# Multiple solutions for Euler equations

 Register Blogs Members List Search Today's Posts Mark Forums Read

 March 25, 2001, 15:48 Multiple solutions for Euler equations #1 Farid Moussaoui Guest   Posts: n/a I am searching the definition of airfoils admitting multiple solutions for the Euler equations. Thanks. F++

 March 26, 2001, 23:26 Re: Multiple solutions for Euler equations #2 T. Matsuzawa Guest   Posts: n/a Hello The nonunique solutions of the Euler equations were closely investigated by Prof. Jameson in AIAA Paper 91-1625. First you should try to find this report. Best Regards. T. Matsuzawa

 March 27, 2001, 02:21 Re: Multiple solutions for Euler equations #3 Selina Tracy Guest   Posts: n/a Interesting. I heard about the bifurcation but could you explain of the mean 'multiple solutions' for airfoil? What factor decides the flow? Just briefly. Selina.

 March 27, 2001, 13:28 Re: Multiple solutions for Euler equations #4 kalyan Guest   Posts: n/a You get a unique solution for lift around airfoils only if they have a sharp trailing edge and the Kutta condition is imposed there. If there are no sharp edges, it is not clear where the Kutta condition should be imposed. A good example is an ellipse at an angle of attack. So the lift prediction can not be made using invicid flow computations. The reason for this is quite simple (though it is often not explained along side the Kutta condition). Inviscid flows can not produce vorticity in a flow that is initially irrotational except in the presence of baroclinic torque. Baroclinic torque can often be small or absolutely zero if the fluid has constant density. In that case, Euler equations can not produce any body force (lift or drag). If you solved the Euler equations around an ellipse, you would end up with zero lift (the flow pattern would look similar to a Hele-Shaw flow). For airfoils with sharp leading edges, you impose the Kutta condition the justification for which is the fact that no real fluid (i.e., viscous fluid) can fully turn around a sharp corner. This constraint generates vorticity around the airfoil and the lift. The condition itself has nothing to do with Euler equations. It is a physical observation based on real fluid behavior. You would however end with non-zero drag if you the flow around ellipse shaped airfoils numerically. The trailing edge separation point would depend on the extent of truncation error (artifial dissipation) and so would the lift. So, two different Euler schemes would give two different lift coefficients.

 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 pete Site Help, Feedback & Discussions 20 June 16, 2015 13:52 Ganesh FLUENT 13 January 22, 2014 05:11 asaijo OpenFOAM Installation 9 April 6, 2011 12:21 Fab Main CFD Forum 3 February 28, 2008 06:01 Hanjie Lee FLUENT 3 August 15, 2006 17:21

All times are GMT -4. The time now is 11:09.