Resumen:
В рамках физической линеаризации уравнений Навье–Стокса об однонаправленном аксиальном ламинарном течении ньютоновской жидкости
найдено аналитическое решение задачи идентификации поля скоростей во
входной области кольцевого канала, что позволило получить в явном виде
соотношение для расчета длины начального гидродинамического участка. In the frameworks of physical linearization of the Navier-Stokes equations in a cylindrical coordinates
system on the one-way axial force-feed laminar flow of Newtonian fluid, a mathematical model of
the flow development in the entrance region of a horizontal annular channel is formulated. The unknown
constant gradient of pressure along the channel is connected with the equation of continuity written in an
integral form of stability of liquid flow in any cross section of a channel. Use of the one-way integral
Laplace transformation along the longitudinal coordinate allowed to obtain an analytical expression of
the local hydrodynamic field at the entrance region and determine pressure losses coincided with the
classic data. Analysis of the characteristic structure of the hydrodynamic field of dimensionless velocities
at the entrance region showed that for small values of the ratio of the radii of the inner and outer coaxial
cylindrical tubes constituting the annular channel, asymmetry of the longitudinal velocity profile is
observed with a shift of the maximum value towards the surface of a coaxial cylinder of smaller radius,
and an increase in the Reynolds number practically linearly increases the length of the hydrodynamic
entrance region. Assumption about the absence of drift of the radial coordinate of the maximum velocity
in the entrance hydrodynamic region, limited to the so-called "regular" regime, made it possible to identify
the length of the entrance hydrodynamic region in the annular channel by the completed expression
in an explicit form that correlates with the classical estimates obtained as a result of computational experiments.
It is noted that when the ratio of the radii of the inner and outer coaxial cylinders approaches
zero or infinity (corresponding to particular cases of a circular tube and a flat channel), the known results
for the lengths of the entrance hydrodynamic regions are obtained. Difference between velocity
values calculated by the proposed model and experimental values in the region adjacent to the entry section
is explained by the fact that kinetic energy of the liquid flow is not accounted for by leveling the
pressure inhomogeneity along the channel cross-section. Nonetheless, it is shown that it does not have a
significant influence on the length of hydrodynamic entrance region.
Descripción:
А.В. Ряжских,
Воронежский государственный технический университет, г. Воронеж, Российская Федерация
E-mail: ryazhskihav@bk.ru. A.V. Ryazhskikh
Voronezh State Technical University, Voronezh, Russian Federation
E-mail: ryazhskihav@bk.ru
