Original Research

The computation of flow in a rotating annulus by the method of artificial compressibility

H. Grobler, J. A. Snyman
Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie | Vol 6, No 1 | a940 | DOI: https://doi.org/10.4102/satnt.v6i1.940 | © 1987 H. Grobler, J. A. Snyman | This work is licensed under CC Attribution 4.0
Submitted: 17 March 1987 | Published: 17 March 1987

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H. Grobler,, South Africa
J. A. Snyman,, South Africa

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Abstract

The flow of an incompressible viscuous fluid is studied via the numerical solution of the discretised continuity and Navier-Stokes governing equations. In particular flow in an annulus formed by two coaxial cylinders, each of which may rotate with respect to the other, and where a pressure drop is prescribed over the lengths of the cylinders, is considered. As method of solution Chorin’s method of artificial compressibility is applied in which the time-independent governing equations are transformed into time-dependent auxiliary equations via the introduction of an artificial equation of state. The solution of the auxiliary equations converges to a stationary solution which corresponds to the solution of the original time-independent equations. The behaviour of the fluid, once fully developed laminar flow is reached, is successfully computed. A simple model is also proposed by which the development of flow along the annulus may be computed for any given inflow velocity profile. The computed results are in agreement with what one would expect from the physics of the problem.

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