Analysis of a compliant gas foil seal with turbulence effects

Abstract

A method is presented to include the turbulence effects in fluid flow analysis of a high speed compliant gas foil seal (CFS). The method takes into account certain wellestablished facts concerning turbulent shear flow. The compressible fluid flow field is assumed to depend on local film thickness, surface velocity, pressure gradient and surface compliance. The non-linear effects due to compliance of the flow boundaries, compressibility of the fluid, and coupling of the shear induced circumferential flow and pressure driven axial flow are considered. The turbulence effect is accounted for using non-linear coefficients in the coupled compressible governing equations of the flow pressure and film thickness. The computational method employs the successive overrelaxation (SOR) method for solving the governing equations of the flow field and fluid film thickness. No optimization study has been conducted for the rate of convergence in the numerical analysis. The relaxation factor is found to be a key parameter in convergence solution when the compliant foil seal is operating at high speed, high eccentricity ration or low differential pressure across the seal. It is found that due to non-symmetric boundary condition, the method of Column Matrix which is used for compliant foil bearing did not result in a convergence solution. INTRODUCTION Compliant foil bearings are used in a wide variety of rotating machinery, including air cycle machines, cryogenic turbo-expanders and gas turbine engines to name a few. Their application offers performance and reliability improvements through the elimination of oil and the lubricant supply system. A compliant foil seal (CFS), similar to a compliant foil bearing (CFB), is a selfacting hydrodynamic mechanical components that develop a high pressure gas film. This generated gas film ultimately has sufficient load capacity to separate the seal top surface from the rotating journal, thus permitting continuous non-contacting operation. The basic configuration of a CFS is shown schematically in Figure 1. The thin high pressure gas film is formed between the surface of a rotor (or a journal) and the top foil. With the proper choice of structural compliance, the seal surface deformation can be tailored to deform in a manner that enhances the seal performance. For example, the compliant seal design can be tailored to form a variable axial converging wedge shape for improved sealing performance. In the previous work by Salehi et al. (1999) computational analysis of a CFS was addressed. The combined hydrodynamic and structural governing equations were solved simultaneously using finite difference method. This coupled structural and hydrodynamic analysis excluded the stiffness contribution of the top foil but did account for the influence of the top foil on individually calculated nodal deflections due to pressure. Since the Foil y^i-i | j j 1 1 ) 11^<