Hydrostatic pressure in 2-phase flow modeling (long)

DS & HB

Long post. Thanks for your patient and time.

We have some confusions here about hydrostatic pressure in 2-phase flow modeling, and would like to hear your appreciated inputs to clear us out.We'll try to explain the case and questions as clear as possible.

1. The modeling case:

A vertical oriented pipe, with one end (its top) attached to a larger liquid tank , and the other end (its lower portion) submerged into another lower-level liquid pool. The actualy pipe inner geometry is much more complicated, of course, including some steps, throttlings ...

The liquid flow is gravity-driven, gas (1-20% in voulume) is injected from a portion of porous inner wall of the pipe.

Computational domain : pipe only, not including tank or pool

Models: Turbulence (K-e), 2-phase (liquid-gas bubbles, also liquid-only 1-phase simulation), isothermal, incompressible, steady-state, 3-D flow

Boundary conditions:

1) Top of the Pipe : Fixed liquid velocity (based on the liquid flow rate through the pipe) or Fixed pressure (based on the liquid head in the tank above the pipe).

2) Bottom of the pipe: Fixed pressure (based on the submerged depth of the pipe in the downstream pool).

3) On a portion of the inner pipe wall: Fixed gas normal velocity (based on the gas injection flow rate).

*** We are using CFX4.2 for the simulations *****

2. The problem:

Even though the buoyant flow option is turned on and the the gravity is specified in our 2-phase flow runs, the pressure solution seems not including the hydrostatic pressure. This can be told by comparing the pressure solution for 2-phase with very small amount of gas (0.1%) and 1-phase flow without boy-force specified. They are almost same.

CFX tenicians (they are very nice guys ) told us "To display the pressure including hydrostatic pressure, one need to add one user scalar and save REAL PRESSURE to it.". However, the resulting "REAL PRESSURE" looks physically wrong (a larger negative pressure was shown at the top of the pipe. It was comfirmed that what CFX was doing to obtained "REAL PRESSURE" was:

(REAL PRESSURE) = (PRESSURE) + (rho*g*z).

where z is the coordinate in vertical direction. The z=0 was set at the bottom of the pipe, and z > 0 upward (so all z are positive in the domain), and the gravity vector was specified as (0, 0, -9.8), therefore g=-9.8.

Another thing noticed is that the "fixed pressure" type boundary conditions were honored in PRESSURE (notice: not REAL PRESSURE) solution plot.

3. The Questions/confusions

We need the pressure solution for our further-post-processing, using Bernoulli's equation to find out the relationship between the pressure-drop, flow-rate, and liquid head/submerged-depth. The Bernoulli's Equation is in form of :

p + rho*g*z + 0.5* rho*v*v = constant

The question here is "what is the corresponding relation between the first term "p" of Bernoulli equation and the CFX pressure solution ? " Should we use "PRESSURE" , which does not include the hydrostatic pressure ( coz the rho*g*z represent the hydrostaic term ??) or should "REAL PRESSURE" be used in the Equation above ??

What may cause the "REAL PRESURE" physically wrong ? Anyone has the experience with CFX "REAL PRESSURE" ?

By intuitive, we would think to modify "pressure without including hydrostatis pressure" at a certain point into a "pressure including hydrostatis pressure" is to add the liquid head above that point. Any comment on this statement ??

Thanks for the inputs.

HB & DS