Laminar Boundary-Layer Flow Near the Entry of a Curved Circular Pipe

1980 ◽  
Vol 47 (4) ◽  
pp. 697-702 ◽  
Author(s):  
W. S. Yeung
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Cross Flow ◽  
Outer Edge ◽  
Core Region ◽  
Large Reynolds Number ◽  
Normal Velocity ◽  
Curved Pipe ◽  
The Core ◽  
Layer Flow

The fluid mechanics of a viscous, incompressible fluid entering a circular curved pipe at large Reynolds number is investigated numerically. The flow field is divided into two regions, the boundary-layer region and the inviscid core region. The boundary layer is assumed to be laminar and the method of integral relations is used to solve the governing equations. The core region, on the other hand, is assumed irrotational and is solved by a modified version of Telenin’s method. The coupling of the two regions is accounted for through the imposition of the outer edge normal velocity as a boundary condition for the core region. Results are presented for a Reynolds number of 104 and a curvature ratio of 0.1. It has been shown that the cross flow in the core region is initially directed from the outer to the inner bend and reverses its direction downstream for the entry condition of uniform axial motion. The core velocity profiles are consistent with a recent experimental investigation, while the boundary-layer results are qualitatively similar to those of Yao and Berger, although a direct quantitative comparison is not applicable, due to the different range of Reynolds number considered.

scholarly journals On the uniqueness of steady flow past a rotating cylinder with suction

2000 ◽  
Vol 411 ◽  
pp. 213-232 ◽  
Author(s):  
E. V. BULDAKOV ◽  
S. I. CHERNYSHENKO ◽  
A. I. RUBAN
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Cross Flow ◽  
Rotation Velocity ◽  
Rotating Cylinder ◽  
Large Reynolds Number ◽  
Order Unity ◽  
Flow Past ◽  
Exponentially Small

The subject of this study is a steady two-dimensional incompressible flow past a rapidly rotating cylinder with suction. The rotation velocity is assumed to be large enough compared with the cross-flow velocity at infinity to ensure that there is no separation. High-Reynolds-number asymptotic analysis of incompressible Navier–Stokes equations is performed. Prandtl's classical approach of subdividing the flow field into two regions, the outer inviscid region and the boundary layer, was used earlier by Glauert (1957) for analysis of a similar flow without suction. Glauert found that the periodicity of the boundary layer allows the velocity circulation around the cylinder to be found uniquely. In the present study it is shown that the periodicity condition does not give a unique solution for suction velocity much greater than 1/Re. It is found that these non-unique solutions correspond to different exponentially small upstream vorticity levels, which cannot be distinguished from zero when considering terms of only a few powers in a large Reynolds number asymptotic expansion. Unique solutions are constructed for suction of order unity, 1/Re, and 1/√Re. In the last case an explicit analysis of the distribution of exponentially small vorticity outside the boundary layer was carried out.

Oscillating flow over a cylinder at large Reynolds number

1973 ◽  
Vol 61 (4) ◽  
pp. 753-767 ◽  
Author(s):  
H. A. Dwyer ◽  
W. J. Mccroskey
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layer Flow ◽  
Theoretical Calculations ◽  
Inviscid Flow ◽  
Oscillating Flow ◽  
Large Reynolds Number ◽  
Experimental Part ◽  
Layer Flow ◽  
Flow Reversals

The boundary-layer flow over a circular cylinder at a Reynolds number of 1·06 × 105 has been studied both experimentally and theoretically. The investigation was designed to concentrate on the self-induced oscillations occurring in the flow; at this Reynolds number, these oscillations have generally been ignored heretofore. In the experimental part of the investigation both the inviscid flow and boundary-layer flow reversals were measured as functions of time. The theoretical part of the study started with the measured inviscid flow and calculated all the boundary-layer characteristics. The boundary-layer calculations themselves revealed some very interesting fine-scale structure of the flow, which strongly indicated that the vanishing of wall shear does not signal the onset of separation for unsteady flow. In general, the agreement between the theoretical calculations and the experimental results was excellent and the unsteady component of this supposedly steady flow was found to be very significant.

Asymptotic analysis of turbulent channel and boundary-layer flow

1972 ◽  
Vol 56 (4) ◽  
pp. 657-681 ◽  
Author(s):  
William B. Bush ◽  
Francis E. Fendell
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layer Flow ◽  
Eddy Viscosity ◽  
Applied Pressure ◽  
Large Reynolds Number ◽  
Thin Wall ◽  
Turbulent Stress ◽  
Special Cases ◽  
Layer Flow

Asymptotic expansion techniques are used, in the limit of large Reynolds number, to study the structure of fully turbulent shear layers. The relevant Reynolds number characterizes the ratio of the local turbulent stress to the local laminar stress, so that a relatively thick outer defect layer, in which, to lowest order, there is a balance between turbulent stress and convection of momentum, may be distinguished from a relatively thin wall layer, in which, to lowest order, there is a balance between turbulent and laminar stresses. The two cases examined are channel (or pipe) flow and two-dimensional boundary-layer flow with an applied pressure gradient, upstream of any separation. Attention, for these two cases, is confined to the flow of incompressible constant property fluids. Closure is effected through the introduction of an eddy-viscosity model formulated with sufficient generality for most existing models to be special cases. Results are carried to higher orders of approximation to indicate what properties for the friction velocity, integral thicknesses, and velocity profiles, and what conditions for similarity are implied by current eddy-viscosity closures.

Effect of Wall Movement on a Jet Depositing on a Moving Wall at Moderate Reynolds Number

2010 ◽  
Author(s):  
Md. Yahia Hussain ◽  
Roger E. Khayat
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Free Surface ◽  
Core Region ◽  
Relaxation Length ◽  
Moving Wall ◽  
The Core ◽  
Wall Movement ◽  
Moderate Reynolds Number ◽  
Surface Jet

The steady flow of a moderately inertial jet depositing on a moving wall, is examined theoretically near channel exit. The free surface jet emerges from a channel and adheres to a wall, which may move in the same or opposite direction to the acting channel pressure gradient. The problem is solved using the method of matched asymptotic expansions. The small parameter involved in the expansions is the inverse Reynolds number. The flow field is obtained as a composite expansion by matching the flow in the boundary layer regions near the free surface, with the flow in the core region. The influence of inertia and wall velocity on the shape of the free surface, the velocity and stress is emphasized. It is found that the viscous relaxation length is essentially uninfluenced by the velocity of a forward moving wall. In contrast, it diminishes rapidly with the velocity of a backward moving wall.

Effect of Reynolds number on drag reduction in turbulent boundary layer flow over liquid–gas interface

2020 ◽  
Vol 32 (12) ◽  
pp. 122111
Author(s):  
Hongyuan Li ◽  
SongSong Ji ◽  
Xiangkui Tan ◽  
Zexiang Li ◽  
Yaolei Xiang ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Drag Reduction ◽  
Boundary Layer Flow ◽  
Turbulent Boundary Layer Flow ◽  
Layer Flow

An example of steady laminar flow at large Reynolds number

1960 ◽  
Vol 9 (4) ◽  
pp. 593-602 ◽  
Author(s):  
Iam Proudman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Tangential Velocity ◽  
Fluid Flows ◽  
The Other ◽  
Large Reynolds Number ◽  
Rotational Flows ◽  
Flow Domain ◽  
Source Of Information

The purpose of this note is to describe a particular class of steady fluid flows, for which the techniques of classical hydrodynamics and boundary-layer theory determine uniquely the asymptotic flow for large Reynolds number for each of a continuously varied set of boundary conditions. The flows involve viscous layers in the interior of the flow domain, as well as boundary layers, and the investigation is unusual in that the position and structure of all the viscous layers are determined uniquely. The note is intended to be an illustration of the principles that lead to this determination, not a source of information of practical value.The flows take place in a two-dimensional channel with porous walls through which fluid is uniformly injected or extracted. When fluid is extracted through both walls there are boundary layers on both walls and the flow outside these layers is irrotational. When fluid is extracted through one wall and injected through the other, there is a boundary layer only on the former wall and the inviscid rotational flow outside this layer satisfies the no-slip condition on the other wall. When fluid is injected through both walls there are no boundary layers, but there is a viscous layer in the interior of the channel, across which the second derivative of the tangential velocity is discontinous, and the position of this layer is determined by the requirement that the inviscid rotational flows on either side of it must satisfy the no-slip conditions on the walls.

scholarly journals Sound propagation in a lined nozzle with shear and bias flows

2018 ◽  
Vol 18 (1) ◽  
pp. 3-48
Author(s):  
LMBC Campos ◽  
C Legendre
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Boundary Layers ◽  
Lower Boundary ◽  
Cross Flow ◽  
Core Flow ◽  
The Core ◽  
Wide Range ◽  
Bias Flow ◽  
Number Formula

In this study, the propagation of waves in a two-dimensional parallel-sided nozzle is considered allowing for the combination of: (a) distinct impedances of the upper and lower walls; (b) upper and lower boundary layers with different thicknesses with linear shear velocity profiles matched to a uniform core flow; and (c) a uniform cross-flow as a bias flow out of one and into the other porous acoustic liner. The model involves an “acoustic triple deck” consisting of third-order non-sinusoidal non-plane acoustic-shear waves in the upper and lower boundary layers coupled to convected plane sinusoidal acoustic waves in the uniform core flow. The acoustic modes are determined from a dispersion relation corresponding to the vanishing of an 8 × 8 matrix determinant, and the waveforms are combinations of two acoustic and two sets of three acoustic-shear waves. The eigenvalues are calculated and the waveforms are plotted for a wide range of values of the four parameters of the problem, namely: (i/ii) the core and bias flow Mach numbers; (iii) the impedances at the two walls; and (iv) the thicknesses of the two boundary layers relative to each other and the core flow. It is shown that all three main physical phenomena considered in this model can have a significant effect on the wave field: (c) a bias or cross-flow even with small Mach number [Formula: see text] relative to the mean flow Mach number [Formula: see text] can modify the waveforms; (b) the possibly dissimilar impedances of the lined walls can absorb (or amplify) waves more or less depending on the reactance and inductance; (a) the exchange of the wave energy with the shear flow is also important, since for the same stream velocity, a thin boundary layer has higher vorticity, and lower vorticity corresponds to a thicker boundary layer. The combination of all these three effects (a–c) leads to a large set of different waveforms in the duct that are plotted for a wide range of the parameters (i–iv) of the problem.

The boundary layer in crossed-fields m.h.d.

1966 ◽  
Vol 25 (2) ◽  
pp. 229-240 ◽  
Author(s):  
W. R. Sears
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Flat Plate ◽  
Flow Problem ◽  
Inviscid Flow ◽  
Magnetic Reynolds Number ◽  
Large Reynolds Number ◽  
Zero Values ◽  
Plate Solution ◽  
A Current

This study of the boundary layer of steady, incompressible, plane, crossed-fields m.h.d. flow at large Reynolds numberReand magnetic Reynolds numberRmbegins with a review of Hartmann's case, where a boundary layer occurs whose thickness is proportional to (Re Rm)−½. Following this clue, it is shown that in general the boundary layer is a ‘local Hartmann boundary layer’. Its profiles are always exponential and it is determined completely by local quantities. The skin friction and the total electric current in the layer are proportional to the square root of the magnetic Prandtl number, i.e. to (Rm/Re)½. Thus the exterior-flow problem, the solution of which precedes a boundary-layer solution, generally involves a current sheet at the fluid-solid interface.This inviscid-flow problem becomes tractable if (Rm/Re)½is small enough to permit a linearized solution. The flow field about a flat plate at zero incidence is calculated in this approximation. It is pointed out that the thin-cylinder solutions of Sears & Resler (1959), which pertain toRm/Re= 0, can immediately be extended to small, non-zero values of this parameter by linear combination with this flat-plate solution.

Two-dimensional global low-frequency oscillations in a separating boundary-layer flow

2008 ◽  
Vol 614 ◽  
pp. 315-327 ◽  
Author(s):  
UWE EHRENSTEIN ◽  
FRANÇOIS GALLAIRE
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Perturbation Analysis ◽  
Boundary Layer Flow ◽  
Stokes Equations ◽  
Low Frequency ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Optimal Perturbation ◽  
Layer Flow

A separated boundary-layer flow at the rear of a bump is considered. Two-dimensional equilibrium stationary states of the Navier–Stokes equations are determined using a nonlinear continuation procedure varying the bump height as well as the Reynolds number. A global instability analysis of the steady states is performed by computing two-dimensional temporal modes. The onset of instability is shown to be characterized by a family of modes with localized structures around the reattachment point becoming almost simultaneously unstable. The optimal perturbation analysis, by projecting the initial disturbance on the set of temporal eigenmodes, reveals that the non-normal modes are able to describe localized initial perturbations associated with the large transient energy growth. At larger time a global low-frequency oscillation is found, accompanied by a periodic regeneration of the flow perturbation inside the bubble, as the consequence of non-normal cancellation of modes. The initial condition provided by the optimal perturbation analysis is applied to Navier–Stokes time integration and is shown to trigger the nonlinear ‘flapping’ typical of separation bubbles. It is possible to follow the stationary equilibrium state on increasing the Reynolds number far beyond instability, ruling out for the present flow case the hypothesis of some authors that topological flow changes are responsible for the ‘flapping’.

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