Computation of magnetic liquid flow in annular channel of magnetic-fluid seal of a shaft with high-speed wall

Aeronautical and Space-Rocket Engineering

Thermal engines, electric propulsion and power plants for flying vehicles


Аuthors

Marchukov E. Y.1*, Polyakov K. S.2, Kulalaev V. V.3**, Petrienko V. G.2***

1. ,
2. Lyulka Experimental Design Bureau, branch of the United Engine Corporation – Ufa Engine Industrial Association, 13, Kasatkina str., Moscow, 129301, Russia
3. Lyulka Desing Bureau, 13, Kasatkina str., Moscow, 129301, Russia

*e-mail: kaf205@mail.ru
**e-mail: kulalayev.viktor@gmail.com
***e-mail: viktor.petrienko@okb.umpo.ru

Abstract

Purposes and objectives of the article consist in the following: formulating hydrodynamic boundary problem of computation of magnetic-fluid seal (MFS) parameters, which belong to the group of noncontact slot seals operating as a hydraulic lock. While developing MFS the annular packets of conducting magnetic brushes were used as magnetic field concentrators instead of teeth. A magnetic fluid resides between the bristles of these brushes in a narrow annular channel. Such a seal gives the minimum friction between the interfaced parts. Numerous calculation methods for the abovementioned hydrodynamic boundary problems developed historically almost independently from each other. General principles for creating numerical methods acceptable for all hydrodynamic boundary problems in general were slated. The aggregate of these concepts and methods allows eventually reduce the algorithm for solving complex hydrodynamics boundary problems to algorithms for solving simple problems of standard structure. An integral relations method employed in this work was developed based on conservation laws and eventually reduced to ordinary differential equation solving. At the domain boundary herewith the boundary conditions are specified both at the rigid wall and the boundaries through which the flow inflows and outflows. Additionally, adhesion conditions are specified. The presented article formulates the new boundary conditions of tracking-concatenation of viscous incompressible flow for internal flows in narrow annular channels. It gives mathematical formulation of the boundary problem for viscous incompressible magnetic flow with possible internal backflows, which detection experimentally is impossible. The boundary problem was set and algorithm for computation of viscous magnetic liquid flow field in the annulus with movable walls of the magnetic-fluid seal (MFS) by the structured method with the exact fulfillment of the boundary and initial conditions was presented.

The article shows that application of mathematical apparatus for solving the boundary problems by the structured method allows calculate in total parameters of the magnetic liquid flow: heat flows, coefficients of friction, heat transfer and distribution of these parameters through the radial clearance of annulus, revealing the areas of potential backflows.

The results of this work may be useful while developing and computing new type of magnetic-fluid seals (MFS) for high-speed shafts of structures and units for various industrial purposes.

Keywords:

magnetic-fluid sealing, bounded cylindrical annulus, swirling flow, sewing function, matrix, boundary problem

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