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.

ON FULLY DEVELOPED TURBULENT FLOW IN CURVED CHANNELS

1956 ◽  
Vol 34 (11) ◽  
pp. 1134-1146 ◽  
Author(s):  
A. W. Marris
Keyword(s):  
Experimental Data ◽  
Turbulent Flow ◽  
Velocity Distribution ◽  
Radius Of Curvature ◽  
Mixing Length ◽  
Mean Velocity ◽  
Curved Channels ◽  
Fully Developed Turbulent Flow ◽  
The Mean ◽  
Theoretical Results

Formulae for the radial distribution of velocity and vorticity for the case of fully developed turbulent flow in the channel between concentric and infinitely long cylinders are developed on a similarity vorticity transfer theory, by postulating an Eulerian mixing length function dependent on both position and radius of curvature. The theoretical results obtained for the mean velocity distribution across the channel compare satisfactorily with existing experimental data when the curvature dependent parameters are given appropriate numerical values.

On the Rigid-Lid Hypothesis Application to the Flow Simulation of Step-Feed A/O Process

2014 ◽  
Vol 886 ◽  
pp. 319-322
Author(s):  
Shen Zhao ◽  
Xue Yi You ◽  
Sheng Jun Liu ◽  
Yu Huang ◽  
Feng Shi ◽  
...  
Keyword(s):  
Free Surface ◽  
Flow Field ◽  
Velocity Distribution ◽  
Flow Simulation ◽  
The Other ◽  
Surface Model ◽  
Mean Velocity ◽  
Field Simulation ◽  
The Mean ◽  
Free Surface Model

The feasibility of the rigid-lip hypothesis was studied in the flow field simulation of the reaction tank in the step-feed A/O process. Two models were built. One model applied the rigid-lip hypothesis was called as rigid-lid model and the other was called free surface model. The results showed that the velocity distribution of the rigid-lid model is basically consistent with that of the free-surface model. On the vertical monitor sections, the error of the mean velocity between the two models is less than 8%. The results showed that the much less expensive rigid-lid model is applicable to simulate the flow field of reaction tank.

scholarly journals Distribution of velocity and temperature between concentric rotating cylinders

1935 ◽  
Vol 151 (874) ◽  
pp. 494-512 ◽  
Keyword(s):  
Turbulent Flow ◽  
Velocity Distribution ◽  
The Other ◽  
Momentum Transport ◽  
Rotating Cylinders ◽  
Simultaneous Measurements ◽  
Other Hand ◽  
Vorticity Transport

It is not possible to distinguish between the Momentum Transport and the Vorticity Transport theories of turbulent flow by measurements of the distribution of velocity in a fluid flowing under pressure through pipes or between parallel planes. Only simultaneous measurements of temperature and velocity distribution are capable of distinguishing between the two theories in these cases. On the other hand, it will be seen later that measurements of the distribution of velocity between concentric rotating cylinders are capable of distinguishing between the two theories; in fact the predictions of the two theories in this case are sharply contrasted and mutually exclusive.

scholarly journals Wind Turbulence Statistics of the Atmospheric Inertial Sublayer under Near-Neutral Conditions

Atmosphere ◽  
2020 ◽  
Vol 11 (10) ◽  
pp. 1087
Author(s):  
Eslam Reda Lotfy ◽  
Zambri Harun
Keyword(s):  
Boundary Layer ◽  
Atmospheric Stability ◽  
Turbulent Velocity ◽  
Stability Conditions ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Turbulent Statistics ◽  
The Mean ◽  
The Law ◽  
Velocity Variances

The inertial sublayer comprises a considerable and critical portion of the turbulent atmospheric boundary layer. The mean windward velocity profile is described comprehensively by the Monin–Obukhov similarity theory, which is equivalent to the logarithmic law of the wall in the wind tunnel boundary layer. Similar logarithmic relations have been recently proposed to correlate turbulent velocity variances with height based on Townsend’s attached-eddy theory. The theory is particularly valid for high Reynolds-number flows, for example, atmospheric flow. However, the correlations have not been thoroughly examined, and a well-established model cannot be reached for all turbulent variances similar to the law of the wall of the mean-velocity. Moreover, the effect of atmospheric thermal condition on Townsend’s model has not been determined. In this research, we examined a dataset of free wind flow under a near-neutral range of atmospheric stability conditions. The results of the mean velocity reproduce the law of the wall with a slope of 2.45 and intercept of −13.5. The turbulent velocity variances were fitted by logarithmic profiles consistent with those in the literature. The windward and crosswind velocity variances obtained the average slopes of −1.3 and −1.7, respectively. The slopes and intercepts generally increased away from the neutral state. Meanwhile, the vertical velocity and temperature variances reached the ground-level values of 1.6 and 7.8, respectively, under the neutral condition. The authors expect this article to be a groundwork for a general model on the vertical profiles of turbulent statistics under all atmospheric stability conditions.

Experimental Study on Near-Wall Bubble Clustering Behaviors in Bubbly Channel Flow (Keynote)

2003 ◽  
Author(s):  
Soo-Hyun So ◽  
Shu Takagi ◽  
Akiko Fujiwara ◽  
Yoichiro Matsumoto
Keyword(s):  
Liquid Phase ◽  
Bubble Size ◽  
The Other ◽  
Image Processing Technique ◽  
Cluster Center ◽  
Turbulence Structure ◽  
Mean Velocity ◽  
Bubble Cluster ◽  
The Mean ◽  
Near Wall

The turbulence properties of gas-liquid bubbly flows and the near-wall bubble clustering behaviors are investigated for upward flow in a rectangular channel. Bubble size distributions are well-controlled and the flow with mono-dispersed 1mm-diameter and that with 1–4mm diameter bubbles are compared. Bubble size, turbulent properties of liquid phase and the bubble cluster motion were measured using image-processing technique, Laser Doppler Velocimetry (LDV) and Particle Image Velocimetry (PIV), respectively. To create the mono-dispersed small bubbles by the bubble generator, being made of stainless steel pipes, a small amount of surfactant (20ppm of 3-pentanol) was added into the flow. In this study, experiments with three different bulk Reynolds numbers (1350, 4100, 8200) were conducted with void fractions less than 0.6% in the fluid with/without the surfactant. In all cases with surfactant, there was a very high accumulation of bubbles near the wall. The local void fraction has a wall-peak distribution and the horizontal bubble clusters are formed near the wall. As a result, the local mean velocity of the liquid phase becomes larger near the wall due to the driving force of buoyant bubbles and the stream-wise turbulent intensity in the vicinity of the wall was enhanced. On the other hand, the turbulent fluctuations and Reynolds stress are remarkably suppressed in the other region. At the Reynolds number of 8200, the bubble cluster was investigated. Experimental observation showed that the bubble cluster changes its shape in time and that the shape change is caused by the difference of the rising velocity between the cluster center and the both ends. The clusters accelerated the mean streamwise velocity near the wall, thus the mean velocity profile of the liquid phase becomes flattened. It is suggested that the highly concentrated bubbles in the vicinity of the wall disturb the transport of turbulence energy produced in the wall shear layer toward the center of channel. Moreover, in the middle of channel, the turbulence structure is governed by pseudo-turbulence induced by present bubbles.

Measurements with a pulsed-wire and a hot-wire anemometer in the highly turbulent wake of a normal flat plate

1976 ◽  
Vol 77 (3) ◽  
pp. 473-497 ◽  
Author(s):  
L. J. S. Bradbury
Keyword(s):  
Turbulent Flow ◽  
Flat Plate ◽  
Flow Direction ◽  
Operating Conditions ◽  
Turbulent Intensity ◽  
Hot Wire ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean ◽  
Better Than

This paper describes an investigation into the response of both the pulsed-wire anemometer and the hot-wire anemometer in a highly turbulent flow. The first part of the paper is concerned with a theoretical study of some aspects of the response of these instruments in a highly turbulent flow. It is shown that, under normal operating conditions, the pulsed-wire anemometer should give mean velocity and longitudinal turbulent intensity estimates to an accuracy of better than 10% without any restriction on turbulence level. However, to attain this accuracy in measurements of turbulent intensities normal to the mean flow direction, there is a lower limit on the turbulent intensity of about 50%. An analysis is then carried out of the behaviour of the hot-wire anemometer in a highly turbulent flow. It is found that the large errors that are known to develop are very sensitive to the precise structure of the turbulence, so that even qualitative use of hot-wire data in such flows is not feasible. Some brief comments on the possibility of improving the accuracy of the hot-wire anemometer are then given.The second half of the paper describes some comparative measurements in the highly turbulent flow immediately downstream of a normal flat plate. It is shown that, although it is not possible to interpret the hot-wire results on their own, it is possible to calculate the hot-wire response with a surprising degree of accuracy using the results from the pulsed-wire anemometer. This provides a rather indirect but none the less welcome check on the accuracy of the pulsed-wire results, which, in this very highly turbulent flow, have a certain interest in their own right.

Poiseuille Flow and Thermal Transpiration of a Rarefied Gas Between Parallel Plates: Effect of Nonuniform Surface Properties of the Plates in the Transverse Direction

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
Toshiyuki Doi
Keyword(s):  
Distribution Function ◽  
Flow Rate ◽  
Poiseuille Flow ◽  
Transverse Direction ◽  
Rarefied Gas ◽  
Mean Free Path ◽  
Accommodation Coefficient ◽  
Parallel Plates ◽  
Nonuniform Surface ◽  
The Mean

Poiseuille flow and thermal transpiration of a rarefied gas between parallel plates with nonuniform surface properties in the transverse direction are studied based on kinetic theory. We considered a simplified model in which one wall is a diffuse reflection boundary and the other wall is a Maxwell-type boundary on which the accommodation coefficient varies periodically and smoothly in the transverse direction. The spatially two-dimensional (2D) problem in the cross section is studied numerically based on the linearized Bhatnagar–Gross–Krook–Welander (BGKW) model of the Boltzmann equation. The flow behavior, i.e., the macroscopic flow velocity and the mass flow rate of the gas as well as the velocity distribution function, is studied over a wide range of the mean free path of the gas and the parameters of the distribution of the accommodation coefficient. The mass flow rate of the gas is approximated by a simple formula consisting of the data of the spatially one-dimensional (1D) problems. When the mean free path is large, the distribution function assumes a wavy variation in the molecular velocity space due to the effect of a nonuniform surface property of the plate.

Simplified theory of the near-wall turbulent layer of Newtonian and drag-reducing fluids

1982 ◽  
Vol 119 ◽  
pp. 423-441 ◽  
Author(s):  
M. A. Goldshtik ◽  
V. V. Zametalin ◽  
V. N. Shtern
Keyword(s):  
Velocity Profile ◽  
Turbulent Flow ◽  
Drag Reduction ◽  
Outer Boundary ◽  
Viscous Sublayer ◽  
Viscous Layer ◽  
Mean Velocity ◽  
Turbulent Layer ◽  
The Mean ◽  
Near Wall

We propose a simplified theory of a viscous layer in near-wall turbulent flow that determines the mean-velocity profile and integral characteristics of velocity fluctuations. The theory is based on the concepts resulting from the experimental data implying a relatively simple almost-ordered structure of fluctuations in close proximity to the wall. On the basis of data on the greatest contribution to transfer processes made by the part of the spectrum associated with the main size of the observed structures, the turbulent fluctuations are simulated by a three-dimensional running wave whose parameters are found from the problem solution. Mathematically the problem reduces to the solution of linearized Navier-Stokes equations. The no-slip condition is satisfied on the wall, whereas on the outer boundary of a viscous layer the conditions of smooth conjunction with the asymptotic shape of velocity and fluctuation-energy profiles resulting from the dimensional analysis are satisfied. The formulation of the problem is completed by the requirement of maximum curvature of the mean-velocity profile on the outer boundary applied from stability considerations.The solution of the problem does not require any quantitative empirical data, although the conditions of conjunction were formulated according to the well-known concepts obtained experimentally. As a result, the near-wall law for the averaged velocity has been calculated theoretically and is in good agreement with experiment, and the characteristic scales for fluctuations have also been determined. The developed theory is applied to turbulent-flow calculations in Maxwell and Oldroyd media. The elastic properties of fluids are shown to lead to near-wall region reconstruction and its associated drag reduction, as is the case in turbulent flows of dilute polymer solutions. This theory accounts for several features typical of the Toms effect, such as the threshold character of the effect and the decrease in the normal fluctuating velocity. The analysis of the near-wall Oldroyd fluid flow permits us to elucidate several new aspects of the drag-reduction effect. It has been established that the Toms effect does not always result in thickening of the viscous sublayer; on the contrary, the most intense drag reduction takes place without thickening in the viscous sublayer.

Accuracy Investigation of Active Flow Control Using Synthetic Jets

2015 ◽  
Vol 741 ◽  
pp. 475-480
Author(s):  
Na Gao ◽  
Chen Pu ◽  
Bao Chen
Keyword(s):  
Flow Control ◽  
Velocity Distribution ◽  
Active Flow Control ◽  
Flow Fields ◽  
Synthetic Jet ◽  
Synthetic Jets ◽  
Experimental Results ◽  
Center Line ◽  
Mean Velocity ◽  
The Mean

2nd order implicit format is implemented in the Navier-Stokes code to deal with instantaneous item unsteady flows. Three simulations are made to testify the method on flow control. First, the external flow fields of synthetic jets are simulated, the mean velocity on the center line, the jet width and velocity distribution are compared well with experimental results. Secondly, the flow fields of synthetic jet in a crossflow are simulated, orifice slot, the mean velocity on the center line and velocity distribution are compared well with experimental results. Finally, the flow control experiments on separation of airfoil are simulated, control methods include steady suction and synthetic jets. Both methods show their ability to favorably effect the flow separation, shortening the length of separation bubble and improving the pressure levels in separation areas in different degrees.

Structure of the Mean Velocity and Turbulence in Premixed Axisymmetric Acetylene Flames

1994 ◽  
Vol 116 (3) ◽  
pp. 631-642 ◽  
Author(s):  
M. Matovic ◽  
S. Oka ◽  
F. Durst
Keyword(s):  
Flow Field ◽  
Probability Density ◽  
Turbulent Velocity ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Common Features ◽  
Density Distributions ◽  
The Mean ◽  
Probability Density Distributions ◽  
Insight Into

Laser-Doppler measurements of axial mean velocities and the corresponding rms values of turbulent velocity fluctuations are reported for premixed, axisymmetric, acetylene flames together with the probability density distributions of the turbulent velocity fluctuations. All this information provides an insight into the structure of the flow field. Characteristic zones of the flow field are defined that show common features for all acetylene flames studied by the authors. These features are discussed in the paper and are suggested to characterize, in general, interesting parts of the flames.

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