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Encyclopedia > Boundary layer

In physics and fluid mechanics, a boundary layer is that layer of fluid in the immediate vicinity of a bounding surface. In the Earth's atmosphere the planetary 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 Reynolds number. Physics (Greek: (phÃºsis), nature and (phusikÃ©), knowledge of nature) is the science concerned with the discovery and characterization of universal laws which govern matter, energy, space, and time. ... Fluid mechanics is the subdiscipline of continuum mechanics that studies fluids, that is, liquids and gases. ... A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ... Layers of Atmosphere - not to scale (NOAA)[3] Earths atmosphere is a layer of gases surrounding the planet Earth and retained by the Earths gravity. ... The planetary boundary layer (PBL) is also known as the atmospheric boundary layer (ABL). ... Look up aircraft in Wiktionary, the free dictionary. ... A Laughing Gull with its wings extended in a gull wing profile Aircraft wing planform shapes: a swept wing KC-10 Extender (top) refuels a trapezoid-wing F/A-22 Raptor A wing is a surface used to produce lift and therefore flight, for travel in the air or another... flOw is a Flash game created by Jenova Chen and Nicholas Clark. ... A pattern is a form, template, or model (or, more abstractly, a set of rules) which can be used to make or to generate things or parts of a thing, especially if the things that are generated have enough in common for the underlying pattern to be inferred or discerned... Viscosity is a measure of the resistance of a fluid to deform under shear stress. ... In physics, force is an influence that may cause an object to accelerate. ... In fluid mechanics, the Reynolds number is the ratio of inertial forces (vsÏ) to viscous forces (Î¼/L) and consequently it quantifies the relative importance of these two types of forces for given flow conditions. ...

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. Thermal boundary layers also exist in heat transfer. Multiple types of boundary layers can coexist near to a surface simultaneously. A Blasius boundary layer describes the steady two-dimensional boundary layer that forms on a semi-infinite plate which is held parallel to a constant unidirectional flow . ... Several equivalence relations in mathematics are called similarity. ... In standard boundary-layer theory, the effects of viscous diffusion are usually balanced by convective inertia. ...

## Contents

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. This article does not cite any references or sources. ... Ludwig Prandtl (4 February 1875 - 15 August 1953) was a German physicist. ... Map of Germany showing Heidelberg Heidelberg (halfway between Stuttgart and Frankfurt) is a city in Baden-Württemberg, Germany. ... Viscosity is a measure of the resistance of a fluid to deform under shear stress. ... An object falling through a gas or liquid experiences a force in direction opposite to its motion. ... The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations which describe the motion of fluid substances such as liquids and gases. ... In physics, heat, symbolized by Q, is defined as transfer of thermal energy [1] Generally, heat is a form of energy transfer associated with the different motions of atoms, molecules and other particles that comprise matter when it is hot and when it is cold. ...

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 fluid dynamics, the no-slip condition states that fluids stick to surfaces past which they flow. ... The Prandtl Number is a dimensionless number approximating the ratio of momentum diffusivity and thermal diffusivity. ...

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. Gliders are un-powered heavier-than-air aircraft. ... Displacement thickness is distance by which a surface would have to be moved parallel to itself towards the reference plane in an ideal fluid stream of velocity to give the same volumetric flow as occurs between the surface and the reference plane in a real fluid. ... In physics and mechanics, shear refers to a deformation that causes parallel surfaces to slide past one another (as opposed to compression and tension, which cause parallel surfaces to move towards or away from one another). ... In Aerodynamics, skin friction is the component of parasitic drag arising from the friction of the fluid against the skin of the object that is moving through it. ...

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 (see Boundary layer suction). This can result in a reduction in drag, but is usually impractical due to the mechanical complexity involved. In fluid mechanics, the Reynolds number is the ratio of inertial forces (vsÏ) to viscous forces (Î¼/L) and consequently it quantifies the relative importance of these two types of forces for given flow conditions. ... laminar and turbulent water flow over the hull of a submarine In fluid dynamics, laminar flow is a flow regime characterized by high momentum diffusion, low momentum convection, and pressure and velocity independence from time. ... Turbulent flow around an obstacle; the flow further away is laminar Laminar and turbulent water flow over the hull of a submarine Turbulence creating a vortex on an airplane wing In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by low-momentum diffusion, high momentum convection, and... The process of a laminar boundary layer becoming turbulent is known as boundary layer transition. ... A pore, in general, is some form of opening, usually very small. ... Boundary layer suction is technique in which an air pump is used to extract the boundary layer at the wing of an aircraft. ...

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 will tend 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. This is the principle behind the dimpling on golf balls, as well as vortex generators on light aircraft. 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. In fluid mechanics, the Reynolds number is the ratio of inertial forces (vsÏ) to viscous forces (Î¼/L) and consequently it quantifies the relative importance of these two types of forces for given flow conditions. ... An adverse pressure gradient occurs when the static pressure increases in the direction of the flow. ... Airflow separating from a wing which is at a high angle of attack All solid objects travelling through a fluid (or alternatively a stationary object exposed to a moving fluid) acquire a boundary layer of fluid around them where friction between the fluid molecules and the objects rough surface... Parasitic drag (also called parasite drag) is drag caused by moving a solid object through a fluid. ... A turbulator is a device for improving the flow of air over a wing. ... 1967 Model Cessna 182K in flight showing after-market vortex generators on the wing leading edge A vortex generator is an aerodynamic surface, basically a small vane, that creates a vortex. ...

## Boundary layer equations

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 are given by The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations which describe the motion of fluid substances such as liquids and gases. ... Viscosity is a measure of the resistance of a fluid to deformation under shear stress. ... A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ... flOw is a Flash game created by Jenova Chen and Nicholas Clark. ... In linear algebra, the characteristic equation of a square matrix A is the equation in one variable &#955; where I is the identity matrix. ... In mathematics, a partial differential equation (PDE) is a relation involving an unknown function of several independent variables and its partial derivatives with respect to those variables. ... In mathematics, a partial differential equation (PDE) is a relation involving an unknown function of several independent variables and its partial derivatives with respect to those variables. ... In mathematics, an incompressible surface is a kind of two-dimensional surface inside of a 3-manifold. ...

${partial uoverpartial x}+{partial voverpartial y}=0$
$u{partial u over partial x}+v{partial u over partial y}=-{1over rho} {partial p over partial x}+{nu}({partial^2 uover partial x^2}+{partial^2 uover partial y^2})$
$u{partial v over partial x}+v{partial v over partial y}=-{1over rho} {partial p over partial y}+{nu}({partial^2 vover partial x^2}+{partial^2 vover partial y^2})$

where u and v are the velocity components, ρ is the density, p is the pressure, and ν is the kinematic viscosity of the fluid at a point. Viscosity is a measure of the resistance of a fluid to deformation under shear stress. ...

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 to become In fluid mechanics, the Reynolds number is the ratio of inertial forces (vsÏ) to viscous forces (Î¼/L) and consequently it quantifies the relative importance of these two types of forces for given flow conditions. ... In mathematics and applications, particularly the analysis of algorithms, asymptotic analysis is a method of classifying limiting behaviour, by concentrating on some trend. ...

${partial uoverpartial x}+{partial voverpartial y}=0$
$u{partial u over partial x}+v{partial u over partial y}=-{1over rho} {partial p over partial x}+{nu}{partial^2 uover partial y^2}$

and the remarkable result that

${1over rho} {partial p over partial y}=0$

The asymptotic analysis also shows that v, the wall normal velocity, is small compared with u the streamwise velocity, and that variations in properties in the streamwise direction are generally much lower than those in the wall normal direction.

Since the static pressure p is independent of y, then pressure at the edge of the boundary layer is the pressure throughout the boundary layer at a given streamwise position. The external pressure may be obtained through an application of Bernoulli's Equation. Let u0 be the fluid velocity outside the boundary layer, where u and u0 are both parallel. This gives upon substituting for p the following result In fluid dynamics, Bernoullis equation, derived by Daniel Bernoulli, describes the behavior of a fluid moving along a streamline. ...

$u{partial u over partial x}+v{partial u over partial y}=u_0{partial u_0 over partial x}+{nu}{partial^2 uover partial y^2}$

with the boundary condition

${partial uoverpartial x}+{partial voverpartial y}=0$

For a flow in which the static pressure p also does not change in the direction of the flow then

${partial poverpartial x}=0$

so u0 remains constant.

Therefore, the equation of motion simplifies to become

$u{partial u over partial x}+v{partial u over partial y}={nu}{partial^2 uover partial y^2}$

These approximations are used in a variety of practical flow problems 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. laminar and turbulent water flow over the hull of a submarine In fluid dynamics, laminar flow is a flow regime characterized by high momentum diffusion, low momentum convection, and pressure and velocity independence from time. ... Turbulent flow around an obstacle; the flow further away is laminar Laminar and turbulent water flow over the hull of a submarine Turbulence creating a vortex on an airplane wing In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by low-momentum diffusion, high momentum convection, and... In statistics, mean has two related meanings: Look up mean in Wiktionary, the free dictionary. ...

## Turbulent boundary layers

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. Applying this technique to the boundary layer equations give the full turbulent boundary layer equations not often given in literature, viz. In fluid dynamics and turbulence, Reynolds decomposition is a mathematical technique to separate the average and fluctuating parts of a quantity. ...

${partial overline{u}overpartial x}+{partial overline{v}overpartial y}=0$
$overline{u}{partial overline{u} over partial x}+overline{v}{partial overline{u} over partial y}=-{1over rho} {partial overline{p} over partial x}+{nu}({partial^2 overline{u}over partial x^2}+{partial^2 overline{u}over partial y^2})-frac{partial}{partial y}(overline{u'v'})-frac{partial}{partial x}(overline{u'^2})$
$overline{u}{partial overline{v} over partial x}+overline{v}{partial overline{v} over partial y}=-{1over rho} {partial overline{p} over partial y}+{nu}({partial^2 overline{v}over partial x^2}+{partial^2 overline{v}over partial y^2})-frac{partial}{partial x}(overline{u'v'})-frac{partial}{partial y}(overline{v'^2})$

Using the same order-of-magnitude analysis as for the instantaneous equations, these turbulent boundary layer equations generally reduce to become in their classical form:

${partial overline{u}overpartial x}+{partial overline{v}overpartial y}=0$
$overline{u}{partial overline{u} over partial x}+overline{v}{partial overline{u} over partial y}=-{1over rho} {partial overline{p} over partial x}+{nu}{partial^2 overline{u}over partial y^2}-frac{partial}{partial y}(overline{u'v'})$
${partial overline{p} over partial y}=0$

The additional term $overline{u'v'}$ 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. The terms a priori and a posteriori are used in philosophy to distinguish between two different types of propositional knowledge. ... Turbulence modeling is the area of physical modeling where a simpler mathematical model than the full time dependent Navier-Stokes Equations is used to predict of the effects of turbulence. ...

## Boundary layer turbine

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). The Tesla turbine is a bladeless turbine design patented by Nikola Tesla in 1913. ... Nikola Tesla (1856-1943)[1] was a world-renowned Serbian inventor, physicist, mechanical engineer and electrical engineer. ... A Siemens steam turbine with the case opened. ... Ludwig Prandtl (4 February 1875 - 15 August 1953) was a German physicist. ...

Boundary layer suction is technique in which an air pump is used to extract the boundary layer at the wing of an aircraft. ...

Results from FactBites:

 Boundary Layer (785 words) The details of the flow within the boundary layer are very important for many problems in aerodynamics, including wing stall, the skin friction drag on an object, and the heat transfer that occurs in high speed flight. For lower Reynolds numbers, the boundary layer is laminar and the streamwise velocity changes uniformly as one moves away from the wall, as shown on the left side of the figure. The effects of the boundary layer on lift are contained in the lift coefficient and the effects on drag are contained in the drag coefficient.
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