Application of power addition as modelling technique for flow processes: Two case studies

Date
2011
Authors
De Wet P.
Prieur du Plessis J.
Woudberg S.
Journal Title
Journal ISSN
Volume Title
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Abstract
In many of the continuum processes typically found in chemical engineering, the functional dependency of the dependent variable is only known for large and small values of the independent variable. Exact solutions in the transitional regime are often obscure for various reasons (e.g. narrow band within which the transition from one regime to the other occurs, inadequate knowledge of the physics in this area, etc.). An established method for the matching of limiting solutions is reviewed and subsequently applied. The method regards the known solutions as asymptotes and proposes addition to a power of such asymptotes. It yields a single, adjustable correlating equation that is applicable over the entire domain. This procedure circumvents the introduction of ad hoc curve fitting measures for the different regions and subsequent, unwanted discontinuities in piece-wise fitted correlative equations for the dependent variables. Experimental data of two diverse processes, namely flow in a straight-through diaphragm valve and the fluidisation of a packed bed, are analysed as case studies. Empirical results are investigated for possible asymptotic bounds whereafter power addition is applied to the functional dependencies. The outcome is compared to those of the empirical models and the results discussed. The procedure is revealed to be highly useful in the summarising and interpretation of experimental data in an elegant and simplistic manner. It may also, in general, aid the setup of experimental apparatus for investigation of continuum processes. © 2011 Elsevier Ltd.
Description
Keywords
Asymptotic bounds, Continuum process, Correlating equations, Dependent variables, Diaphragm valves, Empirical model, Empirical results, Entire domain, Exact solution, Experimental apparatus, Experimental data, Flow process, Fluidisation, Functional dependency, Independent variables, Mathematical modelling, Modelling techniques, Narrow bands, Non-Newtonian fluids, Piece-wise, Porous Media, Curve fitting, Flow measurement, Fluidization, Non Newtonian flow, Non Newtonian liquids, Packed beds, Porous materials, Rheology, Slurries, Viscous flow, Mathematical models
Citation
Chemical Engineering Science
66
9