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Control of a surface of discontinuity in continuous thickness

Published online by Cambridge University Press:  17 February 2009

N. G. Barton ,
C.-H. Li  and
S. J. Spencer
N. G. Barton
Affiliation:
CSIRO Division of Mathematics and Statistics, P.O. Box 218, Lindfield, NSWAustralia2070.
C.-H. Li
Affiliation:
CSIRO Division of Mathematics and Statistics, P.O. Box 218, Lindfield, NSWAustralia2070.
S. J. Spencer
Affiliation:
CSIRO Division of Mathematics and Statistics, P.O. Box 218, Lindfield, NSWAustralia2070.
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Abstract

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This paper examines the control of an interface between a suspension of sedimenting particles in liquid and a bed of dense-packed particles at the bottom of the suspension. The problem arises in the operation of continuous thickeners (e.g. in mineral processing) and is here mathematically described by a first order inhomogeneous partial differential equation for the concentration C(x, t) of particles. The controlled variable is the height H* of the bed, and the control variables are the volume fluxes injected at the feed level and removed at the bed. A strategy to control the interface is devised, and control is confirmed and demonstrated by a series of numerical experiments.

Type
Research Article
Information
The ANZIAM Journal , Volume 33 , Issue 3 , January 1992 , pp. 269 - 289
Copyright
Copyright © Australian Mathematical Society 1992

References

[1] Auzerais, F. M. et al. , “The resolution of shocks and the effects of compressible sediments in transient settling”, J. Fluid Mech. 195 (1980) 437–462.CrossRefGoogle Scholar
[2] Barton, N. G. et al. , “Sedimentation in concentrated suspensions”, Xth Int. Congress of Rheology, Sydney (1988) 173–176.Google Scholar
[3] Barton, N. G. et al. , “Experimental and theoretical studies of the sedimentation of concentrated suspensions”, Proc. 5th Australasian Conf. on Heat and Mass Transfer, Christchurch, (1989).Google Scholar
[4] Boris, J. P. and Book, D. L., “Flux-corrected transport. III. Minimal-error F.C.T. algorithms“, J. Comp. Physics 20 (1976) 397–431.CrossRefGoogle Scholar
[5] Carrier, G. F. and Pearson, C. E., Partial differential equations. Theory and technique, (Academic Press, New York, 1976).Google Scholar
[6] Courant, R. and Hilbert, D., Methods of mathematical physics Vol. 2, (J. Wiley, New York, 1962).Google Scholar
[7] Dixon, D. C., “Momentum-balance aspects of free-settling theory. I. Batch thickening”, Separation Science 12 (1977) 171–191.CrossRefGoogle Scholar
[8] Fitch, B., “Batch tests predict thickener performance”, Chemical Engineering August 23, (1971) 83–88.Google Scholar
[9] Fitch, B., “Kynch theory and compression zones”, AIChE J. 29 (1983) 940–947.CrossRefGoogle Scholar
[10] Fryer, C. and Uhlherr, P. H. T., “Continuous thickeners—behaviour and design”, Eighth Aust. Chem. Eng. Conf., Melbourne (1980) 80–84.Google Scholar
[11] Howells, I. et al. , “Time-dependent batch settling of flocculated suspensions”, Appl. Math. Modelling Vol. 14 (1990) 77–86.CrossRefGoogle Scholar
[12] Kynch, G. J., “A theory of sedimentation” Trans. Faraday Soc. 48 (1952) 166–176.CrossRefGoogle Scholar
[13] Landman, K. A., White, L. R. and Buscall, R., “The continuous-flow gravity thickener steady state behavior”, AIChE J. 34 (1988) 239–252.CrossRefGoogle Scholar
[14] Morrow, R. and Steinle, P., “Implicit flux-corrected transport” in Computational Techniques and Applications: CTAC-87, (eds. Noye, J. and Fletcher, C.), (Hemisphere Publishing, New York, 1988) 499–508.Google Scholar
[15] Park, K. H., Andrews, J. R. G. and Uhlherr, P. H. T., “Batch sedimentation and thickener behaviour”, Proc. 3rd Pacific Chem. Eng. Congress Vol. 1 (1983) 100–105.Google Scholar
[16] Spencer, S. J., Jenkins, D. R. and Barton, N. G., “Modelling of batch and continuous sedimentation of suspensions”, in Computational Techniques and Applications: CTAC- 89 (eds. Hogarth, W. L. and Noye, B. J.), (Hemisphere, New York, 1989) 501–508.Google Scholar
[17] Spencer, S. J., “Modelling of continuous sedimentation of suspensions”, Technical Report NSW 89/22 (CSIRO Division of Mathematics and Statistics, Sydney, 1990).Google Scholar
[18] Steinle, P. and Morrow, R., “An implicit flux-corrected transport algorithm”, J. Comp. Physics 80 (1989) 61–71.CrossRefGoogle Scholar
[19] Tiller, F. M., “Revision of Kynch sedimentation theory”, AIChE J. 27 (1981) 823–829.CrossRefGoogle Scholar
[20] Zalesak, S. T., “Fully multidimensional flux-corrected transport algorithms for fluids”, J. Comp. Physics 31 (1979) 335–362.CrossRefGoogle Scholar