scholarly journals Boundary layer and variational eigencurve in two-parameter single pendulum type equations

2006 ◽  
Vol 5 (1) ◽  
pp. 147-154 ◽  
Author(s):  
Tetsutaro Shibata ◽  
Keyword(s):  
Boundary Layer ◽  
Pendulum Type Equations ◽  
Two Parameter

A Two-Parameter Method for Calculating the Two-Dimensional Incompressible Laminar Boundary Layer

1967 ◽  
Vol 71 (674) ◽  
pp. 117-123 ◽  
Author(s):  
N. Curle
Keyword(s):  
Boundary Layer ◽  
Exact Solutions ◽  
Careful Examination ◽  
Parameter Method ◽  
Boundary Layer Equations ◽  
First Approximation ◽  
Dimensional Parameters ◽  
Image Position ◽  
Momentum Integral ◽  
Two Parameter

Summary:In most one-parameter methods of calculating laminar boundary layers it is assumed that the non-dimensional parameters H=δ1/δ2, I=δ2τW/μu1 and L = 2{I−λ(H+2)}, depend only upon the pressure gradient parameter λ=u1δ22/v. In this paper it is shown theoretically that a more accurate, two-parameter representation isL=F0(λ)−μG0(λ)I2=F1(λ)−μG1(λ),where μ=λ2U1U1/(U1)2. Careful examination of the available range of exact solutions of the boundary layer equations has enabled the four functions F0, G0, F1, G1, to be tabulated, and the above functional forms agree with the exact solutions to a remarkable accuracy.In view of the fact that a reasonable first approximation to L is usually , we write,and it is then shown that the momentum integral equation becomesThis equation is easily solved by iteration, setting g=0 in the first approximation, and convergence is extremely rapid.The method is, in effect, a refinement of that due to Thwaites, which is universally accepted as one of the better of the existing calculation methods. Detailed calculations made by the present method indicate that the errors are only 5% of those given by the Thwaites method.

A Modified Entrainment Theory for the Prediction of Turbulent Boundary Layer Growth in Adverse Pressure Gradients

1969 ◽  
Vol 91 (4) ◽  
pp. 649-655
Author(s):  
W. B. Nicoll ◽  
B. R. Ramaprian
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Layer Growth ◽  
Pressure Gradients ◽  
Shape Factors ◽  
Power Profile ◽  
Half Power ◽  
Separating Flows ◽  
Boundary Layer Growth ◽  
Two Parameter

An approach based on the “entrainment” theory is presented as a tool for the prediction of turbulent boundary layer growth in adverse pressure gradients. The rate of entrainment of free-stream fluid by the boundary layer is assumed to be a unique function of the shape factor. A two parameter velocity profile has been assumed, which reduces to the Spalding [24] profile for zero pressure gradient flows and to the half-power profile of Stratford [26] for separating flows. The integral equations of continuity and momentum are solved with the above empirical input to predict the growth of the boundary layer parameters, both in two-dimensional and axisymmetric flows. The predictions are compared with some of the available experimental data in both the cases. The technique is found to give improved predictions compared with those of previous methods. Results in the case of conical diffusers indicate that the theory predicts slightly higher shape factors than actual, especially in the far downstream portions of the diffuser and thus furnishes a slightly conservative method for design.

Two-Parameter Characterization of Elastic-Plastic Crack-Tip Fields

1991 ◽  
Vol 58 (1) ◽  
pp. 104-110 ◽  
Author(s):  
C. Betego´n ◽  
J. W. Hancock
Keyword(s):  
Boundary Layer ◽  
Radial Distance ◽  
Crack Tip ◽  
Elastic Field ◽  
Full Field ◽  
Elastic Plastic ◽  
Crack Tip Fields ◽  
Full Plasticity ◽  
Two Parameter

Plane-strain elastic-plastic crack-tip fields have been modeled with modified boundary layer formulations based on the first two terms K and T, of the elastic field. These formulations match the appropriate full field solutions. Compressive T stresses reduce the stresses by an amount which is independent of radial distance, corresponding to the introduction of a second term in addition to the dominant plastic singularity. Geometries which maintain J-dominance are characterized by zero or positive T stresses, while geometries with negative T stresses can be described by a two-parameter characterization using J and T into full plasticity.

Laminar flow of a stably stratified fluid past a flat plate

1968 ◽  
Vol 34 (4) ◽  
pp. 795-808 ◽  
Author(s):  
Yih-Ho Pao
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Flat Plate ◽  
Salt Water ◽  
Stratified Fluid ◽  
Uniform Density ◽  
Perturbation Expansions ◽  
Visualization Technique ◽  
Parameter Perturbation ◽  
Two Parameter

Laminar flow of a stably stratified fluid with uniform upstream velocity and density gradient past a flat plate is investigated experimentally and theoretically. In the experimental study, the flat plate, parallel to the direction of motion, is towed horizontally at uniform speeds in a tank of stratified salt water at uniform density gradients. The horizontal velocity in front of, above, and behind the flat plate is measured with a flow visualization technique. One of the striking phenomena is the strong upstream influence (the upstream wake) of an obstacle in a flow of stably stratified fluid when the gravity effect is comparable to, or more than the inertial effect. The velocity profiles of the upstream wake and boundary layer above the flat plate are wavy and found to be governed by the ratio of Reynolds number Be to Richardson number Ri. The problem is also analysed theoretically with Boussinesq's approximation and two-parameter perturbation expansions for the upstream wake and the boundary layer. The solutions for the upstream wake and for the boundary layer are compared with measurements.

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