The work presented here is a preliminary study of the Mach number effect based on the usual lubrication assumptions except, for the retention of convective terms in the equations of motion. The essential step in this analysis is to adopt the momentum integral method, i.e., to assume a velocity profile satisfying the prescribed boundary conditions. The first attempt is to assume a second-order polynomial for the velocity profile. Although this may not be able to give a sufficient detail of the velocity field. Nevertheless, the results should, hopefully, give us some more insight into this problem. Analytical results based on perturbation theory are presented for journal, slider, and step bearings. Numerical results for a plane slider are also presented here. All results indicate that when a dimensionless mean speed parameter, namely, the modified Mach number, approaches to unity the pressrue field converges very quickly to the limiting solution ph = constant even at moderate values of the compressibility number. In addition, both small perturbation analysis and numerical results reveal that under some circumstances, e.g., in a plane slider, the pressure boundary condition at the trailing edge should be modified in order to obtain a physically meaningful solution.
A Qualitative Study of Gas Bearings Operating at High Subsonic and Supersonic Tangential Speeds
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Constantinescu, V. N., and Hsing, F. C. (December 1, 1971). "A Qualitative Study of Gas Bearings Operating at High Subsonic and Supersonic Tangential Speeds." ASME. J. Appl. Mech. December 1971; 38(4): 803–812. https://doi.org/10.1115/1.3408958
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