Researchers cannot measure or fully explain the complex interaction between
fluid and particles in a vortex
A functional overview:
The principal of operation of a hydrocyclone is based on
the concept of the terminal settling velocity of a solid particle in a centrifugal
field. The rock slurry feed enters tangentially into the cylindrical section
and follows a circular path with a net inward flow of fluid from the outside
to the vortex finder on the axis. The high circulating field is usually high
enough to create an air core on the axis that extends from the spigot opening
at the bottom of the conical section through the vortex finder to the overflow
at the top. The centrifigal force field is many times larger than the gravitational
field.
TParticles that experience this centrifugal field will tend to move outwards
relative to the carrier fluid because of a greater relative density. The larger
heavier particles migrate rapidly to the outside walls and will then be forced
to move downward on the inside of the conical wall. Small, light particles
will be dragged inwards by the fluid as it moves toward the vortex finder.
It is this drag force that creates much of the complexity of particle behavior
and is a function of the hydrodynamic conditions inside and the shape and
size of the particle.
The classification
action of the hydrocyclone is determined by the net effect of the two competing
forces that act on each particle - the outward centrifugal force and inward
drag force. A particle that experience equilibrium between these two forces
will have an equal chance of exiting the overflow or underflow. This
size particle tends to orbit and get moved towards either exit by random collisions
with other particles and random eddy motion of the highly turbulent flow
field.
Condition that define the equilibrium orbit:
Drag
force = Centrifigal force
.5 Cd(Vr - Ur)^2 pA = Vo^2/r *Vp(ps-pf) Cd=drag coefficient,
Vr=radial velocity of fluid, Ur=radial velocity of particle, p=fluid density
A=particle cross sectional area, Vo=tangential component of particle velocity
vector, r=radius of tangent motion, Vp=particle volume, ps=density of the
particle.
This theoretical model of particle behavior when solved for particle size
would be impossible to use in an online computer model of the particle leaving
the overflow. However, the description indicates which external grinding circuit
parameters would be useful as secondary measurements to infer particle size
= = = = = slurry flow
