On the propagation of disturbances in a laminar boundary layer. II

1973 ◽  
Vol 73 (3) ◽  
pp. 505-514 ◽  
Author(s):  
S. N. Brown ◽  
K. Stewartson
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Laminar Boundary Layer ◽  
Asymptotic Methods

AbstractThe assumption that disturbances are confined to the neighbourhood of the wall in the problem of Part I is invalidated by an exact solution of the resulting equation which shows that disturbances rapidly travel out of the region in which the equation is applicable. The asymptotic methods of Part I are also applied to this equation, which was studied by Lam and Rott (1), and an assessment is made of the role of the eigensolutions found by these authors.

Similar and Asymptotic Solutions of the Incompressible Laminar Boundary Layer Equations with Suction

1967 ◽  
Vol 18 (2) ◽  
pp. 103-120 ◽  
Author(s):  
M. Zamir ◽  
A. D. Young
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Asymptotic Solution ◽  
Laminar Boundary Layer ◽  
Incompressible Flow ◽  
Suction Parameter ◽  
Suction Velocity ◽  
Boundary Layer Equations ◽  
Wide Range ◽  
Similar Solutions

SummarySimilar solutions of the boundary layer equations for incompressible flow with external velocity u1 ∞ xm and suction velocity υw ∞ x(m-1)/2 are obtained for negative values of m, in the range −0-1 to −0-9, and a wide range of suction quantities.The results are used, in combination with, existing solutions for positive m, to provide a guide to the ranges of m and suction parameter [(υw/u1√x] for which a general form of the classical asymptotic solution can be regarded as a good approximation to the exact solution.It is shown that the values of both m and suction parameter are generally important in this comparison, but for values of the latter greater than about 8 the approximation is a very good one for all values of m considered. For m≃−0·14 the approximation is good (i.e. the error is less than about 1 per cent) down to values of the suction parameter as low as 1·0.

Experimental Investigation of the Laminar Boundary Layer Flow on a Rotating Wavy Disk

2016 ◽  
Author(s):  
Christian Helcig ◽  
Christian Teigeler ◽  
Stefan aus der Wiesche
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Laminar Flow ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Similar Solution ◽  
Surface Shape ◽  
Self Similar Solution ◽  
Self Similar ◽  
Layer Flow

Since nearly one century, the flow on a flat rotating disk has provided the paradigm for studying rotating flows. For the laminar flow regime, a self-similar solution was obtained by von Kármán [6] in 1921, and a rather special feature of his exact solution of the Navier-Stokes equation is a constant boundary layer thickness not depending on the radial coordinate. A substantial modification of this canonical configuration is given by a wavy disk with a sinusoidal surface shape. Although axis-symmetric, no exact solution for the laminar flow on a wavy disk is known so far. In this study, detailed measurements of the velocity profiles were performed within the laminar boundary layer flow on a wavy disk. Based upon the experimental data, the potential of a self-similar solution approach for describing the resulting flow field was assessed. It was found that such an approach is useful for approximating the far-field solution but systematic deviations were observed in the vicinity of the disk origin.

Approximate Calculations of the Incompressible Laminar Boundary Layer

1967 ◽  
Vol 18 (3) ◽  
pp. 259-272 ◽  
Author(s):  
M. R. Head ◽  
N. Hayasi
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Approximate Method ◽  
Laminar Boundary Layer ◽  
Calculation Method ◽  
Close Agreement ◽  
Computer Solution ◽  
Three Solutions ◽  
Recent Calculation ◽  
Good Agreement

SummaryA recent calculation method proposed by Curle has been applied to the flow U=U0ξe-ξ for which a computer solution exists. An earlier approximate method due to Head, presented here in a simplified form, has been applied to the same problem. All three solutions are found to be in close agreement. A further problem, already examined by Curle, is treated by Head’s method. Again the results are in good agreement with each other and with an exact solution obtained subsequently.

On unsteady laminar boundary layers

1960 ◽  
Vol 9 (2) ◽  
pp. 300-304 ◽  
Author(s):  
H. A. Hassan
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Boundary Layers ◽  
Laminar Boundary Layer ◽  
Two Dimensions ◽  
Universal Functions ◽  
Boundary Layer Equations ◽  
Laminar Boundary Layers ◽  
Pressure Distributions

A transformation is introduced which, for a class of outer pressure distributions, reduces the unsteady incompressible laminar boundary-layer equations in two dimensions to an equation in which the time does not appear explicitly. A formally exact solution of the resulting equation is then presented in the form of a series and it is shown that the solution can be expressed in terms of universal functions.

A Statistical Study of Process Variables to Optimize a High Speed Curtain Coater: Part I

TAPPI Journal ◽  
2009 ◽  
Vol 8 (1) ◽  
pp. 20-26 ◽  
Author(s):  
PEEYUSH TRIPATHI ◽  
MARGARET JOYCE ◽  
PAUL D. FLEMING ◽  
MASAHIRO SUGIHARA
Keyword(s):  
Boundary Layer ◽  
Experimental Design ◽  
High Speed ◽  
Statistical Study ◽  
Process Variables ◽  
High Speeds ◽  
The Stability ◽  
Air Removal ◽  
Removal System

Using an experimental design approach, researchers altered process parameters and material prop-erties to stabilize the curtain of a pilot curtain coater at high speeds. Part I of this paper identifies the four significant variables that influence curtain stability. The boundary layer air removal system was critical to the stability of the curtain and base sheet roughness was found to be very important. A shear thinning coating rheology and higher curtain heights improved the curtain stability at high speeds. The sizing of the base sheet affected coverage and cur-tain stability because of its effect on base sheet wettability. The role of surfactant was inconclusive. Part II of this paper will report on further optimization of curtain stability with these four variables using a D-optimal partial-facto-rial design.

Automatic control of laminar boundary-layer transition

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 85-90
Author(s):  
P. A. Nelson ◽  
M. C. M. Wright ◽  
J.-L. Rioual
Keyword(s):  
Boundary Layer ◽  
Automatic Control ◽  
Laminar Boundary Layer ◽  
Boundary Layer Transition ◽  
Layer Transition
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