Russian Journal of Applied Chemistry, 2011, Vol. 83, No. 6, pp. 1089−1093.
Pleiades Publishing, Ltd., 2010.
Original Russian Text
Yu.G. Pazin, A.N. Verigin, N.A. Nezamaev, 2010, published in Khimicheskaya Promyshlennost’, 2010, Vol. 88, No. 1, pp. 15−19.
PROCESSES AND DEVICES
OF CHEMICAL MANUFACTURES
Investigation of Structure of Single-Phase Vortex Flows
Yu. G. Pazin, A. N. Verigin, and N. A. Nezamaev
St. Petersburg State Technological Institute (Technical University), St. Petersburg, Russia
Received March 12, 2011
Abstract—The design of the vortex chamber, which is a cylinder with a partially cut wall was developed. Several
such chambers may be contained in the device. One of the structural elements of the device is rotated at a given
speed. An intensity of the arisen vortex depends on the relative speed of a couple chamber–agitator, and the opening
angle of the vortex chamber. Investigation of the structure of vortex ﬂ ows is to determine proﬁ les of peripheral and
axial velocities in the vortex chambers. Studies have revealed the presence of self-oscillations in the investigated
ﬂ ows. Rational values of the opening angle of the vortex chamber that ensure maximum peripheral speed should
be selected from a range of 60–100°.
It is known a lot of ways to create a vortex ﬂ ow [1–5].
The proposed design of a vortex chamber is a cylinder
with a partially cut wall (Fig. 1). Several such chambers
may be contained in the device. It is assumed that one
of the structural elements of the device is rotated at
a given speed. This may be a rotor (agitator) then the
vortex camera is stationary. Or the vortex chamber itself
is rotated, and in this case the device body is immobile.
An intensity of an arisen vortical motion depends on the
relative speed of the couple agitator–chamber and the
opening angle of the vortex chamber (Fig. 1).The vortex
motion is created along the length of the chamber, the
radius of which can be arbitrarily small. With decreasing
the chamber size the vortex intensity increases that
allows the development of devices of chemical industry
with a high rate of processing of dispersed materials.
Investigation of the structure of vortex ﬂ ows was to
determine the proﬁ les of peripheral and axial velocities
in the vortex chamber. Figure 2 shows the proﬁ les of the
peripheral velocity measured in three radial directions
every 90 degrees in the cross section of vortex chamber
for various frequencies of the agitator rotation.
In the direction of the ﬂ ow a variation in the proﬁ le of
peripheral velocity occurs along the chamber perimeter.
The maximum value of the peripheral velocity decreases
and the curves become ﬂ atter.
The thickness of the near-wall layer in the direction
of motion increases. These features of the vortex ﬂ ow is
identical to the properties of semi-bounded (near-wall)
of submerged jets.
According to the solution of the momentum
equation for the turbulent boundary layer in the case of
longitudinal ﬂ ow around a ﬂ at plate a ratio of a thickness
of a momentum loss to the longitudinal coordinate δ¨/x
is calculated from the semi-empirical expressions of
the form δ¨/x = 0.0153Re
. Assuming that the
thickness of the boundary layer δ is proportional to the
momentum thickness δ¨ we can write
δ ≈ δ¨ = 0.0153Re
From this equation it is clear that the thickness
of boundary layer over the chamber perimeter
varies as close to the line and only slightly
depends on the velocity at the boundary layer.
Processing of experimental data yielded an empirical
relationship describing a change in the thickness of
δ = (x
= (100 + x)Re
coefﬁ cient of friction
on the plate