Title: Simulation of developing flow through rotating channel using Q₁Q₀ finite elements

Authors: Krishnan V. Pagalthivarthi, Pankaj K. Gupta

Addresses: Department of Applied Mechanics, Indian Institute of Technology, Delhi, New Delhi-110016, India. ' Department of Applied Mechanics, Indian Institute of Technology, Delhi, New Delhi-110016, India

Abstract: Galerkin Finite Element Method with Q₁Q₀ (bilinear velocity-constant pressure) elements is shown to efficiently and reliably solve the elliptic equations governing developing mean flow in a channel rotating in orthogonal mode. This approach departs from the (partially) parabolic finite volume methods previously used in the literature for this classical problem. Combined quasi-Newton|s iteration is used to simultaneously solve for velocity and pressure fields. The possible checkerboard effect of pressure field resulting from the use of Q₁Q₀ elements is remedied by using: (1) a graded mesh and (2) a least squares solution for the pressure field from the velocity field. Rotation-modified eddy viscosity and wall functions are introduced. Results indicate good mesh independence, agreement with solutions using Q₂Q₁ elements, and compare favourably with experiments. In particular, a significant experimental result that the pressure-side friction velocity reaches a saturation limit beyond a certain distance along the channel (i.e., beyond a critical local rotation number) is well predicted by the present study.

Keywords: developing flow; Galerkin Finite Element Method; Q₁Q₀ elements; rotating channel; rotation-modified eddy viscosity; rotation-modified wall functions.

DOI: 10.1504/PCFD.2004.004602

Progress in Computational Fluid Dynamics, An International Journal, 2004 Vol.4 No.6, pp.285 - 298

Published online: 26 May 2004 *

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