ANZIAM J. 46(E) ppC167--C180, 2005.

Modelling blockage effects using a spectral element method

M. D. Griffith

K. Hourigan

M. C. Thompson

(Received 27 October 2004, revised 1 March 2005)

Abstract

We employ a two-dimensional spectral element method to investigate the effect of various semi-circular blockages on the laminar flow between two flat plates. This simplified geometry has a general relevance to blocked flows, but more academically, also relates to work on the backward-facing step, presenting a qualitatively similar flow with a single, independent step, or blockage, parameter. The parameter space for Reynolds number between 50 and 3000, and blockage ratio ranging from 0.05 to 0.9 is mapped out. The results with blockage ratio of 0.5 compare favourably with previous work on the flow over a backward-facing step, with the analysis suggesting that the onset of three-dimensionality in the flow is likely to be closely matched. Flow phenomena associated with blockage ratios above and below the customary half-blockage are summarised, including smaller than expected flow separation lengths for lower blockages, and vortex shedding and unusual structures within the recirculation zones for higher blockages.

Download to your computer

Authors

M. D. Griffith
K. Hourigan
M. C. Thompson
Dept. Mechanical Engineering, Monash University, Melbourne, Australia. martin.griffith@eng.monash.edu.au

Published April 21, 2005. ISSN 1446-8735

References

  1. Armaly, B. F., Durst, F., Pereira, J. C. F. and Schoenung B., Experimental and theoretical investigation of backward-facing step flow, J. Fluid Mech., 127, 1983, 473--496.
  2. Barkley, D., Gomes, M. G. M. and Henderson, R. D., Three-dimensional instability in flow over a backward-facing step, J. Fluid Mech., 473, 2002, 167--190. http://dx.doi.org/10.1017/S002211200200232X
  3. Kaiktis, L., Karniadakis, G. E. and Orszag, S. A., Onset of three-dimensionality, equilibria, and early transition in flow over a backward-facing step, J. Fluid Mech., 231, 1991, 501--528.
  4. Kaiktis, L., Karniadakis, G. E. and Orszag, S. A., Unsteadiness and convective instabilities in two-dimensional flow over a backward-facing step, J. Fluid Mech., 321, 1996, 157-187.
  5. Sahin, M. and Owens, R. G., A numerical investigation of wall effects up to high blockage ratios on two-dimensional flow past a confined circular cylinder, Phys. Fluids, 16, 2004, 1305--1320. http://dx.doi.org/10.1063/1.1668285
  6. Sheard, G. S., Thompson, M. C. and Hourigan, K., From spheres to circular cylinders: classification of bluff ring transitions and structure of bluff ring wakes, J. Fluid Mech., 492, 2003, 147--180. http://dx.doi.org/10.1017/S0022112003005512
  7. Thompson, M. C., Hourigan, K. and Sheridan, J., Three-dimensional instabilities in the wake of a circular cylinder, Exp. Therm. Fluid Sci., 12, 1996, 190--196. http://dx.doi.org/10.1016/0894-1777(95)00098-4
  8. Williams, P. T, and Baker, A. J., Numerical simulations of laminar flow over a 3D backward-facing step, Int. J. Numer. Methods Fluids, 24, 1997, 1159--1183. http://www3.interscience.wiley.com/cgi-bin/abstract/61002259
Copyright Austral. Mathematical Soc.; prepared April 21, 2005, from Grif.tex with anziamje.sty (v2.3c)