On the stability of the decelerating laminar boundary layer

1984 ◽  
Vol 138 ◽  
pp. 297-323 ◽  
Author(s):  
Mohamed Gad-El-Hak ◽  
Stephen H. Davis ◽  
J. Thomas Mcmurray ◽  
Steven A. Orszag
Keyword(s):  
Boundary Layer ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Velocity Profiles ◽  
Hairpin Vortices ◽  
Boundary Layer Equations ◽  
Numerical Predictions ◽  
Layer Flow ◽  
Lift Off ◽  
The Stability

The stability of a decelerating boundary-layer flow is investigated experimentally and numerically. Experimentally, a flat plate having a Blasius boundary layer is decelerated in an 18 m towing tank. The boundary layer becomes unstable to two-dimensional waves, which break down into three-dimensional patterns, hairpin vortices, and finally turbulent bursts when the vortices lift off the wall. The unsteady boundary-layer equations are solved numerically to generate instantaneous velocity profiles for a range of boundary and initial conditions. A quasi-steady approximation is invoked and the stability of local velocity profiles is determined by solving the Orr–Sommerfeld equation using Chebyshev matrix methods. Comparisons are made between the numerical predictions and the experimentally observed instabilities.

On three-dimensional boundary layer flow over surface irregularities

1980 ◽  
Vol 373 (1754) ◽  
pp. 311-329 ◽  
Keyword(s):  
Boundary Layer ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Iterative Solution ◽  
Solution Technique ◽  
Parabolic Boundary ◽  
Boundary Layer Equations ◽  
Surface Irregularities ◽  
Dimensional Boundary ◽  
Layer Flow

The three-dimensional pipeflow boundary layer equations of Smith (1976) are shown to apply to certain external flow problems, and a numerical method for their solution is developed. The method is used to study flow over surface irregularities, and some three-dimensional separated flows are calculated. Upstream influence in the form of so-called ‘free interactions’ requires an iterative solution technique, in which the initial conditions for the parabolic boundary layer equations must be determined to satisfy a downstream condition

Three-Dimensional Boundary-Layer Flow About an Ablating Slender Cone

1969 ◽  
Vol 91 (4) ◽  
pp. 632-648 ◽  
Author(s):  
T. K. Fannelop ◽  
P. C. Smith
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Cone Angle ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Boundary Layer Equations ◽  
Transverse Curvature ◽  
Dimensional Boundary ◽  
Layer Flow

A theoretical analysis is presented for three-dimensional laminar boundary-layer flow about slender conical vehicles including the effect of transverse surface curvature. The boundary-layer equations are solved by standard finite difference techniques. Numerical results are presented for hypersonic flow about a slender blunted cone. The influences of Reynolds number, cone angle, and mass transfer are studied for both symmetric flight and at angle-of-attack. The effects of transverse curvature are substantial at the low Reynolds numbers considered and are enhanced by blowing. The crossflow wall shear is largely unaffected by transverse curvature although the peak velocity is reduced. A simplified “channel flow” analogy is suggested for the crossflow near the wall.

The interacting boundary-layer flow due to a vortex approaching a cylinder

1997 ◽  
Vol 346 ◽  
pp. 319-343 ◽  
Author(s):  
Z. XIAO ◽  
O. R. BURGGRAF ◽  
A. T. CONLISK
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Boundary Layer Separation ◽  
Two Dimensions ◽  
Unsteady Boundary Layer ◽  
Reynolds Number Flow ◽  
Boundary Layer Equations ◽  
Number Flow ◽  
Layer Flow ◽  
High Reynolds

In this paper the solution to the three-dimensional and unsteady interacting boundary-layer equations for a vortex approaching a cylinder is calculated. The flow is three-dimensional and unsteady. The purpose of this paper is to enhance the understanding of the structure in three-dimensional unsteady boundary-layer separation commonly observed in a high-Reynolds-number flow. The short length scales associated with the boundary-layer eruption process are resolved through an efficient and effective moving adaptive grid procedure. The results of this work suggest that like its two-dimensional counterpart, the three-dimensional unsteady interacting boundary layer also terminates in a singularity at a finite time. Furthermore, the numerical calculations confirm the theoretical analysis of the singular structure in two dimensions for the interacting boundary layer due to Smith (1988).

Study of the Boundary Layer on Ship Forms

1970 ◽  
Vol 14 (03) ◽  
pp. 153-167
Author(s):  
W. C. Webster ◽  
T.T. Huang
Keyword(s):  
Boundary Layer ◽  
Shape Factor ◽  
Three Dimensional ◽  
Momentum Thickness ◽  
Flow Conditions ◽  
Integral Boundary ◽  
Outer Flow ◽  
Boundary Layer Equations ◽  
Pressure Distributions ◽  
Layer Flow

This paper presents a theoretical investigation of the development of the boundary layer about a ship. The "outer flow" conditions, including the streamlines and pressure distributions, are found from linearized, thin-ship theory using the method of Guilloton. Linearized, integral boundary-layer equations appropriate for three-dimensional turbulent flow are integrated numerically along the streamlines to determine the momentum thickness, the shape factor, and the angle of the boundary-layer flow to the outer flow. The results of computations for Series 60, block 0.60 and 0.80 are presented for various Froude numbers and ship lengths.

The boundary-layer flow due to a vortex approaching a cylinder

1994 ◽  
Vol 275 ◽  
pp. 33-57 ◽  
Author(s):  
H. Affes ◽  
Z. Xiao ◽  
A. T. Conlisk
Keyword(s):  
Boundary Layer ◽  
Secondary Flow ◽  
Three Dimensional ◽  
Adverse Pressure Gradient ◽  
Inviscid Flow ◽  
Main Stream ◽  
Boundary Layer Equations ◽  
Narrow Region ◽  
Secondary Flow Structure ◽  
Layer Flow

The three-dimensional unsteady boundary layer induced by a vortex filament moving outside a circular cylinder is considered. In the present paper, we focus attention on the situation where the inviscid flow is fully three-dimensional but is symmetric with respect to the top centreline of the cylinder. The motion of the vortex toward the cylinder leads to separation of the boundary layer; in the present work a large unsteady adverse pressure gradient develops as well. Results for the three-dimensional streamlines, the vorticity distribution, and the velocity component normal to the cylinder indicate the presence of a region of unsteady three-dimensional secondary flow structure of rather complex shape located deep within the boundary layer. Within this three-dimensional secondary flow the fluid is progressively squeezed into a narrow region under the main vortex and it is expected that a local three-dimensional jet will develop sending boundary-layer fluid out into the main stream. It is pointed out that such three-dimensional eruptive behaviour has been observed in experiments. The results indicate the development of a three-dimensional singularity in the boundary-layer equations.

Limitations of the Boundary-Layer Equations for Predicting Laminar Symmetric Sudden Expansion Flows

1986 ◽  
Vol 108 (2) ◽  
pp. 208-213 ◽  
Author(s):  
J. P. Lewis ◽  
R. H. Pletcher
Keyword(s):  
Boundary Layer ◽  
Initial Conditions ◽  
Boundary Layer Equation ◽  
Reynolds Numbers ◽  
Equation Model ◽  
Sudden Expansion ◽  
Boundary Layer Equations ◽  
Flow Parameters ◽  
Numerical Predictions ◽  
Global Iteration

A finite-difference solution scheme is used to study the limitations and capabilities of the boundary-layer equation model for flow through abrupt, symmetric expansions. Solutions of the boundary-layer equations are compared with previous numerical predictions and experimental measurements. Some flow parameters are not well predicted for Reynolds numbers below 200. Global iteration over the flow field to include upstream effects does not significantly influence the predictions. Axisymmetric and two-dimensional flows are investigated. The effect of initial conditions is discussed

Effects of Streamwise Vortices on Laminar Boundary-Layer Flow

1968 ◽  
Vol 35 (2) ◽  
pp. 424-426 ◽  
Author(s):  
T. K. Fannelop
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Stokes Equations ◽  
Transverse Velocity ◽  
Three Dimensional ◽  
Perturbation Expansion ◽  
Navier Stokes ◽  
Boundary Layer Equations ◽  
Dimensional Boundary ◽  
Layer Flow

The effects of periodic transverse velocity fluctuations are investigated for boundary-layer flow over a flat plate. The method used is a perturbation expansion of the three-dimensional boundary-layer equations in terms of the small transverse velocity component. The equations are reduced to similarity form by means of suitable transformations. The second-order terms are expressed in terms of the first-order (Blasius) variables and are found to increase linearly with the streamwise coordinate. The present heat-transfer solution agrees with the more qualitative results of Persen. The derived velocity profiles are in exact agreement with the results of Crow’s more elaborate analysis based on the Navier-Stokes equations.

scholarly journals Boundary layer flow of air over water on a flat plate

1995 ◽  
Vol 284 ◽  
pp. 159-169 ◽  
Author(s):  
John J. Nelson ◽  
Amy E. Alving ◽  
Daniel D. Joseph
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Initial Conditions ◽  
Leading Edge ◽  
Water Layer ◽  
Large Reynolds Number ◽  
Boundary Layer Equations ◽  
Numerical Studies ◽  
Air Blowing ◽  
Layer Flow

A non-similar boundary layer theory for air blowing over a water layer on a flat plate is formulated and studied as a two-fluid problem in which the position of the interface is unknown. The problem is considered at large Reynolds number (based on x), away from the leading edge. We derive a simple non-similar analytic solution of the problem for which the interface height is proportional to x1/4 and the water and air flow satisfy the Blasius boundary layer equations, with a linear profile in the water and a Blasius profile in the air. Numerical studies of the initial value problem suggest that this asymptotic non-similar air–water boundary layer solution is a global attractor for all initial conditions.

Inviscid instability of a stably stratified compressible boundary layer on an inclined surface

2012 ◽  
Vol 694 ◽  
pp. 524-539 ◽  
Author(s):  
Julien Candelier ◽  
Stéphane Le Dizès ◽  
Christophe Millet
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Acoustic Waves ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Maximum Velocity ◽  
Shear Plane ◽  
Layer Flow ◽  
The Stability ◽  
Inclined Surface

AbstractThe three-dimensional stability of an inflection-free boundary layer flow of length scale$L$and maximum velocity${U}_{0} $in a stably stratified and compressible fluid of constant Brunt–Väisälä frequency$N$, sound speed${c}_{s} $and stratification length$H$is examined in an inviscid framework. The shear plane of the boundary layer is assumed to be inclined at an angle$\theta $with respect to the vertical direction of stratification. The stability analysis is performed using both numerical and theoretical methods for all the values of$\theta $and Froude number$F= {U}_{0} / (LN)$. When non-Boussinesq and compressible effects are negligible ($L/ H\ll 1$and${U}_{0} / {c}_{s} \ll 1$), the boundary layer flow is found to be unstable for any$F$as soon as$\theta \not = 0$. Compressible and non-Boussinesq effects are considered in the strongly stratified limit: they are shown to have no influence on the stability properties of an inclined boundary layer (when$F/ \sin \theta \ll 1$). In this limit, the instability is associated with the emission of internal-acoustic waves.

A Mathematical Study for Three-Dimensional Boundary Layer Flow of Jeffrey Nanofluid

2015 ◽  
Vol 70 (4) ◽  
pp. 225-233 ◽  
Author(s):  
Tasawar Hayat ◽  
Taseer Muhammad ◽  
Sabir Ali Shehzad ◽  
Ahmed Alsaedi
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Mathematical Formulation ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Jeffrey Fluid ◽  
Electrically Conducting ◽  
Boundary Layer Equations ◽  
Dimensional Boundary ◽  
Layer Flow

AbstractIn this article we investigated the characteristics of Brownian motion and thermophoresis in the magnetohydrodynamic (MHD) three-dimensional boundary layer flow of an incompressible Jeffrey fluid. The flow is generated by a bidirectional stretching surface. Fluid is electrically conducting in the presence of a constant applied magnetic field. Mathematical formulation of the considered flow problem is made through the boundary layer analysis. A newly proposed boundary condition requiring zero nanoparticle mass flux is employed in the flow analysis of Jeffrey fluid. The governing nonlinear boundary layer equations are reduced into the nonlinear ordinary differential systems through appropriate transformations. The resulting systems have been solved for the velocities, temperature, and nanoparticle concentration expressions. The contributions of various interesting parameters are studied graphically. The values of the Nusselt number are computed and examined.

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