Numerical comparison of two methods for predicting the porous gas bearing pressure

In this work, the numerical analysis of the modified Reynolds equation is compared. The difference between the two analyses is the porous media flow equation; the first considers the Darcy model, and the other the Darcy–Forchheimer model. The solution algorithms were developed using finite center differences for the geometric variable. This numerical scheme resulted in a non-linear set of equations solved with the Newton–Raphson method. Due to the nonlinearity of the problem, the relationship between the steps between axial and circumferential dimensions and the initial assumption is the main conditions for the solution to converge; the precision of the results obtained, in comparison with previous works, was acceptable; this contributes an additional effort in the development of the technology of the porous gas bearings. This work analyzed the differences in predicting the static behavior of a porous gas bearing using the Darcy model and the extended Darcy–Forchheimer model to determine the flow behavior through the porous medium. The solution algorithm of the modified Reynolds equation with the Darcy–Forchheimer model offers a broader range of solutions because it is capable of predicting both the linear and non-linear behavior of the flow through the porous medium and the influence in the lubricant film; this is essential for the design of porous gas bearings for industrial applications. The Finite Difference solutions are compared with a Finite Element and Finite Volume solution. The results show similar approximations with the advantage that the finite difference solution is more straightforward and can be coupled with a dynamic lump-mass model.