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ON VISCOUS FLOW IN CURVED PIPES OF NON‐UNIFORM CROSS‐SECTION
Author(s) -
ROBERTSON A. M.
Publication year - 1996
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19960430)22:8<771::aid-fld379>3.0.co;2-5
Subject(s) - laminar flow , cross section (physics) , mechanics , piping , flow (mathematics) , curvature , pipe flow , geometry , radius , radius of curvature , flow conditioning , newtonian fluid , section (typography) , mathematics , physics , turbulence , reynolds number , thermodynamics , computer science , mean curvature flow , mean curvature , quantum mechanics , operating system , computer security
This paper is concerned with steady, laminar flow of an incompressible Newtonian fluid in curved pipes of non‐uniform cross‐section. During the past decade a number of numerical solutions for flow in curved pipes have been obtained using progressively improved computational methods and technology; see e.g. Soh and Berger ( Int. j. numer. methods fluids, 7 , 733–755 (1987)) and Green et al . ( Phil. Trans. R. Soc. Lond. A, 342 , 543–572 (1993)) for relevant references. These results have been confined mainly to fully developed flow in pipes of constant cross‐section. The present study deals with curved pipes of variable cross‐section in which the velocity field is necessarily a function of the axial location along the pipe centreline in addition to the two cross‐sectional co‐ordinates. We use the finite difference method on a staggered grid with Newton's method to solve the Navier–Stokes equations. Results are calculated and presented for non‐uniform pipe geometries with curvature ratios of 0ċ01 and 0ċ1. The velocity field for flow through curved pipes of non‐uniform cross‐section is compared with the corresponding results for flow through straight pipes of non‐uniform radius and curved pipes of uniform radius, revealing important qualitative differences. The basic developments presented are applicable to a variety of flows in pipes, including those in arteries and piping systems.