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May 16, 2010, 05:00 
Velocity and pressure BC at inlet

#1 
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Claus Meister
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Hey folks,
my questions concerns the inlet BC for velocity and pressure. In CFD books, it is alway explained that by known inflow velcoity the inlet pressure is set to zero gradient. However, when I know the velocity than I know via 0.5*rho*v^2=p the inlet pressure. Can I uses this BC also or do I have to apply zeroGradient always? Cheers 

May 18, 2010, 15:08 

#2 
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Patrick Godon
Join Date: Apr 2010
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>>> my questions concerns the inlet BC for velocity and pressure. In CFD books, it is alway explained that by known inflow velcoity the inlet pressure is set to zero gradient. However, when I know the velocity than I know via 0.5*rho*v^2=p the inlet pressure. Can I uses this BC also or do I have to apply zeroGradient always?
A zero gradient means that there is not pressure force at the boundary. If you don't put a pressure gradient =0 condition at the boundary and give the pressure there, you may develop a pressure gradient which in turns will act as a force and increase (or decrease) the velocity at the boundary, and this might all be inconsistent with the imposed velocity at the boundary. So usually a zero pressure gradient is in this case better. Another thing you need to consider is from the point of view of imposing mathematically the correct number of BCs. You are solving a number of equations, and I am not sure what they are. Possibly equations for the velocities (one in each dimension) and an equation for the density and possibly one for the pressure/energy. For each equation you need to know what is the degree of the equation, I mean are the space derivatives only of first order? or do you have second order space derivatives? (which means diffusive terms, as for the inclusion of heat diffusion, viscosity, etc...). For each equation of 1st order you need only ONE BC for each dimension, namely you really need only to have a conditions given at one end/boundary of the domain only. For equations of the second order you have to give one boundary condition at each end/boundary (so TWO BCs for each dimension). If you give too few or too many BCs you may have numerical instabilities, though these might not show up because of (artificial) viscosity or because you are using a low order accuracy solver which damps these instabilities. But mathematically the number of BCs has to be given that way. To avoid all instability you need to actually impose these BCs not on v, P and rho but on the characteristics of the flow (Riemann invariants). But that's another story all together. 

May 19, 2010, 02:50 

#3 
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Claus Meister
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Thanks, PGodon!
For my understanding, it means: When I would have set a velocity inflow BC, say 10 m/s, and at the same time I have set a pressure condition p=1/2*v^2=0.5*10^2=50 then a addtional force of 50 would act on the velocity, i.e. the velocity would increase. Is my narration correct? Cheers in advance 

May 19, 2010, 10:03 

#4 
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Patrick Godon
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"50" is the pressure, not the pressure gradient...
In the equation for the velocity (or momentum  I am not sure what are the set of equations you are solving here) you will have a term with the gradient of the pressure which acts as a force. If P=50 everywhere near the boundary (inside and outside) then the pressure gradient is zero because the pressure is constant (inside and outside) the boundary  the pressure gradient THROUGH the boundary is to be zero if you don't want any force there. Don't mixed up the pressure and the pressure gradient... I know it might seem confusing as pressure divided by area is force too... but that's not what I was refering too. If the pressure on both sides of the boundary are the same (pressure gradient =0) then these pressure forces cancel each other. If the pressure is not the same on both sides of the boundary (pressure gradient different than 0) then there will be a net resulting force  that's what you want to avoid when setting gradP=0. 

May 19, 2010, 10:24 

#5 
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Claus Meister
Join Date: Aug 2009
Location: Wiesbaden, Germany
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Thanks PGodon!
Oh man, it was the entire time in the front of me and I haven't spotted it. Your answer is totally plausible! Cheers 

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