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By Kumar M. Dhanasekharan and Srinivasa L.Mohan, Fluent Inc.
Disk impellers that agitate a liquid by moving up and down are called
vibromixers. These impellers usually contain conical perforations through
the disk, but some varieties function without them. Vibromixers provide
some interesting advantages over conventional impellers for certain applications.
For biochemical reactors, such as fermenters, it has been shown that vibromixers
can generate mass transfer coefficients that are substantially higher
than those obtained in a rotationally stirred reactor.1 In the pharmaceutical
industry, where microscopic solids in suspension need to be maintained
in sterilized, hermetically sealed containers, vibromixers provide a good
alternative to stirred tanks. They are more portable, use a simpler motor
mount, and don’t require a rotating seal.
Iso-surfaces of velocity magnitude illustrate the jets emanating from
the holes
The dynamic mesh model in FLUENT 6 was recently
used to simulate a vibromixer operating in a vessel
of water. The disk has over forty perforations that are
in the shape of truncated cones. When the disk undergoes
periodic motion through the fluid, jets are repeatedly
forced out the tapered ends of these perforations,
due to the venturi effect. Over time, these jets give rise
to large circulation patterns in the tank, which is important
for good turbulent mixing. Depending on the
orientation of the conical perforations, the design can
be used for both up-pumping and down-pumping
applications.
A 650,000 cell mesh of unstructured hexahedral elements was used for
the simulation. Using Coopering tools in GAMBIT, quad cells were created
on the disk surface and extruded in the axial direction to build the volume
mesh. This process created even layers of hexahedra, which is an excellent
mesh environment for the anticipated disk motion. User defined functions
were used to specify the time dependent velocity of the disk, and a new
grid was created automatically at each time step using the dynamic layering
algorithm. During this process, the cells near the disk were either stretched
or contracted, or an entire layer was added or removed to adjust to each
new disk position.
Pathlines colored by time illustrate the circulation patterns generated
by the mixer
Because the tapered ends of the perforations are oriented
upwards, jets are emitted from the tops of the
holes during the downward stroke of the impeller. These
jets can be captured by drawing iso-surfaces of constant
velocity magnitude. During the upward stroke, fluid flows
in the reverse direction into diverging conical volumes.
Jets formed as the fluid passes into these volumes through
the tapered ends are weak, and they quickly dissipate.
After the vibromixer has been operating for several cycles,
pathlines can be used to illustrate the circulation patterns
that have developed in the surrounding fluid.
References:
1 Ni, X., Gao, S., Cumming, R. H., and Pritchard, D.W, A Comparative
Study of Mass Transfer in Yeast for a Batch Pulsed Baffled Bioreactor
and a Stirred Tank Fermenter, Chem. Eng. Sci. 50:2127-2136, 1995.
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