Permeability and Inertial Coefficients of Porous Media for Air Bearing Feeding Systems

Abstract

In porous resistances, Darcy’s law provides a good approximation of mass flow rate when the differences between upstream and downstream pressures are sufficiently small. In this range, the mass flow rates are proportional to the porous resistance’s permeability. For gas bearings, the pressure difference is normally higher, and it is known experimentally that the mass flow rates are lower than would result from Darcy’s law. Forchheimer’s law adds an inertial term to Darcy’s law and, when an appropriate coefficient is selected for this term, provides a good approximation of flow rates for the same applications even with the highest pressure differences. This paper presents an experimental and theoretical investigation of porous resistances used in gas bearing and thrust pad supply systems. The porous resistances considered in the investigation were made by sintering bronze powders with different grain sizes to produce cylindrical inserts that can be installed in bearing supply devices. The paper describes the test setup and experimental results obtained for: (i) mass flow rate through single porous resistances at different upstream and downstream pressures and (ii) mass flow rate and pressure distribution on a pneumatic pad featuring the same porous resistances. The theoretical permeability of the chosen porous resistances was calculated, and the results from setup (i) were then used to obtain experimental permeability and to determine the inertial coefficients. The results, which are expressed as a function of the Reynolds number, confirmed the validity of using Forchheimer’s law. The mass flow rates from setup (ii) were compared to those from setup (i) at the same pressure differentials across the resistance.