-depth ratio of 27·4. By reducing the background turbulence down to a level of 0·05 %, we succeeded in maintaining the flow laminar at Reynolds numbers up to 8000, which is much larger than the critical Reynolds number of the linear theory, about 6000. The downstream development of the sinusoidal disturbance introduced by the vibrating ribbon technique was studied in detail at various frequencies in the range of Reynolds number from 3000 to 7500. This paper presents the experimental results and clarifies the linear stability, the nonlinear subcritical instability and the breakdown leading to the transition.

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.

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.

On Turbulent Flow Between Parallel Plates

1953 ◽  
Vol 20 (1) ◽  
pp. 109-114
Author(s):  
S. I. Pai
Keyword(s):  
Turbulent Flow ◽  
Velocity Distribution ◽  
Poiseuille Flow ◽  
The Other ◽  
Turbulent Velocity ◽  
Parallel Plates ◽  
Mean Velocity ◽  
Reynolds Equations ◽  
Mean Pressure ◽  
The Mean

Abstract The Reynolds equations of motion of turbulent flow of incompressible fluid have been studied for turbulent flow between parallel plates. The number of these equations is finally reduced to two. One of these consists of mean velocity and correlation between transverse and longitudinal turbulent-velocity fluctuations u 1 ′ u 2 ′ ¯ only. The other consists of the mean pressure and transverse turbulent-velocity intensity. Some conclusions about the mean pressure distribution and turbulent fluctuations are drawn. These equations are applied to two special cases: One is Poiseuille flow in which both plates are at rest and the other is Couette flow in which one plate is at rest and the other is moving with constant velocity. The mean velocity distribution and the correlation u 1 ′ u 2 ′ ¯ can be expressed in a form of polynomial of the co-ordinate in the direction perpendicular to the plates, with the ratio of shearing stress on the plate to that of the corresponding laminar flow of the same maximum velocity as a parameter. These expressions hold true all the way across the plates, i.e., both the turbulent region and viscous layer including the laminar sublayer. These expressions for Poiseuille flow have been checked with experimental data of Laufer fairly well. It also shows that the logarithmic mean velocity distribution is not a rigorous solution of Reynolds equations.

Flow Characteristics of Pulsating Flow Obstructed by an Array of Square Rods

2000 ◽  
Author(s):  
Hiroyuki Murata ◽  
Ken-ichi Sawada ◽  
Michiyuki Kobayashi
Keyword(s):  
Pressure Gradient ◽  
Flow Characteristics ◽  
Pulsating Flow ◽  
Pulsation Period ◽  
Simulation Code ◽  
Cross Sectional ◽  
Gradient Parameter ◽  
Streamwise Pressure Gradient ◽  
Time Variations ◽  
Visualization Experiments

Abstract A series of flow visualization experiments of pulsating flow obstructed by an array of square rods was carried out to investigate its characteristics. When the pulsation is absent, Karman vortices shed periodically from each rod. When the pulsation period is relatively long compared with the shedding period and its amplitude is large, the flow is stabilized during the accelerating phase and, during the decelarating phase, the flow is destabilized and Karman vortices break down. When the pulsation period is shorter than shedding period and its amplitude is large, the flow pulsation controls the generation and breakdown of the Karman vortices. A numerical simulation code was developed and compared with the experimental results. When the pressure gradient parameter of the code is changed sinusoidally with time, computed results become the pulsating flow. Time variations of the streamwise pressure gradient and cross-sectional averaged velocity show similarity between the experimental and computed results.

scholarly journals Non-normal origin of modal instabilities in rotating plane shear flows

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190550
Author(s):  
Sharath Jose ◽  
Rama Govindarajan
Keyword(s):  
Reynolds Number ◽  
Shear Flows ◽  
Critical Reynolds Number ◽  
Flow System ◽  
Neutral Line ◽  
Plane Couette Flow ◽  
Plane Shear ◽  
Perturbation Amplitude ◽  
Fundamental Reason ◽  
The Stability

Small variations introduced in shear flows are known to affect stability dramatically. Rotation of the flow system is one example, where the critical Reynolds number for exponential instabilities falls steeply with a small increase in rotation rate. We ask whether there is a fundamental reason for this sensitivity to rotation. We answer in the affirmative, showing that it is the non-normality of the stability operator in the absence of rotation which triggers this sensitivity. We treat the flow in the presence of rotation as a perturbation on the non-rotating case, and show that the rotating case is a special element of the pseudospectrum of the non-rotating case. Thus, while the non-rotating flow is always modally stable to streamwise-independent perturbations, rotating flows with the smallest rotation are unstable at zero streamwise wavenumber, with the spanwise wavenumbers close to that of disturbances with the highest transient growth in the non-rotating case. The instability critical rotation number scales inversely as the square of the Reynolds number, which we demonstrate is the same as the scaling obeyed by the minimum perturbation amplitude in non-rotating shear flow needed for the pseudospectrum to cross the neutral line. Plane Poiseuille flow and plane Couette flow are shown to behave similarly in this context.

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