Stagnation point

Photo showing stagnation point and attached vortex at an un-faired wing-root to fuselage junction on a Schempp-Hirth Janus C glider

In fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is zero.[1]: § 3.2  The Bernoulli equation shows that the static pressure is highest when the velocity is zero and hence static pressure is at its maximum value at stagnation points: in this case static pressure equals stagnation pressure.[2][1]: § 3.5 

The Bernoulli equation applicable to incompressible flow shows that the stagnation pressure is equal to the dynamic pressure and static pressure combined.[1]: § 3.5  In compressible flows, stagnation pressure is also equal to total pressure as well, provided that the fluid entering the stagnation point is brought to rest isentropically.[1]: § 3.12 

A plentiful, albeit surprising, example of such points seem to appear in all but the most extreme cases of fluid dynamics in the form of the "no-slip condition" - the assumption that any portion of a flow field lying along some boundary consists of nothing but stagnation points (the question as to whether this assumption reflects reality or is simply a mathematical convenience has been a continuous subject of debate since the principle was first established).

Pressure coefficient

This information can be used to show that the pressure coefficient ${\displaystyle C_{p}}$ at a stagnation point is unity (positive one):[1]: § 3.6 

${\displaystyle C_{p}={p-p_{\infty } \over q_{\infty }}}$

where:

${\displaystyle C_{p}}$ is pressure coefficient

${\displaystyle p}$ is static pressure at the point at which pressure coefficient is being evaluated

${\displaystyle p_{\infty }}$ is static pressure at points remote from the body (freestream static pressure)

${\displaystyle q_{\infty }}$ is dynamic pressure at points remote from the body (freestream dynamic pressure)

Stagnation pressure minus freestream static pressure is equal to freestream dynamic pressure; therefore the pressure coefficient ${\displaystyle C_{p}}$ at stagnation points is +1.[1]: § 3.6 

Kutta condition

On a streamlined body fully immersed in a potential flow, there are two stagnation points—one near the leading edge and one near the trailing edge. On a body with a sharp point such as the trailing edge of a wing, the Kutta condition specifies that a stagnation point is located at that point.[3] The streamline at a stagnation point is perpendicular to the surface of the body.

See also

• Stagnation point flow

Notes

1. Clancy, L.J. (1975), Aerodynamics, Pitman Publishing Limited, London. ISBN 0-273-01120-0
2. Fox, R. W.; McDonald, A. T. (2003). Introduction to Fluid Mechanics (4th ed.). Wiley. ISBN 0-471-20231-2.
3. Anderson, John D. (1984) Fundamentals of Aerodynamics, section 4.5 McGraw-Hill Inc. ISBN 0-07-001656-9