4
$\begingroup$

picture of flow over an airfoil We know that in real viscous flow, boundary layer exists around the airfoil and there will be a separation point which flow starts to separate from the back of the airfoil( velocity gradient equal zero at separation point). If the flow speed increases, will separation occur earlier or later?

$\endgroup$
  • $\begingroup$ Is this a homework question of some sort, or otherwise assigned to you? $\endgroup$ – Ralph J Feb 16 at 16:00
  • $\begingroup$ @RalphJ Nope just curious about it $\endgroup$ – Hanzhi Zhang Feb 16 at 17:51
  • $\begingroup$ @mins yeah that's exactly what I mean $\endgroup$ – Hanzhi Zhang Feb 23 at 1:02
6
$\begingroup$

In a subsonic flow, the separation point moves downstream as Reynolds number increases, and Reynolds number increases with free stream velocity.

Demonstration on a cylinder-shaped airfoil:

enter image description here
Source


From Wikipedia:

Reynolds number is the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities

Separation occurs at the location the laminar airflow stops being accelerated, and is decelerated by areas of upstream turbulent airflow in separation bubbles created by friction (viscosity):

enter image description here
Source

Velocity gradients in the boundary layer at different points in the transition area where the flow transitions from laminar to turbulent:

enter image description here

Source, adapted

Velocity is decreasing near the surface due to friction, and at some point becomes negative. Separation bubbles appear between the laminar flow and the airfoil. In a bubble there is a secondary reverse flow and a region where air is stagnant. Downstream the bubble, air is turbulent:

enter image description here
Source, adapted

While other elements affect the boundary layer separation point, this one is the largest. To counter this effect, the momentum of the laminar stream must be increased relatively to frictional forces. This is done (by definition) by increasing the Reynolds number, e.g. by increasing the airspeed.

Increasing airspeed can be obtained by accelerating the aircraft, but also by other ways. For example, different devices are used to delay the separation of the boundary layer when the aircraft must be slowed down. It consists on accelerating ("re-energizing") "dead air" near the surface, e.g. using high speed jets or vortex generators.

This is for instance the principle behind slats and slotted flaps:

enter image description here
Source, adapted


The boundary layer separation is due to flow deceleration as it moves away from the leading edge and an adverse pressure gradient appears (potential flow theory).

The lower energy flow is more prone to perturbations, vortexes appear and disappear, increasing in importance. Portions of vortexes have a velocity opposed to the free stream velocity, this creates areas of "dead air". Viscosity takes over inertia. This ratio between inertia and viscosity effects is the very definition of the Reynolds number.

By increasing velocity (actually the Reynolds number), this effect is minimized: The separation point moves downstream, as the effects of the adverse pressure gradient are countered on a longer distance as visible on the velocity gradients shown on the flap/slat picture above.

Flaps/slats have the additional advantage (over vortex generators for instance) of increasing the wing surface, hence restoring lift lost when the airplane was slowed down.

$\endgroup$
  • 1
    $\begingroup$ Thank u very much. This answer is exactly what I want. Initially, I thought in this way: higher speed means more time to decelerate the velocity gradient to 0( where separation occurs). So the separation point moves downwards. It seems too simple to be wrong. Could u explain more about why separation point move downward and why related to Reynolds number directly? $\endgroup$ – Hanzhi Zhang Feb 23 at 15:30
  • 1
    $\begingroup$ @HanzhiZhang: At higher speed the air molecules come with more inertial energy, but viscosity has not changed. This means more "oomph" is available to be eaten up in friction before the air comes to a standstill relative to the wing. $\endgroup$ – Peter Kämpf Feb 23 at 20:35
  • $\begingroup$ @PeterKämpf thanks I understand it 👍 $\endgroup$ – Hanzhi Zhang Feb 24 at 2:43
  • $\begingroup$ What a wonderful answer! $\endgroup$ – uhoh May 18 at 19:18

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.