# Boundary Layer Concept

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# Why boundary layer is important?

The main duty of a design engineer in all disciplines is to increase the efficiency of a product and decrease its energy consumption. One of the most important parameter which defines the efficiency of the air vehicles in aviation industry is the drag force. Decrement of drag force of aircrafts directly contribute to their range, velocity and fuel consumption. Drag, beside of one portion due to lift, is strongly influenced by the growth of boundary layer over aircraft surface. Boundary layer growth is important also for the maneuvers of aircrafts at high angles of attack.

One of the most important part of aircraft design is the design of lifting surfaces, which requires knowledge on the performance of cross sections of wing. Each of these cross sections are called . Therefore, boundary layer growth over airfoils must be systematically studied from general aspects.

Wing Sections

Main influence of boundary layer growth over an airfoil is owing to its tendency for separation and transition to turbulence. These have a considerable effect on aircraft flight performance and are the most important criteria for all aerospace engineering applications in aerodynamics domain.

## What is Prandtl’s Boundary Layer Theory?

Boundary layer is a concept first introduced by Ludwig Prandtl in 1904. According to Prandtl, flow around a geometry can be considered as two different flow regions: one where the viscous effects dominate close to surface, boundary layer, and the region outside boundary layer. Outside the boundary layer is assumed to be inviscid. In flows with high Reynolds number, at the order of millions or more, and when the boundary layer is relatively thin, there is weak or no interaction between the two flow regions, which simplifies analysis significantly.

Boundary Layer Thickness and Velocity Profile

The boundary layer is the region close to an object where fluid particles are decelerated. Fluid particle velocity is zero at the surface and progressively increases normal to the surface, ultimately matching the freestream velocity. Boundary layer consists of fluid particles whose velocity is less than 99% of the freestream velocity.

Illustration of Velocity Profile of Fluid Particles (Left) and Intermolecular/Surface Collisions of Fluid Molecules

### Why Do We Have Boundary Layer : Reflection from molecular scale to viscosity?

The deceleration is due to shear forces between different layers of fluid near the surface which is the effect of viscosity. Viscosity appears due to the interactions at molecular scale. The interaction is molecular collisions which result in momentum transfer between molecules. These interactions are modelled by a viscosity coefficient in continuum approach as the atmosphere is considered as a continuum. In that approach, fluid particles at the surface are assumed to have the same velocity with the surface. This is called no-velocity-jump boundary condition on solid-fluid interface. When the of no slip boundary condition is diffused throughout the fluid particles, this deceleration effect decays normal to surface, and therefore, there is a region of decelerated fluid particles with finite thickness near surface.

Formation of boundary layer at aircraft surfaces is mainly controlled by Reynolds number and pressure distribution around the geometry. This two factors have an influence over the boundary layer growth as they control the tendecy of laminar boundary layer to turn into turbulent state and to seperate. For more information on boundary layer concept with its stability and separation, please follow my articles.

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I am an aerospace engineer specializing on aerodynamics. My aim is to introduce the basic concepts of aerodynamics to aviation enthusiasts as simple as possible.

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