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 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.

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.

scholarly journals On the calculation of the velocity and temperature distributions for flow along a flate plate

1936 ◽  
Vol 154 (882) ◽  
pp. 364-377 ◽  
Keyword(s):  
Kinetic Theory ◽  
Turbulent Flow ◽  
Free Path ◽  
Mean Free Path ◽  
Mixing Length ◽  
Shearing Stress ◽  
Mean Velocity ◽  
Temperature Distributions ◽  
The Mean

Kármán and Prandtl were the first investigators to publish theoretical ults for problems of turbulent flow involving plane boundaries. Before nsidering any particular problem the general considerations of these iters will be outlined. Prandtl's is, perhaps, the easier method to follow. He considered a bulent motion in which the mean velocity u remains parallel to a tain direction—O x , say,—and is a function of y only, O y being perpendicular to O x , and he arrived at the result τ = ρ l 2 | du / dy | du / dy (1) the shearing stress, where ρ is the density of the fluid and l is a length, led the mixing length; it is the analogue of the mean free path in the etic theory of gases. The conception of the mixing length of the sent problem is physically much less surely grounded than the mean e path of the kinetic theory.

scholarly journals Turbulent flow in curved channels

2021 ◽  
Vol 931 ◽  
Author(s):  
Geert Brethouwer
Keyword(s):  
Turbulent Flow ◽  
Outer Region ◽  
Curvature Radius ◽  
Normal Velocity ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Turbulence Structures ◽  
Curvature Effects ◽  
Fully Developed Turbulent Flow ◽  
The Mean

Fully developed turbulent flow in channels with mild to strong longitudinal curvature is studied by direct numerical simulations. The Reynolds based on the bulk mean velocity and channel half-width $\delta$ is fixed at $20\,000$ , resulting in a friction Reynolds number of approximately 1000. Four cases are considered with curvature varying from $\gamma = 2\delta /r_c = 0.033$ to 0.333, where $r_c$ is the curvature radius at the channel centre. Substantial differences between the mean wall shear stress on the convex and concave walls are already observed for $\gamma = 0.033$ . A log-law region is absent and a region with nearly constant mean angular momentum develops in the channel centre for strong curvatures. Spanwise and wall-normal velocity fluctuations are strongly amplified by curvature in the outer region of the concave channel side. Only near the walls, where curvature effects are relatively weak, do the mean velocity and velocity fluctuation profiles approximately collapse when scaled by wall units based on the local friction velocity. Budgets of the streamwise and wall-normal Reynolds-stress equations are presented and turbulence structures are investigated through visualizations and spectra. In the case with strongest curvature, the flow relaminarizes locally near the convex wall. On the concave channel side, large elongated streamwise vortices reminiscent of Taylor–Görtler vortices develop for all curvatures considered. The maximum in the premultiplied two-dimensional wall-normal energy spectrum and co-spectrum shifts towards larger scales with increasing curvature. The large scales substantially contribute to the wall-normal velocity fluctuations and momentum transport on the concave channel side.

The Calculation of Properties of the Flow over a Backward Facing Step With the k-ε Model of Turbulence

1984 ◽  
Vol 8 (3) ◽  
pp. 165-170
Author(s):  
L.P. Hackman ◽  
A.B. Strong ◽  
G.D. Raithby
Keyword(s):  
Experimental Data ◽  
Kinetic Energy ◽  
Turbulent Flow ◽  
Skin Friction ◽  
Turbulent Kinetic Energy ◽  
Reasonable Agreement ◽  
Shear Stresses ◽  
Backward Facing Step ◽  
Mean Velocity ◽  
The Mean

This paper reports predictions of the mean velocity, the turbulent kinetic energy and the pressure and skin friction coefficients for turbulent flow over a backward facing step based on the standard k – ε closure for the turbulence shear stresses. In previous publications, errors due to the numerical algorithm as distinct from the turbulence model have been carefully assessed using different numerical schemes and finite volume geometries and it is argued that the current results are numerically accurate. Thus one can now assess the accuracy of the k – ε model of turbulence independently of numerical error. The results predicted herein were found to be in reasonable agreement with relevant experimental data.

Radial Distributions of Temporal-Mean Peripheral Velocity and Pressure for Fully Developed Turbulent Flow in Curved Channels

1960 ◽  
Vol 82 (3) ◽  
pp. 528-536 ◽  
Author(s):  
A. W. Marris
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Rectangular Cross Section ◽  
Width Ratio ◽  
Curved Channels ◽  
Peripheral Velocity ◽  
Wide Range ◽  
Fully Developed Turbulent Flow ◽  
The Mean ◽  
Moving Fluid

Experimental results are presented for the radial distributions of pressure and peripheral velocity for the turbulent flow of water in two closed curved channels of rectangular cross section and large depth-to-width ratio. The traverses were taken at the equatorial section of the channel and sufficiently far around the curve for the effect of curvature on the mean motion to be fully established. The two channels employed had widely differing mean-radius-to-width ratios n. The data obtained for a wide range of flow rates in the channel with a larger n indicated that Reynolds similarity existed between the flows in this channel. These data are compared with the pressure and velocity profiles predicted by potential flow theory and with a semiempirical logarithmic velocity distribution. Results obtained for the channel with smaller n showed that at above a certain Reynolds number an anomaly occurred in the flow, manifesting itself as an unstable “belt” of faster moving fluid, which moved outward from the inner wall as the Reynolds number was increased. This effect, considered to be the consequence of upstream stall, was accompanied by an adverse longitudinal-pressure gradient at the inner wall of the channel. It appeared to be eliminated by the insertion of an upstream splitter vane.

Large-Eddy Simulation of Turbulent Flow in a Curved Pipe

1996 ◽  
Vol 118 (2) ◽  
pp. 248-254 ◽  
Author(s):  
B. J. Boersma ◽  
F. T. M. Nieuwstadt
Keyword(s):  
Large Eddy Simulation ◽  
Turbulent Flow ◽  
Mean Velocity ◽  
Curved Pipe ◽  
Eddy Simulation ◽  
Turbulent Statistics ◽  
Large Eddy ◽  
Secondary Motion ◽  
Fully Developed Turbulent Flow ◽  
The Mean

In this paper, we use Large-Eddy Simulation (LES) to compute a fully-developed turbulent flow in a curved pipe. The results allow us to study how the curvature influences the mean velocity profile and also various turbulent statistics. We find reasonable agreement with the few experiments that are available. Our simulation also allows a detailed study of secondary motion in the cross section of the pipe which are caused by the centrifugal acceleration due to the pipe curvature. It is known that this secondary motion may consist of one, two, or three circulation cells. In our simulation results we find one circulation cell.

Turbulent Couette Flow

1974 ◽  
Vol 96 (3) ◽  
pp. 265-271 ◽  
Author(s):  
A. K. Wang ◽  
L. W. Gelhar
Keyword(s):  
Energy Balance ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Mixing Length ◽  
Plane Couette Flow ◽  
Rotating Cylinders ◽  
Mean Velocity ◽  
Balance Hypothesis ◽  
The Mean ◽  
Theoretical Results

Turbulent flow between concentric rotating cylinders is analyzed using an energy balance hypothesis proposed by Zagustin. Predictions of the mean velocity profiles are obtained without any additional assumptions regarding the distribution of mixing length. The theoretical results compare favorably with previous observations with only the inner or outer cylinder rotating, and with new data for counter-rotating cylinders. The theoretical results are also consistent with observed features of plane Couette flow.

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