Theoretical Analysis of Brush Seals Leakage Using Local Computational Fluid Dynamics Estimated Permeability Laws

Brush seals are a mature technology that has generated extensive experimental and theoretical work. Theoretical models range from simple correlations with experimental results to advanced numerical approaches coupling the bristles deformation with the flow in the brush. The present work follows this latter path. The bristles of the brush are deformed by the pressure applied by the flow, by the interference with the rotor and with the back plate. The bristles are modeled as linear beams but a nonlinear numerical algorithm deals with the interferences. The brush with its deformed bristles is then considered as an anisotropic porous medium for the leakage flow. Taking into account, the variation of the permeability with the local geometric and flow conditions represents the originality of the present work. The permeability following the principal directions of the bristles is estimated from computational fluid dynamics (CFD) calculations. A representative number of bristles are selected for each principal direction and the CFD analysis domain is delimited by periodicity and symmetry boundary conditions. The parameters of the CFD analysis are the local Reynolds number and the local porosity estimated from the distance between the bristles. The variations of the permeability are thus deduced for each principal direction and for Reynolds numbers and porosities characteristic for brush seal. The leakage flow rates predicted by the present approach are compared with experimental results from the literature. The results depict also the variations of the pressures, of the local Reynolds number, of the permeability, and of the porosity through the entire brush seal.