Effects of gravity in pipe - pressure distribution

Anthony Wachs

Hi everybody,

I am currently simulating fluid-fluid displacement in pipes. As density ratio of the two fluids is a key parameter in this kind of situation (related to buoyancy forces), I first attempted to check how Fluent accounts for gravity.

Let's consider the flow of a single Newtonian fluid in a axisymmetric pipe. A velocity profile, corresponding to parabolic radial distribution is prescribed at the entry and constant radial pressure profile p=0 at the outlet. So it is the simplest problem you can imagine in Fluid Mechanics!! The goal is to obtain the right pressure gradient given by analytical solution.

If there is no gravity, the pressure gradient dp/dz is related to greatest axial velocity umax by :

dp/dz=umax*4*mu/R**2

mu stands for the viscosity, R the radius of the pipe

If gravity is taken into account, for the same flow rate, the pressure gradient dp'/dzis modified by the hydrostatic contribution, and we have :

dp'/dz=dp/dz+ro*g

ro is the density and g=9.81m/s2

What is surprising in Fluent is that the pressure gradient do not change wether gravity is considered or not.

I am now wondering how Fluent include gravity forces in conservation equations ? or how the post-processor plot pressure distribution ?

I studied this simple problem because for fluid-fluid displacement, the pressure distribution along the pipe in the axial direction is correct when viscosity differences between the two fluids is considered (no buoyancy forces), but seems unrealistic for density differences.

Any help or suggestion would be really appreciated

Anthony