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In physics and fluid mechanics, the boundary layer effect is produced by a layer of fluid in the immediate vicinity of a bounding surface. In the atmosphere the boundary layer is the air layer near the ground affected by diurnal heat, moisture or momentum transfer to or from the surface. On an aircraft wing the boundary layer is the part of the flow close to the wing. The Boundary layer effect occurs at the field region in which all changes occur in the flow pattern. The boundary layer distorts surrounding nonviscous flow. It is a phenomenon of viscous forces. This effect is related to the Leidenfrost effect and the Reynolds number.

Laminar boundary layers come in various forms and can be loosely classified according to their structure and the circumstances under which they are created. The thin shear layer which develops on an oscillating body is an example of a Stokes layer, whilst the Blasius boundary layer refers to the well-known similarity solution for the steady boundary layer attached to a flat plate held in an oncoming unidirectional flow. When a fluid rotates, viscous forces may be balanced by Coriolis effects, rather than convective inertia, leading to the formation of an Eckman layer.

The aerodynamic boundary layer was first defined by Ludwig Prandtl in a paper presented at the third Congress of Mathematicians in Heidelberg, Germany. It allows aerodynamicists to simplify the equations of fluid flow by dividing the flow field into two areas: one inside the boundary layer, where viscosity is dominant and the majority of the drag experienced by a body immersed in a fluid is created, and one outside the boundary layer where viscosity can be neglected without significant effects on the solution. This allows a closed-form solution for the flow in both areas, which is a significant simplification over the solution of the full Navier-Stokes equations. The majority of the heat transfer to and from a body also takes place within the boundary layer, again allowing the equations to be simplified in the flow field outside the boundary layer.

The thickness of the velocity boundary layer is normally defined as the distance from the solid body at which the flow velocity is 99% of the freestream velocity, that is, the velocity that is calculated at the surface of the body in an inviscid flow solution. The no-slip condition requires that the flow velocity at the surface of a solid object is zero and that the fluid temperature is equal to the temperature of the surface. The flow velocity will then increase rapidly within the boundary layer, governed by the boundary layer equations, below. The thermal boundary layer thickness is similarly the distance from the body at which the temperature is 99% of the temperature found from an inviscid solution. The ratio of the two thicknesses is governed by the Prandtl number. If the Prandtl number is 1, the two boundary layers are the same thickness. If the Prandtl number is greater than 1, the thermal boundary layer is thinner than the velocity boundary layer. If the Prandtl number is less than 1, which is the case for air at standard conditions, the thermal boundary layer is thicker than the velocity boundary layer.

In high-performance designs, such as sailplanes and commercial transport aircraft, much attention is paid to controlling the behavior of the boundary layer to minimize drag. Two effects must to be considered. First, the boundary layer adds to the effective thickness of the body, through the displacement thickness, hence increasing the pressure drag. Secondly, the shear forces at the surface of the wing create skin friction drag.

At high Reynolds numbers, typical of full-sized aircraft, it is desirable to have a laminar boundary layer. This results in a lower skin friction due to the characteristic velocity profile of laminar flow. However, the boundary layer inevitably thickens and becomes less stable as the flow develops along the body, and eventually becomes turbulent, the process known as boundary layer transition. One way of dealing with this problem is to suck the boundary layer away through a porous surface. This can result in a reduction in drag, but is usually impractical due to the mechanical complexity involved.

At lower Reynolds numbers, such as those seen with model aircraft, it is relatively easy to maintain laminar flow. This gives low skin-friction, which is desirable. However, the same velocity profile which gives the laminar boundary layer its low skin friction also causes it to be badly affected by adverse pressure gradients. As the pressure begins to recover over the rear part of the wing chord, a laminar boundary layer tends to separate from the surface. Such separation causes a large increase in the pressure drag, since it greatly increases the effective size of the wing section. In these cases, it can be advantageous to deliberately trip the boundary layer into turbulence at a point prior to the location of laminar separation, using a turbulator. The fuller velocity profile of the turbulent boundary layer allows it to sustain the adverse pressure gradient without separating. Thus, although the skin friction is increased, overall the drag is decreased. Special wing sections have also been designed which tailor the pressure recovery so that laminar separation is reduced or even eliminated. This represents an optimum compromise between the pressure drag from flow separation and skin friction the induced turbulence.

The deduction of the boundary layer equations was perhaps one of the most important advances in aerodynamics. Using an order of magnitude analysis, the well-known governing Navier-Stokes equations of viscous fluid flow can be greatly simplified within the boundary layer. Notably, the characteristic of the partial differential equations (PDE) becomes parabolic, rather than the elliptical form of the full Navier-Stokes equations. This greatly simplifies the solution of the equations. By making the boundary layer approximation, the flow is divided into an inviscid portion (which is easy to solve by a number of methods) and the boundary layer, which is governed by an easier to solve PDE. The Navier-Stokes equations for a two-dimensional steady incompressible flow in cartesian coordinates.

The approximation states that, for a sufficiently high Reynolds number the flow over a surface can be divided into an outer region of inviscid flow unaffected by viscosity (the majority of the flow), and a region close to the surface where viscosity is important (the boundary layer). Let u and v be streamwise and transverse (wall normal) velocities respectively inside the boundary layer. Using asymptotic analysis, it can be shown that the above equations of motion reduce within the boundary layer. The asymptotic analysis also shows that the wall normal velocity is small compared with the streamwise velocity and that variations in properties in the streamwise direction are generally much lower than those in the wall normal direction.

The practical flow problems are of scientific and engineering interest. The above analysis is for any instantaneous laminar or turbulent boundary layer, but are used mainly in laminar flow studies since the mean flow is also the instantaneous flow because there are no velocity fluctuations present.

The treatment of turbulent boundary layers is far more difficult due to the time-dependent variation of the flow properties. One of the most widely used techniques in which turbulent flows are tackled is to apply Reynolds decomposition. Here the instantaneous flow properties are decomposed into a mean and fluctuating component.

An important factor in the turbulent boundary layer equations is known as the Reynolds shear stress and is unknown a priori. The solution of the turbulent boundary layer equations therefore necessitate the use of a turbulence model, which aims to express the Reynolds shear stress in terms of known flow variables or derivatives. The lack of accuracy and generality of such models is the single major obstacle which inhibits the successful prediction of turbulent flow properties in modern aerodynamics.

Boundary layer suction is technique in which an air pump is used to extract the boundary layer at the wing of an aircraft. Improving the air flow can reduce drag. Improvements in fuel efficiency have been estimated as high as 30%. The air molecules at the surface of a wing are effectively stationary. If the flow is smooth, known as laminar flow, the velocity of the air increases steadily as measurements are taken further away from the surface. However the smooth flow is often disturbed by the boundary layer breaking away from the surface and creating a low pressure region immediately behind the airfoil. This low pressure region results in increased overall drag. Attempts have been made over the years to delay the onset of this flow separation by careful design and smooth surfaces.

As flow separation results from the velocity deficit that is characteristic of boundary layers, suction attempts to remove the boundary layer from the surface before it can separate. The technology was first developed by Werner Pfenninger in the Second World War and has been researched almost continuously since. In the 1990s tests were done by NASA with a F16XL. Loek Boermans is researching the technology for use in gliders at the Technical University of Delft. However about 500 watts of power would be needed to drive the pumps and this would mean covering the glider with solar panels. This would increase the cost greatly

This effect was exploited in the Tesla turbine, patented by Nikola Tesla in 1913. It is referred to as a bladeless turbine because it uses the boundary layer effect and not a fluid impinging upon the blades as in a conventional turbine. Boundary layer turbines are also known as cohesion-type turbines, bladeless turbine, and Prandtl layer turbine (after Ludwig Prandtl).

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Journals

A.D. Polyanin and V.F. Zaitsev, Handbook of Nonlinear Partial Differential Equations, Chapman & Hall/CRC Press, Boca Raton - London, 2004. ISBN 1-58488-355-3

A.D. Polyanin, A.M. Kutepov, A.V. Vyazmin, and D.A. Kazenin, Hydrodynamics, Mass and Heat Transfer in Chemical Engineering, Taylor & Francis, London, 2002. ISBN 0-415-27237-8

Herrmann Schlichting, Klaus Gersten, E. Krause, H. Jr. Oertel, C. Mayes "Boundary-Layer Theory" 8th edition Springer 2004 ISBN 3540662707

John D. Anderson, Jr, "Ludwig Prandtl's Boundary Layer", Physics Today, December 2005

Anderson, John (1991). Fundamentals of Aerodynamics, 2nd edition, Toronto: McGraw-Hill. ISBN 0-07-001679-8, 711-714.

Websites

National Science Digital Library - Boundary Layer

Moore, Franklin K., "Displacement effect of a three-dimensional boundary layer". NACA Report 1124, 1953.

Benson, Tom, "Boundary layer". NASA Glenn Learning Technologies.

Boundary layer equations: Exact Solutions - from EqWorld

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