Boundary Layer Separation

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Boundary layer separation is when the thin layer of viscous fluid leaves the surface of the body that it is flowing over. The viscosity of the fluid causes the boundary layer separation.[1] It is well known that as the Reynolds Number increases, the likelihood of the boundary separating increases.


Contents

[edit] Adverse Pressure

An adverse pressure gradient is just one of the causes of boundary layer separation. Separation is caused when the convective terms in the x-momentum approach zero.[2]

{\mu} {\partial^2 \over \partial y^2}={dP \over dx}

An adverse pressure gradient is caused when the pressure is increasing along x.

{dP \over dx}{>}0

When the momentum of the fluid in the boundary layer is reduced to the point where it is zero, the boundary layer then separates from the bounded surface. When the boundary layer separates from the bounded surface, it then causes reverse flow over the bounded surface.[3]

Graphical representation of the velocity profile in the boundary layer. The 3rd picture represents reverse flow which shows separated flow.
Graphical representation of the velocity profile in the boundary layer. The 3rd picture represents reverse flow which shows separated flow.

[edit] Internal Separation

Boundary layer separation can occur for internal flows. It can result from such causes such as a rapidly expanding duct of pipe. Separation occurs due to an adverse pressure gradient encountered as the flow expands, causing an extended region of separated flow. The part of the flow that separates the recirculating flow and the flow through the central region of the duct is called the dividing streamline.[4] The point where the dividing streamline attaches to the wall again is called the reattachment point. As the flow goes farther downstream it eventually achieves an equilibrium state and has no reverse flow.

[edit] Effects of Boundary Layer Separation

When the boundary layer separates, it produces a wake that causes an increase of pressure drag, which has many adverse effects upon the efficiency of the system.[5] For example, if you could decrease the amount of separation on a car you could greatly increase the fuel efficiency of the car. Another example of an adverse effect of boundary layer separation is the stalling of an aircraft. The stalling of an aircraft is a very serious problem, it can cause the aircraft to crash, most likely being fatal for the passengers and crew members on board the aircraft.

Another effect of boundary layer separation is shedding vortices, known as Kármán vortex street. When the vortices begin to shed off the bounded surface they do so at a certain frequency. The shedding of the vortices then could cause vibrations in the structure that they are shedding off. When the frequency of the shedding vortices reaches the resonance frequency of the structure, it could cause serious structural failures. An example of this is the Tacoma Narrows Bridge. The shedding vortices reached the resonance frequency of the bridge and ultimately caused it to collapse.


[edit] See Also

Boundary Layer


[edit] References

  1. ^ Wilcox, David C. Basic Fluid Mechanics. 3rd ed. Mill Valley: DCW Industries, Inc., 2007. 664-668.
  2. ^ Wilcox, David C. Basic Fluid Mechanics. 3rd ed. Mill Valley: DCW Industries, Inc., 2007. 664-668.
  3. ^ Balmer, David. "Separation of Boundary Layers." School of Engineering and Electronics. 2 Dec. 2007. University of Edinburgh. 12 Mar. 2008 <http://www.see.ed.ac.uk/~johnc/teaching/fluidmechanics4/2003-04/fluids14/separation.html>.
  4. ^ Wilcox, David C. Basic Fluid Mechanics. 3rd ed. Mill Valley: DCW Industries, Inc., 2007. 664-668.
  5. ^ Fielding, Suzanne. "Laminar Boundary Layer Separation." 27 Oct. 2005. The University of Manchester. 12 Mar. 2008 <http://www.maths.manchester.ac.uk/~suzanne/teaching/BLT/sec4c.pdf>.