Russian Journal of Applied Chemistry, 2011, Vol. 83, No. 6, pp. 1080−1084.
Pleiades Publishing, Ltd., 2010.
Original Russian Text
I.O. Mikulionok, L.B. Radchenko, 2010, published in Khimicheskaya Promyshlennost’, 2010, Vol. 88, No. 1, pp. 6−10.
PROCESSES AND DEVICES
OF CHEMICAL MANUFACTURES
Simulation of Liquid Cooling
of an Extruded Sleeve Plastic Film
I. O. Mikulionok and L. B. Radchenko
Ukrainian Technical University “Kyiv Polytechnical Institute”, Kiev, Ukraine
Received January 12, 2011
Abstract—A mathematical model of a liquid cooling was considered for a tubular plastic ﬁ lm produced by
extrusion down. The developed model allows for a preset ﬁ lm speed (extruder) and ﬁ lm parameters to determine
a length of a cooling zone or for a preset length of the cooling zone calculation of maximum speed of the ﬁ lm
with the preset parameters.
Tubular plastic ﬁ lms are among the most common
polymer products . The essence of the method of their
production is to form in an extrusion die a tubular polymer
billet which swells up to a sleeve of the required diameter
and wall thickness by the air supplied inside the sleeve
through the holes of the extrusion die. After cooling, the
molded sleeve is placed by guide plates, pulled by pulling
rollers, and spooled into a roll. Modern extrusion equip-
ment allows obtaining a ﬁ lm with a considerable speed,
but the cooling system can not always provide timely
reduction in a sleeve temperature. As a rule, cooling of
a sleeve is carried out by air blowing, however, in some
cases it is advisable to use a more efﬁ cient liquid cooling,
especially in manufacture of thick ﬁ lms (typically 100
μm). If in the case of air cooling a sleeve is formed by
a “drawing up”, in the liquid cooling is usually used the
scheme of “drawing down.” In this scheme, the sleeve
is cooled by a water ﬁ lm ﬂ owing down on an outer sur-
face of the sleeve. After contact of the water with sleeve
further swelling stops because on the sleeve surface the
polymer solidiﬁ es almost instantaneously .
The cooling system efﬁ ciency (the intensity and uni-
formity of cooling) determines essentially the production
line productivity and quality of the ﬁ lm. Thus, simulation
of this process that allows substantiation of the effective
mode of the cooling is of great importance.
In most papers devoted to mathematical modeling
of the cooling of the sleeve plastic ﬁ lm, a possibility
of determining the average temperature across the
ﬁ lm thickness is examined [2, 3]. Such an approach is
acceptable only for an analysis of the cooling process of
thin ﬁ lms.
The ﬁ lm ﬂ owing of liquid under the force of gravity
is characterized by a presence of a section with a laminar
character of the ﬂ uid ﬂ ow and within which the cooling
of the sleeve is ﬁ nished. In this regard, it is possible
to describe the process by the convective heat transfer
equations for laminar ﬂ uid ﬂ ow.
To develop a mathematical model we choose a ﬁ xed
coordinate system with an origin in a cross section of
the water contact with the sleeve surface (Fig. 1). Since
the thickness of the sleeve wall (the ﬁ lm thickness) is
much smaller than its diameter, then the process will be
considered in a rectangular coordinate system.
The equation of motion for the ﬁ lm of ﬂ uid ﬂ ow
under gravity has the form
is a water density, kg m
; μ, water viscosity,