# Boundary Layer Flow Paradox

 User Name Remember Me Password
 Register Blogs Members List Search Today's Posts Mark Forums Read

 August 21, 2002, 04:00 Re: Boundary Layer Flow Paradox #2 Axel Rohde Guest   Posts: n/a Classical B.L. theory is only valid up to the point of separation. Then it no longer applies.

 August 21, 2002, 16:30 Re: Boundary Layer Flow Paradox #3 Steve Guest   Posts: n/a The circular cylinder does not experience transition until Re= 400000. Between 1 < Re < 400000 the boundary layer is so sluggish that as soon as it hits the adverse pressure gradient it leaves the surface as laminar separation.

 September 24, 2002, 08:47 Re: Boundary Layer Flow Paradox #4 Tom Guest   Posts: n/a This result has been known for a long time - the singularity is known as the Goldstein singularity (Goldstein; 1948) and involves the skin friction tending to zero as sqrt(x_s - x) where x_s is the separation point and x is a point upstream of x_s. This square root behaviour then induces an infinite, like 1/sqrt(x_s - x), vertical velocity which violates the assumption that that the vertical velocity is small. A similar phenomenon occurs in the unsteady boundary layer equations (van Dommelen and Shen - don't have the reference to hand) but now instead of the singularity occurring at the wall it occurs at the edge of the boundary layer. Basically the singularity tells you that the assumption that you can solve the inviscid outer flow independently of the boundary layer is incorrect and when the flow is near separation account must be taking of the displacement of the boundary layer upon the inviscid outer flow - this in turn forces the boundary layer in an feedback loop. This is the essence of Stewartson's triple-deck theory. In practice, on a bluff body such as a circular cylinder, the boundary layer actually separates on the windward side of the body where inviscid potential theory says the pressure gradient is favourable! This fact was used in the seminal paper of Sychev (1971?) to show how, using tripledeck theory, the separation singularity could be removed if the inviscid flow was of Kirchoff type with the freestream line leaving the body smoothly. It's this final condition which forces the separation point to the windward side of the cylinder! As a final point the it takes about a 10% increase in the pressure for separation to occur within the boundary layer - this is one of the reasons that thin aerofoils (5% thickness) don't separate. However once the suction peak has been passed the streamwise velocity develops an inflection point and is unstable to waves whose length is of the order of the boundary-layer thickness. These Rayleigh waves are the early stages of transition within the boundary layer. I think Stephen's paradox is simply the fact that, at the Reynolds numbers where boundary layer theory is valid, the flow should be fully turbulent and so is not applicable while at low(ish) Reynolds numbers it can be quite accurate.

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are On Pingbacks are On Refbacks are On Forum Rules

 Similar Threads Thread Thread Starter Forum Replies Last Post Saturn CFX 45 February 8, 2016 05:42 didiean FLUENT 2 January 16, 2012 22:39 MaxCFM Main CFD Forum 1 September 9, 2009 06:09 David FLUENT 0 June 23, 2005 11:01 Wen Long Main CFD Forum 0 July 29, 2002 23:08

All times are GMT -4. The time now is 10:29.

 Contact Us - CFD Online - Top