|January 17, 2001, 10:15||
Setting Outlets with gravity..
Hi, I have been doing the mathematical background when gravity is present. And need some confirmation and explanation in some terms of the equation.
I'm using the reduced pressure formulation or density_difference model to simulate gravity, this will introduce in the momentum equation a reference pressure p_ref, which satisfies the hydrostatic-equilibrium equation:
grad p_ref + rho_ref * G = 0
and if we define G = - grad(f) (**), where f is the gravitational potential, then you have
grad ( p_ref + rho_ref*f ) = 0
grad(p_ref) + grad(rho_ref*f) = 0
the momentum equation
rho_ref*DU/Dt = - grad(p) + h*grad^2(U) + F (*)
where F is the bouyancy-source term, which is defined like:
F = rho*G
delta_rho = rho-rho_ref,
F = (rho_ref + delta_rho )*G using (**)
F = delta_rho*G - grad(rho_ref*f)
using this in the momentum equation
rho_ref*DU/Dt = - grad(p) + h*grad^2(U) + delta_rho*G - grad(rho_ref*f)
adding cero to the equation
rho_ref*DU/Dt = - grad(p) + h*grad^2(U) + delta_rho*G - grad(rho_ref*f) + grad(p_ref)+grad(rho_ref*f)
reordering and reducing terms, we have
rho_ref*DU/Dt = grad(p-p_ref) + h*grad^2(U) + (rho-rho_ref)*G
So, the question is :
How do I set the value of the pressure in an outlet if I know that his hydrostatic value p is -100 Pa? Do I have to set in the outlet now (p-p_ref)? The pressure ploted in VR-Viewer is p or (p-p_ref)? Now is this calculation correct?
if gravity in the -Z direccion (G=-g*k) then the equation of p_ref, reduces to
d(p_ref)/dz +rho_ref*g =0, so
which value of z have to use? z=0 or z= height of the domain? is it constant? or depends on z? that means that I have know a new field p_ref?
thanks, for any comments
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