Levy, R.

Viscous Primary / Secondary Flow Analysis for Use with Nonorthogonal Coordinate Systems

Levy R., Briley W.R., McDonald H.

Published in 1983

Three-dimentional viscous subsonic flow in complex ducted geometries are investigated by a numerical procedure which allows solution by spatial forward-marching integration, utilizing flow approximations from the velocity-decomposition approach of Briley, McDolald and Kreskovsky. The present analysis extends this approach to encompass complex ducted geometries which may have curved and twisted centerlines, variable cross sectional area and shape, and which require the use of non-orthogonal body-fitted coordinate systems. To address these geometries, a smooth reference line (e.g., a duct centerline) is identified which represents the primary flow direction and thus links the geometry with the flow approximations.

An orthogonal reference coordinate system is then derived, which fits both the reference line and its normal planes, and which remains orthogonal even when the reference line has nonzero torsion. The flow approximations are made in this reference coordinate system and the govering equations are then transformed to a body-fitted coordinate system and solved numerically. The use of planar cross sections and of fluxes aligned with the reference coordinates simplifies the final equations. A numerical solution procedure is outlined, and computed results are compared with experiment for laminar and turbulent flow in circular pipes having both a 180 degree bend and a 22.5/22.5 degree S-bend, and in a straight transition duct whose cross section varies from nearly square to circular. Predictions of primary and secondary velocity components for these flows are very good for laminar flow, and in light of the relatively simple turbulence model used, are generally good for turbulent flows.

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