Fluid flow into a curved pipe

1976 ◽  
Vol 351 (1664) ◽  
pp. 71-87 ◽  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Three Dimensional ◽  
Pressure Variation ◽  
Straight Section ◽  
Dean Number ◽  
Curved Pipe ◽  
Dimensional Boundary ◽  
Curved Section ◽  
Inside Wall

The influence of curvature on a pipeflow is discussed for a pipe that starts bending uniformly after an initial straight section. The Reynolds number and curvature are assumed large and small respectively, and the motion is examined first for distances from the starting of the bend that are com­parable with the tubewidth. When the Dean number is finite, the coreflow remains practically undisturbed, i. e. unidirectional, until the bend and thereafter streams uniformly towards the outside of the curve, inducing a three dimensional boundary layer. This layer, however, has to react before the bending in order to adjust to the downstream conditions. It does so by means of a novel kind of upstream response. The azimuthal pressure variation generated by the bend is felt upstream and therefore both drives an inwards azimuthal motion in the boundary layer and produces an axial shear maximum at the inside wall. In the curved section the centrifuging then causes the maximum to shift to the outer bend at 1.51 pipe-radii beyond the start of bending. Finally, the theory is extended to longer lengthscales, to large Dean numbers and to general initial profiles.

On vortex boundary layers

1985 ◽  
Vol 400 (1819) ◽  
pp. 253-261 ◽  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Three Dimensional ◽  
Radial Pressure ◽  
Outer Flow ◽  
The Core ◽  
Dimensional Boundary ◽  
Radial Pressure Gradient ◽  
Potential Vortex ◽  
Vortex Axis

Flow visualization is used to study the flow that results when a potential vortex rotates normal to a stationary horizontal disc. Viscosity is seen to remove the singularity on the vortex axis and lead to the development of a three-dimensional boundary layer. The flow remains laminar below a Reynolds number, Re , of about 10 4 , where Re is based on radius and velocity at the disc edge. With further increases in Re the boundary layer becomes turbulent but relaminarizes as it is advected radially inwards by the highly favourable radial pressure gradient associated with the outer flow. The radius of the zone of relaminarized fluid decreases with increasing Re . Close to the axis the flow effuses vertically to form the core of the vortex which, for Re < 10 4 , is observed to undergo a massive disruption, either of the axisymmetric or helical form. The sense of the helix was observed on some occasions to be with that of the outer flow and on others to be opposite that of the outer flow.

Reynolds-number-independent instability of the boundary layer over a flat surface

1996 ◽  
Vol 327 ◽  
pp. 101-115 ◽  
Author(s):  
Paolo Luchini
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Flat Surface ◽  
Three Dimensional ◽  
Flow Instabilities ◽  
Bypass Transition ◽  
Linear Amplification ◽  
Boundary Layer Approximation ◽  
Dimensional Boundary ◽  
Amplification Mechanism

A three-dimensional mode of spatial instability, related to the temporal algebraic growth that determines lift-up in parallel flow, is found to occur in the two-dimensional boundary layer growing over a flat surface. This unstable perturbation can be framed within the limits of Prandtl's standard boundary-layer approximation, and therefore develops at any Reynolds number for which the boundary layer exists, in sharp contrast to all previously known flow instabilities which only occur beyond a sharply defined Reynolds-number threshold. It is thus a good candidate for the initial linear amplification mechanism that leads to bypass transition.

An Assessment of Three-Dimensional Turbulent Boundary Layer Prediction Methods

1973 ◽  
Vol 95 (3) ◽  
pp. 415-421 ◽  
Author(s):  
A. J. Wheeler ◽  
J. P. Johnston
Keyword(s):  
Boundary Layer ◽  
Eddy Viscosity ◽  
Three Dimensional ◽  
High Sensitivity ◽  
Boundary Layer Flows ◽  
Mean Velocity ◽  
Eddy Viscosity Model ◽  
Separating Flow ◽  
Dimensional Boundary ◽  
Stress Models

Predictions have been made for a variety of experimental three-dimensional boundary layer flows with a single finite difference method which was used with three different turbulent stress models: (i) an eddy viscosity model, (ii) the “Nash” model, and (iii) the “Bradshaw” model. For many purposes, even the simplest stress model (eddy viscosity) was adequate to predict the mean velocity field. On the other hand, the profile of shear stress direction was not correctly predicted in one case by any model tested. The high sensitivity of the predicted results to free stream pressure gradient in separating flow cases is demonstrated.

Experimental and Theoretical Investigation of the Supersonic Boundary Layer Stability on the Swept Wing

2008 ◽  
Vol 3 (3) ◽  
pp. 34-38
Author(s):  
Sergey A. Gaponov ◽  
Yuri G. Yermolaev ◽  
Aleksandr D. Kosinov ◽  
Nikolay V. Semionov ◽  
Boris V. Smorodsky
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Leading Edge ◽  
Supersonic Boundary Layer ◽  
Mean Flow ◽  
Swept Wing ◽  
Wing Model ◽  
Dimensional Boundary ◽  
The Stability ◽  
Good Agreement

Theoretical and an experimental research results of the disturbances development in a swept wing boundary layer are presented at Mach number М = 2. In experiments development of natural and small amplitude controllable disturbances downstream was studied. Experiments were carried out on a swept wing model with a lenticular profile at a zero attack angle. The swept angle of a leading edge was 40°. Wave parameters of moving disturbances were determined. In frames of the linear theory and an approach of the local self-similar mean flow the stability of a compressible three-dimensional boundary layer is studied. Good agreement of the theory with experimental results for transversal scales of unstable vertices of the secondary flow was obtained. However the calculated amplification rates differ from measured values considerably. This disagreement is explained by the nonlinear processes observed in experiment

Review: Laminar-to-Turbulent Transition of Three-Dimensional Boundary Layers on Rotating Bodies

1994 ◽  
Vol 116 (2) ◽  
pp. 200-211 ◽  
Author(s):  
Ryoji Kobayashi
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Speed Ratio ◽  
Stream Velocity ◽  
Turbulent Transition ◽  
Centrifugal Instability ◽  
Crossflow Instability ◽  
Dimensional Boundary ◽  
Axisymmetric Bodies

The laminar-turbulent transition of three-dimensional boundary layers is critically reviewed for some typical axisymmetric bodies rotating in still fluid or in axial flow. The flow structures of the transition regions are visualized. The transition phenomena are driven by the compound of the Tollmien-Schlichting instability, the crossflow instability, and the centrifugal instability. Experimental evidence is provided relating the critical and transition Reynolds numbers, defined in terms of the local velocity and the boundary layer momentum thickness, to the local rotational speed ratio, defined as the ratio of the circumferential speed to the free-stream velocity at the outer edge of the boundary layer, for the rotating disk, the rotating cone, the rotating sphere and other rotating axisymmetric bodies. It is shown that the cross-sectional structure of spiral vortices appearing in the transition regions and the flow pattern of the following secondary instability in the case of the crossflow instability are clearly different than those in the case of the centrifugal instability.

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