The boundary layer is a zone of interface between a body and the surrounding Fluide at the time of a relative movement between the two. One observes there the effects of the Viscosité. It is an important component in Mécanique fluids, (Aérodynamique, Hydrodynamique), in Météorologie, Océanographie, etc

Summary description of the boundary layer

When a real fluid runs out along a presumedly fixed wall, speeds on the wall are null and ad infinitum, far from the obstacle, they are equal to the rate of the nondisturbed flow. On a normal with the wall speed must thus in all the cases vary between 0 and one maximum. The law of variation depends on the viscosity of the fluid which induces a friction between the close layers: the slowest layer tends to slow down the fastest layer which, in return, tends to accelerate it.

Under these conditions, a strong viscosity equalizes to the maximum speeds. On the contrary, if the fluid is not very viscous, the various layers are much more independent: speed ad infinitum is maintained until a short distance of the obstacle and there is a stronger variation speeds in the small thickness of boundary layer. In the first case, it is necessary to use the general equations of the viscous fluid. In the second, one can use in the boundary layer of the simplified equations supplemented by experimental results. The equations, also simpler, of the true fluid applied beyond the wall “fattened” by the boundary layer provide the boundary conditions for calculation.

In fact, it is not viscosity itself which intervenes. As always in Mechanical of the fluids, it is a Nombre without dimension which characterizes the phenomenon: the Reynolds number. This one described the report/ratio of the forces related to speed with the forces of friction. Thus, instead of increasing viscosity, one can obtain a similar phenomenon by decreasing the speed or dimensions of the obstacle.

Short outline of theory

The definition even of the boundary layer lies in the fact that it represents the area of the flow where the viscous effects are as important as the inertial effects (in terms of order of magnitude). It is indeed not the case far from the wall, where the flow is then known as " of Euler" , and where the viscous effects are practically not made feel. A true fluid is by definition not driver and has its Coefficients of Lamé no one (IE. no viscosity).

One in general defines the thickness of boundary layer such as: $u\; (\backslash \; Delta\; (X))=0.99\backslash cdot\; U\_e~$

with:

• $U\_e~$, the uniform speed of the flow without obstacle
• $\backslash \; Delta\; (X)\; ~$, the thickness of boundary layer according to X.

The profile speed within the boundary layer is moreover Hyperbolique.

Scopes of application

Aeronautics

Aerodynamics

The boundary layer plays an important role in the performances of an airfoil: for example, the limiting separation of layers on a wing of plane causes a fall of the Portance and an increase in the Traînée of the wing, which corresponds to a notable fall of the aerodynamic performances of the plane. The limiting separation of layers occurs when the angle of Incidence of the wing becomes too important, which practically corresponds to a pulled up plate of the plane (with the landing for example). If this angle is too important, it occurs the phenomenon of Décrochage: the boundary layer is strongly separated and the bearing pressure can fall in a very important way, more or less brutally. This phenomenon is in the beginning many plane crashes, the loss of bearing pressure being able to involve the loss of control of the apparatus.

On certain planes one finds small blades, placed either on the wings or with the back of the fuselage, which make it possible to produce a turbulent boundary layer which resists separation. These blades are called " generators of tourbillons" (vortex generator in English).

Undesirable effects

The boundary layer can seriously disturb the operation of a Reaction engine , on the one hand because of turbulences in the flow of air introduced by the engine, and on the other hand by reducing its effectiveness because low air velocity to the level of the layer. This problem does not arise when the air intake is frontal (in the nose of the plane) or that the engine is contained in a nacelle fixed under the wings (case of the great majority of the civil aircrafts).

On the other hand, when the air intake is located along the fuselage (case of the military aircrafts especially), it is generally slightly isolated of this one to be placed out of the boundary layer. A metal plate is sometimes added right before the air intake to maintain the boundary layer against the fuselage: one speaks then about " trap with limite" layer;.

Meteorology

In meteorology, one calls planetary boundary layer the zone of the atmosphere between surface (ground or sea), where the friction slows down the air volume displacement, and free atmosphere where the latter becomes negligible. It varies between 0,5 and 3 km thickness according to the stability of the air and the roughness of surface. It is on average of 1.500 meters. The theoretical study of this section of atmosphere divides in fact the planetary boundary layer as the superposition of two layers of which the thicknesses are very unequal:

• the layer of Ekman (according to the name of the Swedish physicist Vagn Walfrid Ekman) in which wind is caused by a balance between the Gradient of Pression, the Force of Coriolis, had with the daily rotation of the Ground, and a portion of the friction decreasing gradually until the free atmosphere. Speed and the direction at the top of this layer are roughly that of the Vent geostrophic whereas it decreases gradually and turns towards the lowest pressure as one descends towards the ground
• the surfacing or boundary layer from atmospheric turbulence immediately in contact with the ground and of which the thickness does not exceed the tenth of that of the whole of the boundary layer. The air velocity is caused there by the convection which had with the differences of Température S and by the dynamic effects of the Relief S. flow is there turbulent. One also speaks about a rough underlayer very close to the surface, which varies few centimetres with a few tens of meters according to aspéritées of the relief. Speed tends there towards zero.

The exchanges of matter, energy and movement occurring within the planetary boundary layer are paramount into meterologic. One finds there the majority of the elements with Méso-scale which leads to the release of the major Convection and a good part of the elements which lead to the systems with the synoptic scale. The parameterization of the boundary layer is thus paramount in the development of the models of numerical Prévision of time.

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