Powered addition as modelling technique for flow processes

[摘要] ENGLISH ABSTRACT: The interpretation – and compilation of predictive equations to represent the generaltrend – of collected data is aided immensely by its graphical representation. Whilst,by and large, predictive equations are more accurate and convenient for use in applicationsthan graphs, the latter is often preferable since it visually illustrates deviationsin the data, thereby giving an indication of reliability and the range of validity of theequation. Combination of these two tools – a graph for demonstration and an equationfor use – is desirable to ensure optimal understanding. Often, however, the functionaldependencies of the dependent variable are only known for large and small valuesof the independent variable; solutions for intermediate quantities being obscure forvarious reasons (e.g. narrow band within which the transition from one regime tothe other occurs, inadequate knowledge of the physics in this area, etc.). The limitingsolutions may be regarded as asymptotic and the powered addition to a power,s, of such asymptotes, f0 and f¥ , leads to a single correlating equation that is applicableover the entire domain of the dependent variable. This procedure circumventsthe introduction of ad hoc curve fitting measures for the different regions and subsequent,unwanted jumps in piecewise fitted correlative equations for the dependentvariable(s). Approaches to successfully implement the technique for different combinationsof asymptotic conditions are discussed. The aforementioned method of poweredaddition is applied to experimental data and the semblances and discrepancieswith literature and analytical models are discussed; the underlying motivation beingthe aspiration towards establishing a sound modelling framework for analytical andcomputational predictive measures. The purported procedure is revealed to be highlyuseful in the summarising and interpretation of experimental data in an elegant andsimplistic manner.

[发布机构] Stellenbosch University