Powered addition as modelling technique for flow processes

De Wet, Pierre (2010-03)

Thesis (MSc (Applied Mathematics))--University of Stellenbosch, 2010.

Thesis

ENGLISH ABSTRACT: The interpretation – and compilation of predictive equations to represent the general trend – of collected data is aided immensely by its graphical representation. Whilst, by and large, predictive equations are more accurate and convenient for use in applications than graphs, the latter is often preferable since it visually illustrates deviations in the data, thereby giving an indication of reliability and the range of validity of the equation. Combination of these two tools – a graph for demonstration and an equation for use – is desirable to ensure optimal understanding. Often, however, the functional dependencies of the dependent variable are only known for large and small values of the independent variable; solutions for intermediate quantities being 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.). The limiting solutions 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 applicable over the entire domain of the dependent variable. This procedure circumvents the introduction of ad hoc curve fitting measures for the different regions and subsequent, unwanted jumps in piecewise fitted correlative equations for the dependent variable(s). Approaches to successfully implement the technique for different combinations of asymptotic conditions are discussed. The aforementioned method of powered addition is applied to experimental data and the semblances and discrepancies with literature and analytical models are discussed; the underlying motivation being the aspiration towards establishing a sound modelling framework for analytical and computational predictive measures. The purported procedure is revealed to be highly useful in the summarising and interpretation of experimental data in an elegant and simplistic manner.

AFRIKAANSE OPSOMMING: Die interpretasie – en samestelling van vergelykings om die algemene tendens voor te stel – van versamelde data word onoorsienbaar bygestaan deur die grafiese voorstelling daarvan. Ten spyte daarvan dat vergelykings meer akkuraat en geskik is vir die gebruik in toepassings as grafieke, is laasgenoemde dikwels verskieslik aangesien dit afwykings in die data visueel illustreer en sodoende ’n aanduiding van die betroubaarheid en omvang van geldigheid van die vergelyking bied. ’n Kombinasie van hierdie twee instrumente – ’n grafiek vir demonstrasie en ’n vergelyking vir aanwending – is wenslik om optimale begrip te verseker. Die funksionele afhanklikheid van die afhanklike veranderlike is egter dikwels slegs bekend vir groot en klein waardes van die onafhanklike veranderlike; die oplossings by intermediêre hoeveelhede onduidelik as gevolg van verskeie redes (waaronder, bv. ’n smal band van waardes waarbinne die oorgang tussen prosesse plaasvind, onvoldoende kennis van die fisika in hierdie area, ens.). Beperkende oplossings / vergelykings kan as asimptote beskou word en magsaddisie tot ’n mag, s, van sodanige asimptote, f0 en f¥, lei tot ’n enkel, saamgestelde oplossing wat toepaslik is oor die algehele domein van die onafhanklike veranderlike. Dié prosedure voorkom die instelling van ad hoc passingstegnieke vir die verskillende gebiede en die gevolglike ongewensde spronge in stuksgewyspassende vergelykings van die afhankilke veranderlike(s). Na aanleiding van die moontlike kombinasies van asimptotiese toestande word verskillende benaderings vir die suksesvolle toepassing van hierdie tegniek bespreek. Die bogemelde metode van magsaddisie word toegepas op eksperimentele data en die ooreenkomste en verskille met literatuur en analitiese modelle bespreek; die onderliggend motivering ’n strewe na die daarstelling van ’n modellerings-raamwerk vir analitiese- en rekenaarvoorspellingsmaatreëls. Die voorgestelde prosedure word aangetoon om, op ’n elegante en eenvoudige wyse, hoogs bruikbaar te wees vir die lesing en interpretasie van eksperimentele data.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/4166
This item appears in the following collections: