Abstract
This paper investigates the steady slow flow of an incompressible viscous fluid in the region between an inner circular cylinder rotating with constant angular velocity and an outer stationary cylinder of arbitrary cross section. The numerical solution technique known as the boundary integral equation method is employed in which the governing partial differential equations of motion are recast into coupled integral equations by repeated applications of the divergence theorem.
The method is applied to the two dimensional flow within the eccentric journal bearing, and it is found that certain aspects of previous analytic treatments of this bearing have been in error. An extension of the method is applied to solve for the flow within an elliptical bearing, for which no analytic solution or numerical results are available. This extension is able to solve for the flow within any bearing geometry, however complex.
It is found that the present method is particularly suited to the prediction of flow separation within noncircular bearings, and it is hoped that these results and techniques will lead to a better understanding of the conditions causing the phenomenon of cavitation.
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References
WANNIER, G.H., Hydrodynamics of lubrication, Q. appl. Math., Vol.8, pp.7–32, 1950.
KAMAL, M.M., Separation in the flow between eccentric rotating cylinders, Trans. ASME J. Basic Engrg., Vol.D88, pp.717–724, 1966.
DiPRIMA, R.C. and STUART, J.T., Flow between eccentric rotating cylinders, Trans. ASME J. Lub. Tech., Vol.94, pp.266–274, 1972.
JEFFERY, G.B., Plane stress and plane strain in bipolar coordinates, Phil. Trans., Vol.A221, pp.265–293, 1921.
PINKUS, O. and STERNLICHT, B., Theory of Hydrodynamic Lubrication, McGraw-Hill, New York, 1961.
ALLAIRE, P.E., Design of journal bearings for high speed rotating machinery, Proc. Design Engrg. Conf., pp.45–84, Chicago, Illinois, (S.M.Rohde, C.J.Maday and P.E.Allaire, Eds.), ASME, 1979.
CASTELLI, I.V. and SHAPIRO, W., Improved methods for numerical solutions of the general incompressible fluid film lubrication problem, Trans. ASME J. Lub. Tech., Vol.89, pp.211–218, 1967.
BREWE, D.E., HAMROCK, B.J. and TAYLOR, C.M., Effect of geometry on hydrodynamic film thickness, Trans. ASME J. Lub. Tech., Vol.101, pp.231–239, 1979.
HARGREAVES, D.J. and TAYLOR, C.M., The determination of lubricant flowrate from a static grooved rectangular thrust bearing using a stream function formulation, J. Mech. Eng. Sci., Vol.24(1), pp.51–53, 1982.
WADA, S., HAYASHI, H. and MIGITA, M., Application of the finite element method to hydrodynamic lubrication problems. Part 1: infinite width bearings, Bull. JSME, Vol.14(77), pp.1222–1233, 1971.
BOOKER, J.F. and HUEBNER, K.H., Application of finite element methods to lubrication: an engineering approach, Trans. ASME J. Lub. Tech., Vol.94, pp.313–323, 1972.
HAYASHI, H. and TAYLOR, C.M., A determination of cavitation interfaces in fluid film bearings using finite elements analysis, J. Mech. Eng. Sci., Vol.22(6), pp.277–285, 1980.
MIR-MOHAMAD-SADEGH, A. and RAJAGOPAL, K.R., The flow of a non-newtonian fluid past projections and depressions, Trans. ASME J. Appl. Mech., Vo.47(3), pp.485–488, 1980.
KELMANSON, M.A., Modified integral equation solution of viscous flows near sharp corners, Comput. Fluids, Vol.11(4), pp.307–324, 1983.
KELMANSON, M.A., Boundary integral equation solution of viscous flows with free surfaces, J. Eng. Math., Vol.17(4), pp.329–343, 1983.
MILLER, C.W., Numerical solution of 2-D potential theory problems using integral equation techniques, Ph.D. thesis, University of Iowa, 1979.
LANGLOIS, W.E., Slow Viscous Flow, MacMillan, New York, 1964.
SPIEGEL, M.R., Vector Analysis, McGraw-Hill, London, 1974.
SMITH, G.D., Numerical Solution of Partial Differential Equations: Finite Difference Methods, Clarendon Press, Oxford, 1978.
PINKUS, O., Analysis of elliptical bearings, Trans. ASME, Vol.78, pp.965–974, 1956.
MANZOOR, M., Heat flow through extended surface heat exchangers, Ph.D. thesis, University of Leeds, 1982.
BREBBIA, C.A., TELLES, J.C.F AND WROBEL, L.C., Boundary Element Techniques: Theory and Applications in Engineering, Springer Verlag, Berlin and New York, 1984.
FAIRWEATHER, G., RIZZO, F.J., SHIPPY, D.J. and WU, Y.S., On the numerical solution of two dimensional potential problems by an improved boundary integral equation method, J. Comput. Phys., Vol.31(1), pp.96–111, 1979.
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© 1984 Springer-Verlag Berlin, Heidelberg
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Ingham, D.B., Kelmanson, M.A. (1984). A Boundary Integral Equation Method for the Study of Slow Flow in Bearings with Arbitrary Geometries. In: Boundary Integral Equation Analyses of Singular, Potential, and Biharmonic Problems. Lecture Notes in Engineering, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82330-5_6
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DOI: https://doi.org/10.1007/978-3-642-82330-5_6
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