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Tips & Tricks: How to interpret results for multiphase & porous domains using true velocity and superficial velocity
Nov22

Tips & Tricks: How to interpret results for multiphase & porous domains using true velocity and superficial velocity

A commonly asked question is: What is Superficial Velocity and when do I use it?   If a fluid flows through a region that is occupied by either fixed structures (a porous region, pipe rack, catalyst bed, etc...), or shares the channel with other fluids (e.g. gas-liquid flow), there are two ways to describe the fluid velocity.   The first is to use the "True Velocity" which is the actual velocity of the fluid particles. This velocity will vary with location in the porous matrix. This is the velocity you would measure experimentally if you focused on a small region of fluid.   The second is the "Superficial Velocity", which is the velocity the fluid would have if it were flowing through the same domain without any obstructions. This is a very useful quantity as in incompressible flow it is conserved regardless of the variation of the porosity. Therefore, even at a boundary between a porous region and continuous fluid the superficial velocity is unchanged, whereas the true velocity must increase in the porous region so that mass is conserved.   These two velocities are easily related via , where Vs is the superficial velocity, Vtrue is the true velocity and  ε is the porosity (the local fraction of the volume occupied by the fluid).   If you study multiphase flows you will certainly encounter superficial velocity as it is used to characterise a flow system. Using superficial velocity has the benefit that it is conserved (for an incompressible flow with no phase change) regardless of the complexity of the flow regime, e.g. if the flow regime changes from bubbly to slug flow, the superficial velocity stays constant even though the local velocity varies. Maps plotting the gas superficial velocity on one axis and liquid superficial velocity on the other  are known as regime maps and are used to define the boundary between different regimes.  When visualising the results of multiphase flow simulations, ANSYS CFD-Post will automatically give the user the choice of plotting either Superficial Velocity or (True) Velocity variables.   The use of a superficial velocity is also often encountered when dealing with pressure drop correlations for porous regions, be it a true porosity or a porosity used to represent flow obstructions.  An experimentalist can use either superficial or true velocities to characterise their system, but when reviewing experimental data it is worth knowing that it is more common to use superficial velocity as this can be measured outside of the porous region.   Consider Darcy's law for slow flow (negligible inertia) in a porous medium, which relates the volumetric flow through a given face to the pressure drop via  where...

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