The boundary layer due to a three-dimensional vortex loop

1987 ◽  
Vol 185 ◽  
pp. 569-598 ◽  
Author(s):  
S. Ersoy ◽  
J. D. A. Walker
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Symmetry Plane ◽  
Layer Growth ◽  
Plane Wall ◽  
Vortex Loop ◽  
Loop Shape ◽  
Layer Flow ◽  
Boundary Layer Growth ◽  
Moving Vortex

The nature of the boundary layer induced by the motion of a three-dimensional vortex loop towards a plane wall is considered. Initially the vortex is taken to be a ring approaching a plane wall at an angle of attack in an otherwise stagnant fluid; the ring rapidly distorts into a loop shape due to the influence of the wall and the trajectory is computed from a numerical solution of the Biot-Savart integral. As the vortex loop moves, an unsteady boundary-layer flow develops on the wall. A method is described which allows the computation of the flow velocities on and near the symmetry plane of the vortex loop within the boundary layer. The computed results show the development of a variety of complex three-dimensional separation phenomena. Some of the solutions ultimately show strong localized boundary-layer growth and are suggestive that a boundary-layer eruption and a strong viscous-inviscid interaction will be induced by the moving vortex.

Unsteady separation and heat transfer upstream of obstacles

1995 ◽  
Vol 305 ◽  
pp. 1-27 ◽  
Author(s):  
R. I. Puhak ◽  
A. T. Degani ◽  
J. D. A. Walker
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Numerical Solutions ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Symmetry Plane ◽  
Plane Wall ◽  
Three Dimensions ◽  
Spiral Vortex ◽  
Layer Flow

The development of a laminar boundary layer upstream of both two- and threedimensional obstacles mounted on a plane wall is considered. The motion is impulsively started from rest, and it is shown that the boundary layer upstream of the obstacle initially develops independently from that on the obstacle itself. Numerical solutions for the unsteady boundary-layer flow on the plane wall are obtained in both Eulerian and Lagrangian coordinates. It is demonstrated that in both situations the flow focuses into a narrow-band eruption characteristic of separation phenomena at high Reynolds number. For the three-dimensional problem, results are obtained on a symmetry plane upstream of the obstacle which indicate the evolution, and subsequent sharp compression, of a spiral vortex in the near-wall flow in a manner consistent with recent experimental studies. The eruptive response of the two-dimensional boundary layer is found to be considerably stronger than the corresponding event in three dimensions. Calculated results for the temperature distribution are obtained for the situation where the wall temperature is constant but different from that of the mainstream. It is shown that a concentrated response develops in the surface heat transfer rate as the boundary layer starts to separate from the surface.

A Theory for Boundary Layer Growth on the Blades of a Radial Impeller Including Endwall Influence

1983 ◽  
Vol 105 (3) ◽  
pp. 403-411
Author(s):  
H. Ekerol ◽  
J. W. Railly
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Prediction Method ◽  
Suction Side ◽  
Layer Growth ◽  
Secondary Flows ◽  
Curvature Effects ◽  
Momentum Integral ◽  
Boundary Layer Growth

Experimental data on the wall shear stress of a turbulent boundary layer on the suction side of a blade in a two-dimensional radial impeller is compared with the predictions of a theory which takes account of rotation and curvature effects as well as the three-dimensional influence of the endwall boundary layers. The latter influence is assumed to arise mainly from mainstream distortion due to secondary flows created by the endwall boundary layers, and it appears as an extra term in the momentum integral equation of the blade boundary layer which has allowance, also for the Coriolis effect; an appropriate form of the Head entrainment equation is derived to obtain a solution and a comparison made. A comparison of the above theory with the Patankar-Spalding prediction method, modified to include the effects of Coriolis (including mixing length modification, MLM), is also made.

The boundary layer induced by a convected two-dimensional vortex

1984 ◽  
Vol 139 ◽  
pp. 1-28 ◽  
Author(s):  
T. L. Doligalski ◽  
J. D. A. Walker
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Layer Growth ◽  
Two Dimensional ◽  
Wall Boundary Layer ◽  
Constant Height ◽  
Boundary Layer Development ◽  
Layer Flow ◽  
The Right ◽  
Boundary Layer Growth

The response of a wall boundary layer to the motion of a convected vortex is investigated. The principal cases considered are for a rectilinear filament of strength –κ located a distance a above a plane wall and convected to the right in a uniform flow of speed U∞*. The inviscid solution predicts that such a vortex will remain at constant height a above the wall and be convected with constant speed αU∞*. Here α is termed the fractional convection rate of the vortex, and cases in the parameter range 0 [les ] α < 1 are considered. The motion is initiated at time t* = 0 and numerical calculations of the developing boundary-layer flow are carried out for α = 0, 0.2, 0.4, 0.55, 0.7, 0.75 and 0.8. For α < 0.75, a rapid lift-up of the boundary-layer streamlines and strong boundary-layer growth occurs in the region behind the vortex; in addition an unusual separation phenomenon is observed for α [les ] 0.55. For α [ges ] 0.75, the boundary-layer development is more gradual, but ultimately substantial localized boundary-layer growth also occurs. In all cases, it is argued that a strong inviscid–viscous interaction will take place in the form of an eruption of the boundary-layer flow. The generalization of these results to two-dimensional vortices with cores of finite dimension is discussed.

scholarly journals Hall Effect on Two-Phase Laminar Boundary Layer flow of Dusty Liquid due to Stretching of an Elastic Flat Sheet

2017 ◽  
Vol 16 (3) ◽  
pp. 13-26 ◽  
Author(s):  
B Mahanthesh
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Layer Growth ◽  
Dust Particles ◽  
Two Phase ◽  
Electrically Conducting ◽  
Similarity Transformations ◽  
Layer Flow ◽  
Fifth Order ◽  
Boundary Layer Growth

The present investigation is concerned with the effect of Hall current on boundary layer two-phase flow of an electrically conducting dusty fluid over a permeable stretching sheet in the presence of a strong magnetic field. The boundary layer approximation is employed for mathematical modeling. The governing partial differential equations are reduced to a set of ordinary differential equations using suitable similarity transformations. Subsequent equations are solved numerically by using Runge-Kutta-Fehlberg fourth-fifth order method. A comprehensive parametric study is conducted to reveal the tendency of solutions. It is found that the mass concentration of dust particles can be used as a control parameter to control the friction factor at the sheet. The influence of suction and injection are opposite on the momentum boundary layer growth.

Boundary-layer growth at a three-dimensional rear stagnation point

1975 ◽  
Vol 67 (2) ◽  
pp. 289-297 ◽  
Author(s):  
J. A. Howarth
Keyword(s):  
Boundary Layer ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Similarity Solutions ◽  
Layer Growth ◽  
Initial Value ◽  
Stagnation Points ◽  
Boundary Layer Growth ◽  
Rear Stagnation Point

The theory of boundary-layer growth at a rear stagnation point, first presented by Proudman & Johnson, is here extended to cover fully three-dimensional rear stagnation points. Supporting numerical solutions of the full initial-value problem establish the relevance of the in viscid similarity solutions obtained.

Three-Dimensional Boundary-Layer Computation on the Stationary End-Walls of Centrifugal Turbomachinery

1976 ◽  
Vol 98 (3) ◽  
pp. 431-441 ◽  
Author(s):  
W. R. Davis
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Streamwise Velocity ◽  
Layer Growth ◽  
Wall Region ◽  
Boundary Layer Equations ◽  
Computation Technique ◽  
Dimensional Boundary ◽  
Boundary Layer Growth ◽  
Good Agreement

An integral entrainment computation technique is presented for the three-dimensional boundary-layer growth on the stationary end-walls of centrifugal turbomachinery. The analytical model assumes axisymmetric inviscid core flow and viscous flow in the wall region, and the interaction between the two layers is considered. A novel form of the three-dimensional boundary-layer equations is presented. The form is physically appealing for this axisymmetric application and provides distinct advantages in the prediction of boundary-layer growth. It is demonstrated that it is essential to use the meridional boundary-layer profile to compute the Head entrainment function for this type of flow, as opposed to the streamwise velocity profile, as is more commonly done. Comparison with experimental measurements shows good agreement in the integral parameters. In addition, good agreement with experimental velocity profiles was achieved for a separating and reattaching flow.

EXPERIMENTAL INVESTIGATION OF FLOW RESPONSE TO STATIONARY DISTURBANCE IN ROTATING-DISK FLOW

2019 ◽  
Vol XVI (2) ◽  
pp. 13-22
Author(s):  
Muhammad Ehtisham Siddiqui
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Careful Analysis ◽  
Laboratory Frame ◽  
Transition To Turbulence ◽  
Turbulent Regime ◽  
Mean Velocity ◽  
Layer Flow

Three-dimensional boundary-layer flow is well known for its abrupt and sharp transition from laminar to turbulent regime. The presented study is a first attempt to achieve the target of delaying the natural transition to turbulence. The behaviour of two different shaped and sized stationary disturbances (in the laboratory frame) on the rotating-disk boundary layer flow is investigated. These disturbances are placed at dimensionless radial location (Rf = 340) which lies within the convectively unstable zone over a rotating-disk. Mean velocity profiles were measured using constant-temperature hot-wire anemometry. By careful analysis of experimental data, the instability of these disturbance wakes and its estimated orientation within the boundary-layer were investigated.

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