Russian Journal of Applied Chemistry, 2011, Vol. 83, No. 9, pp. 16551669.
Pleiades Publishing, Ltd., 2010.
Original Russian Text
V.Ya. Kats, G. Mazor, 2010, published in Khimicheskaya Promyshlennost’, 2010, Vol. 88, No. 3, pp. 139153.
MODELING AND CALCULATION
OF TECHNOLOGICAL PROCESSES
Hydrodynamics of a Centrifugal Turbine Agitator-Pump
V. Ya. Kats and G. Mazor
Sami Shamoon College of Engineering, Beer-Sheva, Israel
Received March 5, 2011
Abstract—Hydrodynamics and agitation energy of viscous ﬂ uids was considered in apparatuses with a centrifugal
turbine agitator-pump applied in vacuum ﬁ ltration systems for water softening. Using the Navier–Stokes equations
we solved an axisymmetric problem in the variables: pressure–velocity, vorticity–ﬂ ow function. A ﬂ ow region
behind turbine blades is represented as a pair of symmetrical macrovortices forming vortex tubes with vortex cores
and potential ﬂ ow between them. We determined hydrodynamic parameters such as: a circulation around a contour
enclosing the vortices, the drag coefﬁ cient and pressure drop when moving blades, coordinates of centers of the
macrovortices, radial, tangential, and axial ﬂ ows and corresponding them mass ﬂ ows of liquid. We determined
a limiting mode of the absence of cavitation in the turbine and calculated energy dissipation and power criteria:
parameters used to scale turbine agitators. The obtained data underlay the study of mass transfer in the vacuum
ﬁ ltration system designed to remove the calcium cations from water.
The vacuum ﬁ ltration system designed to reduce
calcium concentration in the water, for water softening
was developed in the Institute of Applied Research of
Ben-Gurion University (Negev, Israel)  (Fig. 1).
The most important part of this system is the
centrifugal, turbine agitator pump that engulfs and
discards liquid ﬂ ows to a surface of a special ﬁ lter.
Calculation of the basic hydrodynamic parameters that
characterize the dynamic interaction of turbine blades
with the ﬂ ow of a viscous ﬂ uid should be performed for
examination of the ion exchange, diffusion processes
and mass transfer in such system.
The objectives of the study are: simulation of the
dynamic interaction of the turbine blades with the ﬂ ow
of viscous ﬂ uid and calculation based on this model
velocities and mass ﬂ ows of ﬂ uid in radial, tangential,
and axial directions; determination of the limiting mode
of the absence of cavitation in the centrifugal turbine
agitator pump; experimental calculation of the energy
dissipation and the power criterion for the turbine
STEADY-STATE AXISYMMETRIC VISCOUS
FLOW IN CYLINDRICAL COORDINATES.
The original Navier–Stokes equation at = const in
cylindrical coordinates r, , z has the form [2, 3]:
where * = rV, /r, are dependent variables; a
, various functions corresponding to these
variables (Table 1).
are tangential, radial, and axial
constituents of a velocity vector of the ﬂ ow V