Boundary—Layer Equations in Plane Flow; Plate Boundary Layer

2000 ◽  
pp. 145-164 ◽  
Author(s):  
Herrmann Schlichting ◽  
Klaus Gersten
Keyword(s):  
Boundary Layer ◽  
Plate Boundary ◽  
Plane Flow ◽  
Boundary Layer Equations

Boundary–Layer Equations in Plane Flow; Plate Boundary Layer

2016 ◽  
pp. 145-164
Author(s):  
Hermann Schlichting ◽  
Klaus Gersten
Keyword(s):  
Boundary Layer ◽  
Plate Boundary ◽  
Plane Flow ◽  
Boundary Layer Equations

Laminar Supersonic Boundary Layer Of The Binary Gas Mixture

2016 ◽  
Vol 11 (1) ◽  
pp. 5-15
Author(s):  
Sergey Gaponov ◽  
Boris Smorodsky
Keyword(s):  
Boundary Layer ◽  
Gas Injection ◽  
Plate Boundary ◽  
Supersonic Boundary Layer ◽  
Model Surface ◽  
Transfer Coefficients ◽  
Molecular Weights ◽  
Boundary Layer Equations ◽  
Binary Gas Mixture ◽  
Heavy Gas

Theoretical investigation of the properties of a compressible binary-mixture boundary-layer in the framework of local self-similar boundary-layer equations. We have considered the problem, when the foreign gas of various molecular weights – lighter and heavier than air – has been injected into the flat-plate boundary-layer through the permeable model surface. Computations of the binarymixture velocity, density and temperature profiles as well as foreign gas concentration in such boundary layers at different Mach numbers have been performed. It has been found that increase of a foreign gas injection leads to a monotonous decrease of the skin friction and heat transfer coefficients. It has been established that at free stream Mach number M‹2 action of a heavy gas injection from the model surface into the boundary layer is similar to the action of the model cooling. This injection increases the density of the mixture near the wall. As a result, the profiles of the supersonic boundary layer are modified in such a way that the boundary-layer linear stability should be increased with injection of a foreign gas with high molecular weight. This in turn should lead to a shift in position of the laminar-turbulent transition downstream.

Singularities encountered in three-dimensional boundary layers under an adverse or favourable pressure gradient

1995 ◽  
Vol 352 (1698) ◽  
pp. 45-87 ◽  
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Three Dimensional ◽  
Symmetry Plane ◽  
Plane Flow ◽  
Boundary Layer Equations ◽  
Dimensional Boundary

Singularities in solutions of the classical boundary-layer equations are considered, numerically and analytically, in an example of steady hypersonic flow along a flat plate with three-dimensional surface roughness. First, a wide parametric study of the breakdown of symmetry-plane flow is performed for two particular cases of the surface geometry. Emphasis is put on the structural stability of the singularities’ development to local/global variation of the pressure distribution. It is found that, as usual, the solution behaviour under an adverse pressure gradient involves the Goldstein- or marginal-type singularity at a point of zero streamwise skin friction. As the main alternative, typical of configurations with favourable or zero pressure forcing, an inviscid breakdown in the middle of the flow is identified. Similarly to unsteady flows, the main features of the novel singularity include infinitely growing boundary-layer thickness and finite limiting values of the skin-friction components. Subsequent analytical extensions of the singular symmetry-plane solution then suggest two different scenarios for the global boundary-layer behaviour: one implies inviscid breakdown of the flow at some singular line, the other describes the development of a boundary-layer collision at a downstream portion of the symmetry plane. In contrast with previous studies of the collision phenomenon in steady flows, the present theory suggests logarithmic growth of boundary-layer thickness on both sides of the discontinuity. Finally, an example of numerical solution of the full three dimensional boundary layer equations is given. The flow régime chosen corresponds to inviscid breakdown of a centreplane flow under a favourable pressure gradient and development of the discontinuity/collision downstream. The numerical results near the origin of the discontinuity are found to be supportive, producing quantitative agreement with the local analytical description.

Numerical studies of the hypersonic strong interaction boundary-layer equations

AIAA Journal ◽  
1971 ◽  
Vol 9 (10) ◽  
pp. 2058-2060 ◽  
Author(s):  
M. J. WERLE ◽  
S. F. WORNOM
Keyword(s):  
Boundary Layer ◽  
Strong Interaction ◽  
Boundary Layer Equations ◽  
Numerical Studies
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