A Multizone Time-Marching Technique for Unsteady Separating Three-Dimensional Boundary Layers and Its Application to the Symmetry-Plane Solution of an Impulsively Started Prolate Spheroid

1991 ◽  
Vol 113 (2) ◽  
pp. 228-239 ◽  
Author(s):  
Tzuyin Wu ◽  
Shan-Fu Shen
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Symmetry Plane ◽  
Elliptic Cylinder ◽  
Prolate Spheroid ◽  
Singular Behavior ◽  
Unsteady Separation ◽  
Stage Of Development ◽  
Dimensional Boundary ◽  
Plane Solution

Recent interest in unsteady separation and separated flows brings up the need of an accurate and efficient computational scheme for general unsteady three-dimensional boundary-layer flows. Resolution of the singular behavior at separation is a delicate problem. The task is further complicated by the geometrical singularity and the nonstationary stagnation point. The present paper proposes a numerical scheme to sidestep these difficulties. At the first stage of development, the simpler problem of the symmetry-plane solution of the laminar boundary-layer over an impulsively-started prolate spheroid is calculated. Results show that the present Eulerian calculation satisfactorily captures the singular behavior of the boundary layer when separation is approached. Comparison with Xu and Wang’s recent results and those for the two-dimensional elliptic cylinder calculated by the Lagrangian method are also made. Discussions of the results for unsteady separation at zero, small and large incidences are presented.

Singularities encountered in three-dimensional boundary layers under an adverse or favourable pressure gradient

1995 ◽  
Vol 352 (1698) ◽  
pp. 45-87 ◽  
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Three Dimensional ◽  
Symmetry Plane ◽  
Plane Flow ◽  
Boundary Layer Equations ◽  
Dimensional Boundary

Singularities in solutions of the classical boundary-layer equations are considered, numerically and analytically, in an example of steady hypersonic flow along a flat plate with three-dimensional surface roughness. First, a wide parametric study of the breakdown of symmetry-plane flow is performed for two particular cases of the surface geometry. Emphasis is put on the structural stability of the singularities’ development to local/global variation of the pressure distribution. It is found that, as usual, the solution behaviour under an adverse pressure gradient involves the Goldstein- or marginal-type singularity at a point of zero streamwise skin friction. As the main alternative, typical of configurations with favourable or zero pressure forcing, an inviscid breakdown in the middle of the flow is identified. Similarly to unsteady flows, the main features of the novel singularity include infinitely growing boundary-layer thickness and finite limiting values of the skin-friction components. Subsequent analytical extensions of the singular symmetry-plane solution then suggest two different scenarios for the global boundary-layer behaviour: one implies inviscid breakdown of the flow at some singular line, the other describes the development of a boundary-layer collision at a downstream portion of the symmetry plane. In contrast with previous studies of the collision phenomenon in steady flows, the present theory suggests logarithmic growth of boundary-layer thickness on both sides of the discontinuity. Finally, an example of numerical solution of the full three dimensional boundary layer equations is given. The flow régime chosen corresponds to inviscid breakdown of a centreplane flow under a favourable pressure gradient and development of the discontinuity/collision downstream. The numerical results near the origin of the discontinuity are found to be supportive, producing quantitative agreement with the local analytical description.

Three-dimensional boundary layer near the plane of symmetry of a spheroid at incidence

1970 ◽  
Vol 43 (1) ◽  
pp. 187-209 ◽  
Author(s):  
K. C. Wang
Keyword(s):  
Boundary Layer ◽  
Angle Of Attack ◽  
Three Dimensional ◽  
Prolate Spheroid ◽  
Boundary Layer Region ◽  
Dimensional Boundary ◽  
The Common ◽  
Implicit Finite Difference ◽  
Layer Region

This paper presents incompressible laminar boundary-layer results on both the leeside and windside of a prolate spheroid. The results are obtained by an implicit finite difference method of the Crank–Nicolson type. Particular attention has been given to the determination of separation and of embedded streamwise vortices. No restriction on the angle of attack or the thickness ratio is imposed, nor are there invoked any of the common assumptions such as similarity, conical flow and others. The results suggest an embedded vortex region existing between the regular boundary-layer region and the separated region. At higher angle of attack, the vortex region becomes so thick that it itself may be more appropriately called ‘separated’ also. The latter possibility leads to questions of applicability for existing theories on three-dimensional separation.

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.

Sign in / Sign up

Export Citation Format

Share Document