Skin friction drag

Skin friction drag is a component of profile drag that acts on a body in a fluid flow. "Skin friction drag" applies not only to the "skins" of an aircraft but also to flow of fluids within and about any body subjected to a fluid flow. Friction drag begins as laminar drag but may become turbulent drag at some point along the body in the fluid flow direction. Skin friction drag is calculated or measured and is additive with other forms of drag acting on a body.

Flow and effect on skin friction drag

Laminar flow over a body occurs when layers of the fluid move smoothly past each other in parallel lines. In nature, this kind of flow is rare. As the fluid flows over an object, it applies frictional forces to the surface of the object which works to impede forward movement of the object; the result is called skin friction drag. Skin friction drag is often the major component of parasitic drag on objects in a flow.

The flow over a body may begin as laminar. As a fluid flows over a surface shear stresses within the fluid slow additional fluid particles causing the boundary layer to grow in thickness. At some point along the flow direction, the flow becomes unstable and becomes turbulent. Turbulent flow has a fluctuating and irregular pattern of flow which are made obvious by the formation of vortices. While the turbulent layer grows, the laminar layer thickness decreases. This results in a thinner laminar boundary layer which, relative to laminar flow, depreciates the magnitude of friction force as fluid flows over the object.

Calculation

Fluid flow is characterized by the dimensionless Reynolds number, and hence skin friction drag, either laminar or turbulent. Reynolds number (Re) is the ratio of the inertial forces to the viscous forces acting on a fluid, in other words the frictional shearing forces attempt to move the fluid and the inertial mass resists that force. Reynolds number is calculated:

Re={\frac {\rho {v}{L}}{\mu }}

\mathrm {Re} ={\frac {{v}{L}}{\nu }}\

where:

${\rho }$ is the fluid mass density
${v}$ is the fluid speed far from the body's surface (undisturbed flow)
${L}$ is a characteristic dimension, pipe diameter, chord length of a wing etc.
${\mu }$ is a fluid viscosity
${\nu }$ is the kinematic viscosity of the fluid

Laminar flow

C_{{f}}={\frac {1.328}{{\sqrt {{\mathrm {Re}}}}}}\

, Also known as the Blasius Friction law^[1]

The coefficient may be calculated at any point "x" along the body by replacing ‘L’ in the Reynolds number equation with the distance "x" from the leading edge giving ( ${\mathrm {Re}}_{x}$ ). Then use the following equation:

C_{fx}={\frac {0.664}{\sqrt {\mathrm {Re} _{x}}}}\

Turbulent flow

C_{f}={\frac {0.455}{log(\mathrm {Re} )^{2.58}}}\

Also known as the Schlichting empirical formula

Drag

The total skin friction drag force acting on a body, in units of force can be calculated:

F=C_{f}{\frac {\rho _{f}v^{2}}{2}}\ S_{wetted}

where ${\rho _{f}}$ is the fluid density, ${v}$ is the fluid velocity and ${S_{wetted}}$ is the total surface area that is in contact with the fluid.

References

↑ Streeter, Victor; Wylie, E. Benjamin (1975). Fluid Mechanics (6 ed.). McGraw-Hill. p. 274. ISBN 0-07-062193-4.

Fundamentals of Flight by Richard Shepard Shevell

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