Feeding System of Aerostatic Bearings With Porous Media

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 supply systems. Cylindrical sintered bronze inserts featuring lengths, diameters and particle sizes commonly used in gas bearings and thrust pads were examined. The paper describes the test set-up and experimental results obtained for: a) Mass flow rate through single porous resistances at different upstream and downstream pressures; and b) 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 set-up a) 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 set-up b) were compared with those from set-up a) at the same pressure differentials across the insert.