On the Initial Conditions for Boundary Layer Equations

1965 ◽  
Vol 44 (1-4) ◽  
pp. 353-367 ◽  
Author(s):  
Lu Ting
Keyword(s):  
Boundary Layer ◽  
Initial Conditions ◽  
Boundary Layer Equations

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

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

The unsteady laminar boundary layer on a semi-infinite flat plate due to small fluctuations in the magnitude of the free-stream velocity

1972 ◽  
Vol 51 (1) ◽  
pp. 137-157 ◽  
Author(s):  
R. C. Ackerberg ◽  
J. H. Phillips
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Stream Velocity ◽  
Main Stream ◽  
Mean Flow ◽  
Boundary Layer Equations ◽  
Damped Oscillations ◽  
Asymptotic Values ◽  
The Mean

Asymptotic and numerical solutions of the unsteady boundary-layer equations are obtained for a main stream velocity given by equation (1.1). Far downstream the flow develops into a double boundary layer. The inside layer is a Stokes shear-wave motion, which oscillates with zero mean flow, while the outer layer is a modified Blasius motion, which convects the mean flow downstream. The numerical results indicate that most flow quantities approach their asymptotic values far downstream through damped oscillations. This behaviour is attributed to exponentially small oscillatory eigenfunctions, which account for different initial conditions upstream.

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.

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.

EXISTENCE AND UNIQUENESS OF THE SOLUTION TO THE EDGE PROBLEM IN A TWO-DIMENSIONAL REACTIVE BOUNDARY LAYER

1995 ◽  
Vol 05 (01) ◽  
pp. 1-27 ◽  
Author(s):  
ERIC BOILLAT
Keyword(s):  
Boundary Layer ◽  
Existence And Uniqueness ◽  
Initial Conditions ◽  
Tangential Velocity ◽  
Two Dimensional ◽  
Differential Problem ◽  
Boundary Layer Equations ◽  
Uniqueness Of The Solution ◽  
Thermodynamical Functions ◽  
Physical Quantities

We prove an existence and uniqueness theorem for the ordinary differential problem which characterizes the profiles of the different physical quantities at the edge of two-dimensional reactive boundary layer. The main difficulties to be circumvented are the nonlinearities due to the different thermodynamical functions involved in the reactive boundary layer equations and the degeneracy caused by the natural initial conditions, where the tangential velocity has to vanish. We conclude by making some mathematical considerations about the relations that exist between the reactive boundary layer equations and the corresponding equations which describe the boundary layer in chemical equilibrium.

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