Fully Developed Turbulent Flow in Annuli

1964 ◽  
Vol 86 (4) ◽  
pp. 835-842 ◽  
Author(s):  
J. A. Brighton ◽  
J. B. Jones
Keyword(s):  
Turbulent Flow ◽  
Turbulence Intensity ◽  
Small Diameter ◽  
Reynolds Numbers ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Velocity Gradients ◽  
Circular Pipes ◽  
Fully Developed Turbulent Flow ◽  
Annular Pipes

For annular pipes with diameter ratios from 0.0625 to 0.562 and with Reynolds numbers from 46,000 to 327,000, mean-velocity distributions and the location of the maximum mean velocity for each flow condition are presented. The point of maximum mean velocity in turbulent flow occurs at a smaller radius than in laminar flow. Velocity profiles are compared with the law of the wall and the velocity-defect law and are found to deviate from the usual correlations whenever the radial distribution of Reynolds stress, which was also measured, is far from linear. This occurs in the inner profiles for small diameter ratios. Mixing length and eddy-viscosity distributions were determined from accurate measurements of velocity gradients. Turbulence intensity distributions are presented, and these in conjunction with already published distributions for flow in circular pipes and for flow between parallel planes provide knowledge of turbulence-intensity distributions for all cases of fully developed, one-dimensional flow.

scholarly journals LOCAL VELOCITY PROFILES MEASURED BY PIV IN AN VESSEL AGITATED BY RUSHTON TURBINE

2014 ◽  
Vol 54 (6) ◽  
pp. 430-438 ◽  
Author(s):  
Radek Šulc ◽  
Vít Pešava ◽  
Pavel Ditl
Keyword(s):  
Turbulence Intensity ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Radial Component ◽  
Flat Bottom ◽  
Local Isotropy ◽  
Time Resolved ◽  
Rushton Turbine ◽  
Fully Developed Turbulent Flow ◽  
High Turbulence

<p>The hydrodynamics and flow field were measured in an agitated vessel using 2-D Time Resolved Particle Image Velocimetry (2-D TR PIV). The experiments were carried out in a fully baffled cylindrical flat bottom vessel 300 mm in inner diameter. The tank was agitated by a Rushton turbine 100 mm in diameter. The velocity fields were measured for three impeller rotation speeds 300 rpm, 450 rpm and 600 rpm and the corresponding Reynolds numbers in the range 50 000 &lt; Re &lt; 100 000, which means that the fully-developed turbulent flow was reached. In accordance with the theory of mixing, the dimensionless mean and fluctuation velocities in the measured directions were found to be constant and independent of the impeller rotational speed. The velocity profiles were averaged, and were expressed by Chebyshev polynomials of the 1<sup>st</sup> order. Although the experimentally investigated area was relatively far from the impeller, and it was located in upward flow to the impeller, no state of local isotropy was found. The ratio of the axial rms fluctuation velocity to the radial component was found to be in the range from 0.523 to 0.768. The axial turbulence intensity was found to be in the range from 0.293 to 0.667, which corresponds to a high turbulence intensity.</p>

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.

scholarly journals HYSTERESIS AND VORTICES DYNAMICS IN A TURBULENT FLOW

2009 ◽  
Vol 19 (08) ◽  
pp. 2695-2703 ◽  
Author(s):  
JAVIER BURGUETE ◽  
ALBERTO DE LA TORRE
Keyword(s):  
Turbulent Flow ◽  
Additive Noise ◽  
Potential Model ◽  
Time Dependent ◽  
Small Range ◽  
Mean Velocity ◽  
Fully Developed Turbulent Flow ◽  
Bistable Regime ◽  
The Mean

Recent results about the slow dynamics present in a fully developed turbulent flow are reported. In a previous paper [de la Torre & Burguete, 2007] we showed that the mean velocity field in a turbulent flow bifurcates subcritically breaking some symmetries of the problem and becomes time-dependent because of equatorial vortices moving with a precession movement. This subcriticality produces a bistable regime, whose main characteristics were successfully reproduced using a three-well potential model with additive noise. In this paper we present the characterization of the hysteresis region, not previously observed, in this bifurcation. This hysteresis appears only for an extremely small range of parameters.

STEADY STATE HEAT TRANSFER TO FULLY DEVELOPED TURBULENT FLOW IN A CURVED CHANNEL

1957 ◽  
Vol 35 (4) ◽  
pp. 410-434
Author(s):  
A. W. Marris
Keyword(s):  
Heat Transfer ◽  
Turbulent Flow ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Mean Flow ◽  
Curved Channel ◽  
Mean Velocity ◽  
Fully Developed Turbulent Flow ◽  
Angular Velocities ◽  
The Mean

A vorticity transfer analogy theory of turbulent heat transfer is developed first for the case of fully developed turbulent flow under zero transverse pressure and temperature gradients such as that in the annulus between concentric cylinders rotating with different angular velocities or in a "free vortex". The mean flow is assumed to be two-dimensional. The theory, which requires that the turbulence be statistically isotropic, yields a temperature distribution in agreement with experiment except in narrow regions immediately adjacent to the boundaries. An argument is given to show that the boundary layer thickness should be of the order of the reciprocal of the square root of the mean velocity, these boundaries are introduced, and Nusselt moduli are defined and their dependence on Reynolds and Prandtl numbers is investigated.The temperature distributions for the case of non-zero transverse temperature and pressure gradients, i.e. for the case of flow in a curved channel in which the fluid does not flow back into itself, are then obtained and the applicability of the simpler equations for zero transverse gradients to this case is investigated.

Investigations of Tripping Effect on the Friction Factor in Turbulent Pipe Flows

2009 ◽  
Vol 131 (7) ◽  
Author(s):  
A. Al-Salaymeh ◽  
O. A. Bayoumi
Keyword(s):  
Friction Factor ◽  
Reynolds Numbers ◽  
Original Data ◽  
Turbulent Pipe Flow ◽  
Wall Friction ◽  
Mean Flow ◽  
Mean Velocity ◽  
Fully Developed Turbulent Flow ◽  
The Mean ◽  
The Difference

Tripping devices are usually installed at the entrance of laboratory-scale pipe test sections to obtain a fully developed turbulent flow sooner. The tripping of laminar flow to induce turbulence can be carried out in different ways, such as using cylindrical wires, sand papers, well-organized tape elements, fences, etc. Claims of tripping effects have been made since the classical experiments of Nikuradse (1932, Gesetzmässigkeit der turbulenten Strömung in glatten Rohren, Forschungsheft 356, Ausgabe B, Vol. 3, VDI-Verlag, Berlin), which covered a significant range of Reynolds numbers. Nikuradse’s data have become the metric by which theories are established and have also been the subject of intense scrutiny. Several subsequent experiments reported friction factors as much as 5% lower than those measured by Nikuradse, and the authors of those reports attributed the difference to tripping effects, e.g., work of Durst et al. (2003, “Investigation of the Mean-Flow Scaling and Tripping Effect on Fully Developed Turbulent Pipe Flow,” J. Hydrodynam., 15(1), pp. 14–22). In the present study, measurements with and without ring tripping devices of different blocking areas of 10%, 20%, 30%, and 40% have been carried out to determine the effect of entrance condition on the developing flow field in pipes. Along with pressure drop measurements to compute the skin friction, both the Pitot tube and hot-wire anemometry measurements have been used to accurately determine the mean velocity profile over the working test section at different Reynolds numbers based on the mean velocity and pipe diameter in the range of 1.0×105–4.5×105. The results we obtained suggest that the tripping technique has an insignificant effect on the wall friction factor, in agreement with Nikuradse’s original data.

Flow Regime Characteristics in Porous Media Flows at High Reynolds Numbers

2012 ◽  
Author(s):  
Vishal A. Patil ◽  
James A. Liburdy
Keyword(s):  
Turbulent Flow ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Small Scale ◽  
Mean Velocity ◽  
Time Resolved ◽  
Vortical Structures ◽  
Large Eddy ◽  
High Reynolds ◽  
Media Flows

An experimental study on the turbulent flow characteristics in a randomly packed porous bed is presented and discussed. Time resolved PIV measurements, taken in specific pore spaces are used to evaluate transitional and developed turbulent flow statistics for pore Reynolds numbers from 54 to 3964. Three different regimes of steady laminar, transitional and turbulent flow are presented. Small scale coherent vortical structures are examined, using large eddy scale (LES) decomposition, for pore Reynolds number of greater than 1000. Integral length scales were found to reach asymptotic values of approximately 0.1 times the hydraulic diameter of the bed. The integral Eulerian time scales are found to reach an asymptotic value of approximately 0.3 times the convective time scale in the bed. Mean velocity vector maps show flattening of the velocity distribution due to increased momentum mixing. Turbulent stresses show increasing level of homogeneity at higher pore Reynolds numbers.

A possible reinterpretation of the Princeton superpipe data

2001 ◽  
Vol 439 ◽  
pp. 395-401 ◽  
Author(s):  
A. E. PERRY ◽  
S. HAFEZ ◽  
M. S. CHONG
Keyword(s):  
Boundary Layer ◽  
Reynolds Numbers ◽  
Additive Constant ◽  
Velocity Data ◽  
Hot Wire ◽  
Mean Velocity ◽  
Displacement Effect ◽  
Law Of The Wall ◽  
Hot Wires ◽  
Logarithmic Law

In experiments recently performed at Melbourne, Pitot-tube mean velocity profiles in a boundary layer disagreed with those obtained with hot wires. The standard MacMillan (1956) correction for the probe displacement effect and a correction for turbulence intensity were both required for obtaining agreement between the two sets of mean velocity data. We were thus motivated to reanalyse the Princeton superpipe data using the same two corrections. The result is a plausible conclusion that the superpipe is rough at the higher Reynolds numbers and its data follow the Colebrook (1939) formula for commercial pipes rather well. It also appears that the logarithmic law of the wall is valid, with a Kármán constant close to that found recently by Österlund (1999) from boundary layer measurements with a hot wire. The smooth regime in the pipe gave almost the same additive constant for the log-law as Österlund's. A comparison between the superpipe data and the pipe data of Perry, Henbest & Chong (1997) suggests that the conventional velocity defect law may be valid down to lower Reynolds numbers than concluded by Zagarola & Smits (1998).

scholarly journals Local velocity scaling in upward flow to tooth impeller in a fully turbulent region

2019 ◽  
Vol 213 ◽  
pp. 02081
Author(s):  
Radek Šulc ◽  
Pavel Ditl ◽  
Ivan Fořt ◽  
Darina Jašíkova ◽  
Michal Kotek ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Turbulence Intensity ◽  
Middle Level ◽  
Upward Flow ◽  
Flat Bottom ◽  
Time Resolved ◽  
Image Velocimetry ◽  
Fully Developed Turbulent Flow ◽  
Inner Diameter

The hydrodynamics and flow field were measured in an agitated vessel using 2-D Time Resolved Particle Image Velocimetry (2-D TR PIV). The experiments were carried out in a fully baffled cylindrical flat bottom vessel 400 mm in inner diameter agitated by a tooth impeller 133 mm in diameter. Distilled water was used as the agitated liquid. The velocity fields were investigated in the upward flow to the impeller for three impeller rotation speeds – 300 rpm, 500 rpm and 700 rpm, corresponding to a Reynolds number in the range 94 000 < Re < 221 000. This means that fully-developed turbulent flow was reached. This Re range secures the fully-developed turbulent flow in an agitated liquid. In accordance with the theory of mixing, the dimensionless mean and fluctuation velocities in the measured directions were found to be constant and independent of the impeller Reynolds number. On the basis of the test results the spatial distributions of dimensionless velocities were calculated. The axial turbulence intensity was found to be in the majority in the range from 0.4 to 0.7, which corresponds to the middle level of turbulence intensity.

Boundary Shear Stress in Turbulent Boundary Layers on Smooth Boundaries

1967 ◽  
Vol 71 (673) ◽  
pp. 52-53 ◽  
Author(s):  
Dr. N. Rajaratnam ◽  
C. R. Froelich
Keyword(s):  
Shear Stress ◽  
Turbulent Flow ◽  
Mass Density ◽  
Flow Region ◽  
Viscous Sublayer ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Boundary Shear ◽  
Image Position ◽  
Boundary Shear Stress

It is well known that in the case of turbulent flow over smooth boundaries, the velocity distribution in the neigh- i bourhood of the wall is given by the law of the wall, c written aswhereuis the turbulent mean velocity at a normal distance of y from the boundary,u*is the shear velocity equal tobeing the boundary shear stress andρthe mass density of the fluid andvis the coefficient of kinematic viscosity. In the viscous sublayer, eqn. (1) becomesand in the turbulent flow region above the sublayer and the transition region, foryu*/v> 30, eqn. (1) becomeswhereAandBare coefficients.

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