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August 1, 2005, 23:05 
divergerence free initial conditions for 2d flow

#1 
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Dear all,
I need to generate initial conditions for a 2d flow past an airfoil for my FVM NS solver. What I've done is simply specify u(infinity)=1, v=0 at the left most grid for the initial conditions. The rest of the grids have zero velocity. I've read some paper which talks about getting a divergence free velocity field. Can someone explain that? Do I need to specify some pressure values as well? Thank you. 

August 1, 2005, 23:27 
Re: divergerence free initial conditions for 2d fl

#2 
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Thermodynamic state is defined by two independent properties, what you have is just velocity (2 components of velocity) you need the total pressure too


August 2, 2005, 04:47 
Re: divergerence free initial conditions for 2d fl

#3 
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Hi,
can you explain a bit more? I assume gauge pressure to be zero. I'm not interested in the temperature and I am simulating low Re laminar incompressible flow. In that case, how do I specify the total pressure? Thanks 

August 2, 2005, 06:51 
Re: divergerence free initial conditions for 2d fl

#4 
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Velocity fields are always required to be divergence free, since that is continuity equation for incompressible flow. So, if you've given u=constant, v=0 is right. And usually that's the initial condition for free stream flow. Is your grid starting from stagnation point, or before that. Beginning of grid should be enough upstream of the airfoil to give the condition you are giving.


August 2, 2005, 07:40 
Re: divergerence free initial conditions for 2d fl

#5 
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Hi,
thanks alot. My starting pt is quite a few chords away so I believe it should be ok. 

August 4, 2005, 02:53 
Re: divergerence free initial conditions for 2d fl

#6 
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Allow me to be honest with you, Could you please explain what do you mean by "gauge pressure to be zero." and how this is related to the "p" that appears in the Navier Stokes equation and called "pressure"( equilibrium pressure or thermodynamic pressure) and how are you calculating that "p" in your code. I would recommend that you review the derivation of the momentum equation in the following books 1 Continuum Mechanics by mace and mace 2 Incompressible flow by Panton 3 Boundary Layer Theory by Schlichting. Your mistake is very common among a lot of researchers and practicing engineers, I mean you are not alone in this just review other postings on this forum. The pressure that is measured by a gauge attached to the walls of your device or domain is either the total pressure or the stagnation, not the p that appears in the Navier Stokes equation (which can only be measured if your measuring device is travelling with a fluid particle in the Lagrangian Sense of description of motion).


August 17, 2005, 11:52 
Re: divergerence free initial conditions for 2d fl

#7 
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hi Ahmed. in that case, can u explain a bit on what u said?
i'm solving NS in nondimensional form. hence, the pressure is divided by p(infinity). in other words, if i multiply the p i get for solving the NS eqns by p(infinity), what is this new "pressure" then? Thanks alot! 

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