By definition, p_rgh is deduction of hydro-static pressure (i.e. rho.g.h) from the pressure:
p_rgh = p – rho.g.h =/ 1/2*rho*U^2
p_rgh is not equal to dynamic pressure, specially in multiphase flow where rho changes throughout the domain. It is just the difference between real pressure and the rho*g*z field. That’s one of the reasons that the field is no longer called pd, as in 1.5 version of OF.
Would be good to mention that rho*g*z is not the real hydro-static pressure either!! Even if rho is constant it differs from hydrostastic component by a constant (the distance between the z=0 plane and the atmosphere p=0 plane times rho*g).
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Also, gh is defined in openFoam as:
gh = g & mesh.C()
In other words, gh is the dot product of the g vector and the cell center position vector. As g is usually defined as (0 0 -9.81), gh often results negative in the positive z coordinate!
Finally, as:
p_rgh = p – rho * gh
p_rgh is greater than p if z > 0
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To understand the different pressures, we at Bernoulli:
Dynamic pressure –> 1/2*rho*v^2
Hydro-static pressure–> rho*g*h
Static pressure –> p
1/2*rho*v^2 + rho*g*h + p = Constant
From the openFoam site, p_rgh = p – rho*g*h.
So, p_rgh is the static pressure minus the hydraulic pressure, based on a arbitrary height.
Dynamic pressure has nothing to do with the definition of p_rgh. Dynamic pressure is the pressure of the moving fluid and it will convert into static pressure if you bring the velocity of the fluid to zero. Conservation of energy, back to Bernoulli.
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p_rgh depends on your coordinate system, boundary conditions and eventually a pRefValue and pRefPoint. If you have something like an atmosphere pressure = 0 Pa in the air above the surface by specifying an atmosphere boundary condition or a pRefValue = 0 Pa, and your water density and g is specified correctly, you will get a nice triangular hydrostatic pressure starting from zero at the surface for p, but not for p_rgh. (to be continued …)
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Total pressure:
In fluid dynamics, total pressure ( p_0) refers to the sum of static pressure p, dynamic pressure q, and gravitational head, as expressed by Bernoulli’s principle:
p 0 = p + 1/2*rho*v^2 + rho*g*h