Calculation of hydrostatic forces of multi-gap seals and its dependence on shaft displacement

Abstract

Using the finite volume method, the problem of a three-dimensional fluid flow through a three-shaft seal of a high pressure centrifugal pump at different values of radial shaft displacements has been solved. Numerical calculations were carried out without taking into account deformation of seals under the influence of uneven pressure distribution. Pressure distributions, leakage values and hydrodynamic radial forces were obtained depending on the magnitude of the eccentricity. As a result of numerical calculations, the dependences of the radial forces on the radial shaft displacement were constructed and the hydrostatic stiffness coefficient was determined. These dependencies were also obtained using analytical equations. The obtained numerical results differ from the theoretical ones less than 5%. It should also be noted that the application of the three-gap seal significantly reduces leakage compared to homogeneous and double-layer seals, as well as increases the radial force stiffness, which in its turn provides a low level of rotor vibration.