1070-4272/04/7706-0957 C 2004 MAIK [Nauka/Interperiodica]
Russian Journal of Applied Chemistry, Vol. 77, No. 6, 2004, pp. 957!963. Translated from Zhurnal Prikladnoi Khimii, Vol. 77, No. 6, 2004,
Original Russian Text Copyright C 2004 by Yablonskii.
PROCESSES AND EQUIPMENT
OF CHEMICAL INDUSTRY
Flow Hydrodynamics of non-Newtonian Fluid
in a Cylindrical-Conical Hydrocyclone
V. O. Yablonskii
Volgograd State University, Volgograd, Russia
Received October 1, 2003
Abstract-A system of equations of rheodynamics that describes the flow of a non-Newtonian fluid with
a free surface in a cylindrical-conical hydrocyclone was solved numerically. The fields of velocities and
pressure, as well as the dependence of the thickness of the fluid film on the axial coordinate, were calculated.
The influence exerted by the rheological properties of the fluid and by the defining similarity criteria on
the flow hydrodynamics was studied.
Cylindrical-conical hydrocyclones are the most
widely used industrial apparatus for separating inho-
mogeneous dispersed systems. The simplicity of their
design, small size, and high separation efficiency
ensure their preferential use as compared with cen-
trifuges and separators.
Suspensions separated in chemical industry are in
many cases non-Newtonian fluids whose effective
vscosity depends on the deformation rates. Suspen-
sions of this kind are separated in manufacture of
protein3vitamin concentrates (paprin, haprin, meprin),
in production of suspensions of biomass, glaze, and
, and in purification of wastewater to remove oil,
fats, and other substances. The lack of any adequate
model of the hydrodynamics of non-Newtonian fluids
in a cylindrical-conical hydrocyclone is still the main
obstacle on the way to development of a general pro-
cedure for calculating these apparatus.
The known studies devoted to a theoretical analysis
of the hydrodynamics of cylindrical-conical hydrocy-
clones  cannot be used in developing a proce-
dure for an engineering calculation of a hydrocyclone
because of the fact that the mathematical models of
the flow in a hydrocyclone most frequently do not
reflect the real process and lead to deviation of cal-
culated separation parameters from their true values.
In particular, the studies mentioned did not consider
the fluid flow in a hydrocyclone with a free surface,
which impairs the accuracy and applicability of cal-
culation formulas derived in these studies.
It was mentioned in  that, to construct an ade-
quate model of the flow in a cylindrical-conical hy-
drocyclone, it is necessary to use complete Navier3
Stokes equations, which are transformed into equa-
tions of rheodynamics in the case of separation of
non-Newtonian media. In [5, 6], a conclusion was
made that the rheological equation of state of a non-
Newtonian fluid, which is commonly written in the
form of a power-law Ostwald de Veille equation, is
applicable to suspensions.
In [7, 8], the author modeled the hydrodynamics
of a non-Newtonian fluid in a cylindrical straight-flow
hydrocyclone used to classify particles of the solid
phase of the suspension into fractions and to separate
and purify suspensions in a centrifugal field. Howev-
er, no solution of the complete equations of rheody-
namics of a non-Newtonian fluid for a swirling flow
in a cylindrical-conical hydrocyclone has been re-
ported in the literature.
The mathematical model of the process of devel-
opment of a rotatory flow of a film of a non-New
tonian fluid in a cylindrical-conical hydrocyclone is
a set of equations of rheodynamics, a continuity equa-
tion, boundary conditions, and an equation that ex-
presses the constancy of the fluid flow rate along
the axis of the hydrocyclone. The flow pattern is
shown schematically in Fig. 1.
The hydrocyclone comprises a cylindrical chamber,
into which a fluid is tangentially fed, and a conical
part. The fluid fed into the casing of the hydrocyclone