The spanwise perturbation of two-dimensional boundary layers

1966 ◽  
Vol 24 (1) ◽  
pp. 153-164 ◽  
Author(s):  
S. C. Crow
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Plate Boundary ◽  
Wind Tunnels ◽  
Two Dimensional ◽  
Surface Shear ◽  
Flow Reynolds Number ◽  
Two Dimensional Flow ◽  
Dimensional Boundary ◽  
Small Periodic

Large spanwise variations of boundary-layer thickness and surface shear have been found recently in wind tunnels designed to maintain two-dimensional flow. Bradshaw (1965) argues that these variations are caused by minute deflexions in the free-stream flow rather than by any intrinsic instability of the boundary layers. This paper is a study of the effect of a small, periodic transverse flow on a flat-plate boundary layer. The perturbation flow Reynolds number is assumed to be O(1) as it is in the experiments.

On Numerical Prediction of the Stability of Hypersonic Boundary-Layer Flow Over a Row of Microcavities

2003 ◽  
Author(s):  
Vassilios Theofilis ◽  
Michel O. Deville ◽  
Peter W. Duck ◽  
Alexander Fedorov
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Flow Instability ◽  
Viscous Sublayer ◽  
Hypersonic Boundary Layer ◽  
Two Dimensional ◽  
Flow Stabilization ◽  
Two Dimensional Flow ◽  
Dimensional Boundary ◽  
Layer Flow

This paper is concerned with the structure of steady two–dimensional flow inside the viscous sublayer in hypersonic boundary–layer flow over a flat surface in which microscopic cavities (‘microcavities’) are embedded. Such a so–called Ultra Absorptive Coating (UAC) has been predicted theoretically [1] and demonstrated experimentally [2] to stabilize passively hypersonic boundary–layer flow. In an effort to further quantify the physical mechanism leading to flow stabilization, this paper focuses on the nature of the basic flows developing in the configuration in question. Direct numerical simulations are performed, addressing firstly steady flow inside a singe microcavity, driven by a constant shear, and secondly a model of a UAC surface in which the two–dimensional boundary layer over a flat plate and a minimum nontrivial of two microcavities embedded in the wall are solved in a coupled manner. The influence of flow– and geometric parameters on the obtained solutions is illustrated. Based on the results obtained, the limitations of currently used theoretical methodologies for the description of flow instability are identified and suggestions for the improved prediction of the instability characteristics of UAC surfaces are discussed.

The Interaction of Thermal Radiation in Optically Thick Boundary Layers

1967 ◽  
Vol 89 (4) ◽  
pp. 309-312 ◽  
Author(s):  
J. L. Novotny ◽  
Kwang-Tzu Yang
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Boundary Layers ◽  
Optical Thickness ◽  
Asymptotic Expansions ◽  
Energy Equation ◽  
Two Dimensional ◽  
Small Temperature ◽  
Dimensional Boundary

An analysis is presented to examine the role of the Rosseland or optically thick approximation in convection-radiation interaction situations. The analysis is formulated for the flow of a gray gas in a laminar two-dimensional boundary layer under the restriction of small temperature differences within the flow field. The boundary-layer energy equation is treated using the method of matched asymptotic expansions based on a parameter which characterizes the optical thickness of the gas. Two illustrative examples of the resulting equations are presented.

scholarly journals The equilibria of vesicles adhered to substrates by short-ranged potentials

2013 ◽  
Vol 469 (2153) ◽  
pp. 20120729 ◽  
Author(s):  
Maurice J. Blount ◽  
Michael J. Miksis ◽  
Stephen H. Davis
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Layer Structure ◽  
Two Dimensional ◽  
Adhesive Interaction ◽  
Contact Potential ◽  
Layer Structures ◽  
Bending Stresses ◽  
Dimensional Boundary ◽  
Horizontal Substrate

In equilibrium, a vesicle that is adhered to a horizontal substrate by a long-range attractive, short-range repulsive force traps a thin layer of fluid beneath it. In the asymptotic limit that this layer is very thin, there are quasi-two-dimensional boundary-layer structures near the edges of the vesicle, where the membrane's shape is governed by a balance between bending and adhesive stresses. These boundary layers are analysed to obtain corrections to simpler models that instead represent the adhesive interaction by a contact potential, thereby resolving apparent discontinuities that arise when such models are used. Composite expansions of the shapes of two-dimensional vesicles are derived. When, in addition, the adhesive interaction is very strong, there is a nested boundary-layer structure for which the adhesive boundary layers match towards sharp corners where bending stresses remain important but adhesive stresses are negligible. Outside these corners, bending stresses are negligible and the vesicle's shape is given approximately by the arc of a circle. Simple composite expansions of the vesicle's shape are derived that account for the shape of the membrane inside these corners.

scholarly journals Oblique route to turbulence

2011 ◽  
Vol 674 ◽  
pp. 1-4
Author(s):  
MUJEEB R. MALIK
Keyword(s):  
Boundary Layer ◽  
Numerical Simulations ◽  
Flat Plate ◽  
Boundary Layers ◽  
Plate Boundary ◽  
Direct Numerical Simulations ◽  
Two Dimensional ◽  
Mach 3 ◽  
Transition Scenario ◽  
Flat Plate Boundary Layer

Direct numerical simulations have been performed by Mayer, Von Terzi & Fasel (J. Fluid Mech., this issue, vol. 674, 2011, pp. 5–42) to demonstrate that oblique-mode breakdown leads to fully turbulent flow for a Mach 3 flat-plate boundary layer. Since very low level of initial disturbances is required for this transition scenario, oblique-mode breakdown is the most potent mechanism for transition in two-dimensional supersonic boundary layers in low-disturbance environments relevant to flight.

Singularities associated with separating boundary layers

1965 ◽  
Vol 257 (1084) ◽  
pp. 409-444 ◽  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Delta Wing ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Separation Line ◽  
Two Dimensional Flow ◽  
Dimensional Boundary ◽  
Line Of Singularities ◽  
Appl Math

This paper investigates the nature of flow in the neighbourhood of separation of a laminar boundary layer, and is based on the work of Goldstein (1948 Quart. J. Mech. Appl. Math. 1, 43), Stewartson (1958 Quart. J. Mech. Appl. Math. 11, 399), Terrill (1960 Phil. Trans. A, 253, 55) and Stewartson (1962 J.Fluid Mech. 12, 117). The problem of establishing the existence or nonexistence of a singularity at separation for incompressible two-dimensional flow is investigated in the first three of these papers, and the last mentioned finds that if heat transfer across the boundary is permitted no singularity occurs at a point of vanishing skin friction unless the heat transfer is also zero at this point. The present work examines the possibility of the non-occurrence of singularities in other physical situations including reference to three-dimensional separation. Particular problems considered include that of conefield flow of an incompressible fluid over a delta wing for which the separation line is shown to be a line of singularities, and that of compressible flow over a yawed cylinder in which case the conclusion is that the separation line is a line of regular points if the heat transfer is non-zero along its length. The problem of separation for a general three-dimensional boundary layer is considered but not resolved.

The Law of the Wall in a Thick Axisymmetric Turbulent Boundary Layer

1967 ◽  
Vol 34 (1) ◽  
pp. 237-238 ◽  
Author(s):  
G. N. V. Rao
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Equations Of Motion ◽  
Viscous Sublayer ◽  
Experimental Information ◽  
Two Dimensional ◽  
Law Of The Wall ◽  
Two Dimensional Flow ◽  
Sublayer Thickness

An attempt is made to develop a law of the wall for a thick axisymmetric turbulent boundary layer in which the sublayer thickness is comparable to the radius of transverse curvature. Examination of the equations of motion in the viscous sublayer suggests a law similar to that in two-dimensional flow. Available experimental information is consistent with this law, but the structure of turbulence in such thick axisymmetric boundary layers would seem to need further study.

The Law of the Wake and Plane of Symmetry Flows in Three-Dimensional Turbulent Boundary Layers

1966 ◽  
Vol 88 (1) ◽  
pp. 101-108 ◽  
Author(s):  
F. J. Pierce
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Adverse Pressure Gradient ◽  
Boundary Layer Flows ◽  
Three Dimensional Model ◽  
Law Of The Wall ◽  
Two Dimensional Flow ◽  
Dimensional Boundary ◽  
The Law

Coles’ model incorporating the law of the wall and the law of the wake, proposed for two and three-dimensional turbulent boundary-layer flows, is examined for the special case of plane of symmetry flows in collateral and skewed three-dimensional boundary layers. Contrary to other published results, it is shown that the model is appropriate for adverse pressure gradient plane of symmetry flows in collateral environments away from separation. Additional, it appears that the departure from Coles’ law of the wake for recently reported three-dimensional flows is of the same basic form as that observed for plane of symmetry flows in transient development or two-dimensional flow with imminent separation. Since the Coles’ model, as most velocity profile models, is proposed only in an asymptotic sense for a well-developed flow, the fact that most of the three-dimensional flows heretofore reported are in transient or undeveloped states, suggests that the three-dimensional model be examined in well-developed three-dimensional boundary-layer flows before the question of the model’s validity can be properly answered.

Boundary layer flow of an Oldroyd-B fluid in the region of a stagnation point over a stretching sheet

2010 ◽  
Vol 88 (9) ◽  
pp. 635-640 ◽  
Author(s):  
M. Sajid ◽  
Z. Abbas ◽  
T. Javed ◽  
N. Ali
Keyword(s):  
Boundary Layer ◽  
Stagnation Point ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
Dimensional Boundary ◽  
Layer Flow ◽  
Parameter Values ◽  
The Mathematical Model

In this paper, the mathematical model for the two-dimensional boundary layer flow of an Oldroyd-B fluid is presented. The developed equations are used to discuss the problem of two-dimensional flow in the region of a stagnation point over a stretching sheet. The obtained partial differential equations are reduced to an ordinary differential equation by a suitable transformation. The obtained equation is then solved using a finite difference method. The influence of the pertinent fluid parameters on the velocity is discussed through graphs. The behaviour of f ″(0) is also investigated with changes in parameter values. It is observed that an increase in the relaxation time constant causes a reduction in the boundary layer thickness. To the best of our knowledge, this type of solution for an Oldroyd-B fluid is presented for the first time in the literature.

Resistance of an Inclined Plate Placed on a Plane Boundary in Two-Dimensional Flow

1970 ◽  
Vol 92 (1) ◽  
pp. 21-28 ◽  
Author(s):  
K. G. Ranga Raju ◽  
R. J. Garde
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Experimental Study ◽  
Turbulent Boundary Layer ◽  
Drag Coefficient ◽  
Wind Tunnels ◽  
Plane Boundary ◽  
Two Dimensional ◽  
Inclined Plate ◽  
Two Dimensional Flow

This paper describes the results of an experimental study on the drag coefficient of a two-dimensional sharp-edged plate placed on a plane boundary at different inclinations to the flow. Experimental data were collected to investigate the effects of (i) inclination of the plate to the flow, (ii) the relative submergence of the plate in a turbulent boundary layer, and (iii) the proximity of the tunnel walls to the plate, on the drag coefficient of the plate. Relations have been developed to enable correction for “blockage effect” and also to evaluate the effects of inclination of the plate and the presence of the boundary layer on the drag coefficient of the plate. Data collected by other investigators in wind tunnels of various dimensions have also been used in the development of the foregoing relations.

Equilibrium turbulent boundary layers with lateral streamline convergence or divergence

2009 ◽  
Vol 623 ◽  
pp. 273-282 ◽  
Author(s):  
T. B. NICKELS
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Equilibrium Solutions ◽  
Boundary Layer Equations ◽  
Dimensional Boundary ◽  
Convergence And Divergence ◽  
Necessary Constraints

The constraints necessary for equilibrium solutions of the boundary layer equations are explored for turbulent boundary layers subject to lateral convergence and divergence and with longitudinal pressure gradients. It is shown that in addition to the well-known equilibrium solutions for two-dimensional boundary layers there are additionalpossibleequilibrium states for boundary layers with these extra rates-of-strain acting. The necessary constraints for equilibrium are derived and discussed.

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