An Experimental Investigation of Transition of a Plane Poiseuille Flow

1974 ◽  
Vol 96 (4) ◽  
pp. 384-388 ◽  
Author(s):  
M. A. Karnitz ◽  
M. C. Potter ◽  
M. C. Smith
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Transition Process ◽  
Channel Height ◽  
Experimental Facility ◽  
Parallel Plates ◽  
Plane Poiseuille Flow ◽  
Theoretical Limit ◽  
Tollmien Schlichting ◽  
The Waves

The transition process of laminar flow between parallel plates is investigated experimentally. This problem has recently gained much attention with several reported works; however, the maximum transition Reynolds number reported has been approximately 3000 (based on average velocity and channel height) whereas the theoretical critical Reynolds number is 7700. Primary emphasis in this work is on approaching the theoretical limit in an experimental facility. A high aspect ratio (70 to 1) channel was used with air as the fluid. As the disturbance level at the entrance to the parallel plate section was reduced the transition Reynolds number increased monotonically. At a disturbance level of 0.3 percent the transition Reynolds number was 6700. Near transition small nearly sinusoidal waves in the critical shear layer were observed. The frequency of the waves was approximately 70 hertz, close to the frequency associated with the Tollmien-Schlichting waves of the critical point of linear theory. Sinusoidal waves preceded a turbulent burst which possessed an essentially plane front as it traveled downstream. As the Reynolds number was increased the bursting rate increased and the flow eventually became completely turbulent.

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.

An Experimental Investigation of Incompressible Channel Flow Near Transition

1977 ◽  
Vol 99 (4) ◽  
pp. 693-698 ◽  
Author(s):  
N. A. Feliss ◽  
M. C. Potter ◽  
M. C. Smith
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Critical Reynolds Number ◽  
Transition To Turbulence ◽  
Channel Height ◽  
Parallel Plates ◽  
Disturbance Intensity ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
High Reynolds

This paper complements an earlier paper by Karnitz, Potter, and Smith [1] (1974) in which the mechanism of the transition of a plane Poiseuille flow between parallel plates was examined. In the present investigation an experimental critical Reynolds number of 7500 (based on average velocity and channel height) was achieved at which the flow became unstable and transition to turbulence occurred. The linear theoretical Reynolds number of 7700 for instability appears to be a simple extrapolation of the present data as the disturbance intensity is allowed to shrink to zero. Bursting (an alternating turbulent to laminar flow) was observed at transition. The transient changes in the velocity profile when the flow is intermittent between a turbulent burst and a laminar flow were observed. The major portion of the burst profile is characteristic of the one-seventh power law profile common to fully turbulent flow. Disturbances were observed to amplify to turbulent bursts in the wall boundary layers in the entrance region of the channel in high Reynolds number flows (the Reynolds number must exceed the critical Reynolds number by a sufficient amount). Thus, the wall boundary layer becomes unstable, resulting in a transition to turbulence before the flow becomes fully developed at sufficiently high Reynolds numbers.

A two-dimensional-three-component model for spanwise rotating plane Poiseuille flow

2019 ◽  
Vol 880 ◽  
pp. 478-496 ◽  
Author(s):  
Shengqi Zhang ◽  
Zhenhua Xia ◽  
Yipeng Shi ◽  
Shiyi Chen
Keyword(s):  
Reynolds Number ◽  
Poiseuille Flow ◽  
Reynolds Shear Stress ◽  
Streamwise Velocity ◽  
Channel Height ◽  
Neutral Stability ◽  
Two Dimensional ◽  
Plane Poiseuille Flow ◽  
Rotation Numbers ◽  
3C Model

Spanwise rotating plane Poiseuille flow (RPPF) is one of the canonical flow problems to study the effect of system rotation on wall-bounded shear flows and has been studied a lot in the past. In the present work, a two-dimensional-three-component (2D/3C) model for RPPF is introduced and it is shown that the present model is equivalent to a thermal convection problem with unit Prandtl number. For low Reynolds number cases, the model can be used to study the stability behaviour of the roll cells. It is found that the neutral stability curves, critical eigensolutions and critical streamfunctions of RPPF at different rotation numbers ($Ro$) almost collapse with the help of a rescaling with a newly defined Rayleigh number $Ra$ and channel height $H$. Analytic expressions for the critical Reynolds number and critical wavenumber at different $Ro$ can be obtained. For a turbulent state with high Reynolds number, the 2D/3C model for RPPF is self-sustained even without extra excitations. Simulation results also show that the profiles of mean streamwise velocity and Reynolds shear stress from the 2D/3C model share the same linear laws as the fully three-dimensional cases, although differences on the intercepts can be observed. The contours of streamwise velocity fluctuations behave like plumes in the linear law region. We also provide an explanation to the linear mean velocity profiles observed at high rotation numbers.

PIV and POD Investigations of Coherent Vortices Downstream Circular or Rectangular Obstacles Located Between Two Parallel Plates

2019 ◽  
Author(s):  
Fethi Aloui ◽  
Amal Elawady ◽  
Khaled J. Hammad
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Chaotic Behavior ◽  
Rectangular Channel ◽  
Experimental Investigations ◽  
Parallel Plates ◽  
Piv Measurements ◽  
Coherent Vortices ◽  
Karman Vortex ◽  
Proper Orthogonal

Abstract The study is an experimental investigations using PIV. The measurements were obtained by PIV for an unsteady laminar flow across a rectangular channel with a cross-section 300 × 30mm2, in the middle of which is located a cylindrical or a square obstacle. In the case of the cylindrical configuration and due to the confinement, PIV measurements in the range of 40 < Re < 200 clearly show that the von Karman vortex shedding appears at a critical Reynolds number which is about 66. A post-processing of these PIV measurements using the Proper Orthogonal Decomposition (POD) technique is by keeping only the first most energetic six modes, can be used as a filtering process to remove noise from instantaneous velocity signals. In the case of the square obstacle, PIV measurements obtained in the range of 30 < Re < 350 show the absence of vortex detachments and the chaotic behavior of the wake behind the obstacle beyond a certain Reynolds number. By examining the POD post-possessing results, the existence of a dynamic detachments’ regime (instantaneous breaking and coalescence of vortices), can be clearly observed. Given the chaotic behavior of the wake behind the obstacle, the application of the POD filtering process to only the first most energetic modes, cannot lead to good results.

Transition in oscillating boundary layer flows

1967 ◽  
Vol 29 (1) ◽  
pp. 93-111 ◽  
Author(s):  
H. J. Obremski ◽  
A. A. Fejer
Keyword(s):  
Reynolds Number ◽  
Free Stream ◽  
Rapid Development ◽  
Transition Process ◽  
Critical Value ◽  
Boundary Layer Flows ◽  
Instability Waves ◽  
Dimensionless Amplitude ◽  
Oscillating Boundary ◽  
Tollmien Schlichting

An experimental investigation of transition phenomena in non-steady boundary layers of sinusoidally oscillating flows was conducted, and the effect of various parameters on the transition process was observed.The manner in which transition occurs appears to be related to a dimensionless grouping designated as the non-steady Reynolds number, (Re)NS= LΔU/2πvν. When this number exceeds a certain critical value, transition begins with turbulent bursts appearing periodically at the frequency of the free stream oscillation; these are preceded by instability waves having the appearance of a Tollmien-Schlichting instability. The transition Reynolds number depends, in this case, only on the amplitude of the free stream oscillations and not on their frequency, at least to the first order. Below a critical value of this parameter, transition occurs at a relatively constant Reynolds number which appears independent of the amplitude and frequency of the oscillation, at least over the range tested.When the bursts appear periodically, their development appears to occur in two succeeding phases: an initial or ‘creative’ phase marked by a sequential appearance of turbulence upstream and rapid development and a latter or ‘convective’ phase marked by turbulent spots having relatively constant leading and trailing edge velocities.The dimensionless amplitude, ΔU/U∞, of the imposed oscillations was varied from 0.014 to 0.29 while the oscillation frequencies extended from 4.5 to 62c/s.Pressure gradients imposed on the flat plate model during the course of the study are given bydCp/dx = − 0.004/ft., −0.081/ft. and 0.045/ft. whereCp= 2p/ρU2∞and x is the distance (ft.) along the plate.

Accurate solution of the Orr–Sommerfeld stability equation

1971 ◽  
Vol 50 (4) ◽  
pp. 689-703 ◽  
Author(s):  
Steven A. Orszag
Keyword(s):  
Reynolds Number ◽  
Chebyshev Polynomials ◽  
Critical Reynolds Number ◽  
Great Accuracy ◽  
Accurate Solution ◽  
Plane Poiseuille Flow ◽  
Stability Equation ◽  
Orthogonal Functions ◽  
The Stability ◽  
Sommerfeld Equation

The Orr-Sommerfeld equation is solved numerically using expansions in Chebyshev polynomials and the QR matrix eigenvalue algorithm. It is shown that results of great accuracy are obtained very economically. The method is applied to the stability of plane Poiseuille flow; it is found that the critical Reynolds number is 5772·22. It is explained why expansions in Chebyshev polynomials are better suited to the solution of hydrodynamic stability problems than expansions in other, seemingly more relevant, sets of orthogonal functions.

A Theory of Transitional and Turbulent Flow of Non-Newtonian Slurries Between Flat Parallel Plates

1971 ◽  
Vol 11 (01) ◽  
pp. 52-56 ◽  
Author(s):  
Richard W. Hanks ◽  
Maheshkumar P. Valia
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Critical Reynolds Number ◽  
Frictional Resistance ◽  
Newtonian Fluids ◽  
Transitional Flow ◽  
Parallel Plates ◽  
Bingham Plastic ◽  
Turbulent Transition ◽  
Large Width

Abstract A theoretical model is developed which Permits prediction of velocity profiles and frictional prediction of velocity profiles and frictional resistance factors for the isothermal flow of Bingham plastic non-Newtonian slurries in laminar, transitional, and turbulent flow between that parallel walls, in rectangular ducts of large width-to-height ratios, or in concentric annuli with radius ratios approaching unity. The theory is tested with available frictional resistance data for a range of Hedstrom numbers from 10(4) to 10(8) and a set of theoretical design curves of friction factor vs Reynolds number is developed. The model indices that for certain ranges of Hedstrom number (the non-Newtonian index) turbulence is suppressed relative to Newtonian flow behavior, whereas for other ranges of Hedstrom number, the converse is true. Introduction The handling of non-Newtonian fluids in turbulent motion is an important operation in many modern technological processes. Despite this fact, however, little has been done to develop models which are comparable to those available for Newtonian turbulent flow. In particular, a model of the transitional flow regime is notably lacking. Recently, a theory of laminar-turbulent transition for non-Newtonian slurries flowing in pipes and parallel plates was presented. A theory of parallel plates was presented. A theory of transitional and turbulent flow of Newtonian fluids in pipes and parallel plate ducts has also recently been developed. This theory permits the analytic calculation of the friction factor-Reynolds number curves as a continuous function of Reynolds number from the critical Reynolds number of laminar turbulent transition to any condition of turbulent flow. In this paper these two theories will be combined in order to develop a theory for the transitional and turbulent flow of non-Newtonian slurries in parallel plate ducts, rectangular ducts of large width-to-height ratio, or concentric annuli with radius ratios approaching unity. THEORETICAL ANALYSIS The rheological model which will be used to represent the non-Newtonian slurry behavior is the linear Bingham plastic model, ..............(1) ............(2) For this model the laminar flow curve is given by ..............(3) where q = 2v/b, b is one-half the distance between the plates, w = b(−dp/dz) is the wall shear stress, and D = o/ w. The end of the laminax flow, region is determined by the equations ........(4) .........(5) where N Rec = 4bp vc/ p is the critical Reynolds number, Dc is the critical transitional value of D and N He -16bp o/ p is the Hedstrom number expressed in terms of the hydraulic diameter for parallel plates. parallel plates. The calculation of the transitional flow field for this type of fluid will be based upon the model developed by Hanks for Newtonian fluids. SPEJ P. 52

scholarly journals Thermal Performance Enhancement of the Mixed Convection between two Parallel Plates by using Triangular Ribs

2021 ◽  
Vol 26 (2) ◽  
pp. 11-30
Author(s):  
K.A. Jehhef ◽  
F.A. Badawy ◽  
A.A. Hussein
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Performance Enhancement ◽  
Stokes Equations ◽  
Channel Width ◽  
Heated Wall ◽  
Channel Height ◽  
Parallel Plates

Abstract This paper aims to investigate the mixed convection between two parallel plates of a vertical channel, in the presence of a triangular rib. The non-stationary Navier-Stokes equations were solved numerically in a two-dimensional formulation for the low Reynolds number for the laminar air flow regime. Six triangular ribs heat-generating elements were located equidistantly on the heated wall. The ratio of the ribs to the channel width is varied (h / H = 0.1, 0.2, 0.3 and 0.4) to study the effect of ribs height effects, the ratio of the channel width to the ribs height is fixed constant at (H / w = 2) and the ratio of the channel height to the ribs pitch is fixed at (W/p=10). The influence of the Reynolds number that ranged from 68 to 340 and the Grashof number that ranged from 6.6 ×103 to 2.6 ×104 as well as the Richardson number chosen (1.4, 0.7, 0.4 and 0.2) is studied. The numerical results are summarized and presented as the profile of the Nusselt number, the coefficient of friction, and the thermal enhancement factor. The contribution of forced and free convection to the total heat transfer is analyzed. Similar and distinctive features of the behavior of the local and averaged heat transfer with the variation of thermal gas dynamic and geometric parameters are investigated in this paper. The results showed that the Nusselt number and friction factor increased by using the attached triangular ribs, especially when using the downstream ribs. Also, the results revealed that the Nusselt number increased by increasing the ratio of the ribs to the channel width.

Experimental Determination of Transition to Turbulence in a Rectangular Channel With Eddy Promoters

1994 ◽  
Vol 116 (3) ◽  
pp. 484-487 ◽  
Author(s):  
J. S. Kapat ◽  
J. Ratnathicam ◽  
B. B. Mikic´
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Rectangular Channel ◽  
Transition To Turbulence ◽  
Channel Height ◽  
Laminar To Turbulent Transition ◽  
Turbulent Transition ◽  
Power Spectral ◽  
Unstable Configuration

We report on laminar-to-turbulent transition in a rectangular channel in the presence of periodically placed cylindrical eddy promoters. Transition is identified through the analysis of power spectral density (PSD) of velocity fluctuations. Placement of the eddy promoters in the channel, depending on the geometric configuration, can significantly reduce the value of Reynolds number at transition. The critical Reynolds number (based on the average velocity and the channel height) ranges from 1500 (for an unobstructed channel) to about 400 (for the most unstable configuration we have deployed). For all the configurations tested, demarcation of transition can be correlated with the expression: Reτ≡τ¯w,αv/ρH/2/ν=44˜51, where τw,αv is the spatially averaged value of mean wall shear stress and H is the channel height.

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