Spline method for solving continuous batch grinding and similarity equations
作者： R.C. Everson , D. Eyre , Q.P. Campbell
DOI: 10.1016/S0098-1354(97)88492-X
关键词:
摘要: This paper investigates a numerical technique using cubic splines for solving the continuous batch grinding equation. The same approach is also used to solve similarity equation in case where breakage function has more complicated form than that which analytical solutions are available. In of spline coefficients obtained from solution an algebraic generalized eigenvalue problem. Numerical simplified selection and functions compared with those order assess validity procedures. Experimental results limestone ore test model. method evaluated gold bearing body.
elsevier.com
sci-hub.se 参考文章(13)
H.M. Hulburt, S. Katz, Some problems in particle technology: A statistical mechanical formulation Chemical Engineering Science. ,vol. 19, pp. 555- 574 ,(1964) , 10.1016/0009-2509(64)85047-8
D. Ramkrishna, The Status of Population Balances Reviews in Chemical Engineering. ,vol. 3, pp. 49- 95 ,(1985) , 10.1515/REVCE.1985.3.1.49
L. Austin, K. Shoji, V. Bhatia, V. Jindal, K. Savage, R. Klimpel, Some Results on the Description of Size Reduction as a Rate Process in Various Mills Industrial & Engineering Chemistry Process Design and Development. ,vol. 15, pp. 187- 196 ,(1976) , 10.1021/I260057A032
D. Ramkrishna, Solution of population balance equations Chemical Engineering Science. ,vol. 26, pp. 1134- 1136 ,(1971) , 10.1016/0009-2509(71)80030-1
Q.P. Campbell, R.C. Everson, D. Eyre, H.J. Spamer, Spline solution of the continuous batch grinding equation Minerals Engineering. ,vol. 8, pp. 377- 387 ,(1995) , 10.1016/0892-6875(95)00003-9
Fred Gelbard, John H. Seinfeld, Numerical solution of the dynamic equation for particulate systems Journal of Computational Physics. ,vol. 28, pp. 357- 375 ,(1978) , 10.1016/0021-9991(78)90058-X
P.C. Kapur, Self-preserving size spectra of comminuted particles Chemical Engineering Science. ,vol. 27, pp. 425- 431 ,(1972) , 10.1016/0009-2509(72)85079-6
Carl de Boor, On calculating with B-splines Journal of Approximation Theory. ,vol. 6, pp. 50- 62 ,(1972) , 10.1016/0021-9045(72)90080-9
D. Eyre, Spline-Galerkin Solution of Dynamic Equations for Particle Comminution and Collection Journal of Computational Physics. ,vol. 120, pp. 305- 315 ,(1995) , 10.1006/JCPH.1995.1166
Thomas W. Peterson, Similarity Solutions for the Population Balance Equation Describing Particle Fragmentation Aerosol Science and Technology. ,vol. 5, pp. 93- 101 ,(1986) , 10.1080/02786828608959079