Thesis (PhD)--Stellenbosch University, 2012 / ENGLISH ABSTRACT: This study presents the development and extension of free-surface modelling
techniques for the purpose of modelling two-fluid systems accurately and efficiently.
The volume-of-fluid (VOF) method is extended in two ways: Firstly, it is extended
to account for variations in the gas density through a weakly compressible formulation.
Secondly, a compressive free-surface interface capturing formulation that
preserves the integrity of the interface shape is detailed. These formulations were
implemented and evaluated using the Elemental software.
Under certain flow conditions liquid-gas systems may be subjected to large
variations in pressure, making it necessary to account for changes in gas density.
Modelling this effectively has received relatively little attention in the context of
free-surface modelling and remains a challenge to date. To account for the variations
in gas density a weakly compressible free-surface modelling formulation is
developed for low Mach number flows. The latter is formally substantiated via a
non-dimensional analysis. It is proposed that the new formulation advances on existing
free-surface modelling formulations by effecting an accurate representation
of the dominant physics in an efficient and effective manner.
The proposed weakly compressible formulation is discretised using a vertexcentred
edge-base finite volume approach, which provides a computationally efficient
method of data structuring and memory usage. Furthermore, this implementation
is applicable to unstructured spatial discretisation and parallel computing. In
this light, the discretisation is formulated to ensure a stable, oscillatory free solution.
Furthermore, the governing equations are solved in a fully coupled manner
using a combination of dual time-stepping and a Generalised Minimum Residual
solver with Lower-Upper Symmetric Gauss-Seidel preconditioning, ensuring a fast
and efficient solution.
The newly developed VOF interface capturing formulation is proposed to advance
on the accuracy and efficiency with which the evolution of the free-surface
interface is modelled. This is achieved through a novel combination of a blended
higher-resolution scheme, used to interpolate the volume fraction face value, and
the addition of an artificial compressive term to the VOF equation. Furthermore,
the computational efficiency of the higher-resolution scheme is improved through
the reformulation of the normalised variable approach and the implementation of a
new higher-resolution blending function.
For the purpose of evaluating the newly developed methods, several test cases
are considered. It is demonstrated that the new surface capturing formulation offers
a significant improvement over existing schemes, particularly at large CFL numbers.
It is shown that the proposed method achieves a sharper, better defined interface
for a wide range of flow conditions. With the validation of the weakly compressible
formulation, it is found that the numerical results correlate well with analytical
solutions. Furthermore, the importance of accounting for gas compressibility
is demonstrated via an application study. The weakly compressible formulation is
also found to result in negligible additional computational cost while resulting in
improved convergence rates. / AFRIKAANSE OPSOMMING: Hierdie studie behels die ontwikkeling van numeriese tegnieke met die doel om
twee-vloeistof vloei akkuraat en numeries effektief te modelleer. Die volume-vanvloeistof
metode word op twee maniere uitgebrei: Eerstens word variasie van die
gasdigtheid in ag geneem deur gebruik te maak van ’n swak samedrukbare model.
Tweedens saam is ’n hoë-resolusie metode geformuleer vir die voorstelling van
die vloeistof-oppervlak. Hierdie uitbreidings is met die behulp van die Elemental
programmatuur geïmplementeer en met behulp van die programmatuur geëvalueer.
Onder sekere toestande ervaar vloeistof-gas mengsels groot veranderinge in
druk. Dit vereis dat die variasie in gasdigtheid in berekening gebring moet word.
Die modellering hiervan het egter tot dusver relatief min aandag ontvang. Om hierdie
rede word ’n swak samedrukbare model vir lae Mach-getalle voorgestel om die
variasie in gasdigtheid in te reken. Die formulering volg uit ’n nie-dimensionele
analise. Daar word geargumenteer dat die nuwe formulering die fisika meer akkuraat
verteenwoordig.
’n Gesentraliseerde hoekpunt, rant gebaseerde eindige volume metode word gevolg
om die differensiaalvergelykings numeries te diskretiseer. Dit bied ’n doeltreffende
manier vir datastrukturering en geheuebenutting. Hierdie benadering is
verder geskik vir toepassing op ongestruktureerde roosters en parallelverwerking.
Die diskretisering is geformuleer om ’n stabiele oplossing sonder numeriese ossillasies
te verseker. Die vloeivergelykings word op ’n gekoppelde wyse opgelos
deur gebruik te maak van ’n kombinasie van ’n pseudo tyd-stap metode en ’n Veralgemene
Minimum Residu berekeningsmetode met Onder-Bo Simmetriese Gauss-
Seidel voorafbewerking.
Die nuut ontwikkelde skema vir die modellering van die vloeistof-oppervlak
is veronderstel om ’n meer akkurate voorstelling te bied en meer doeltreffend te
wees vir numeriese berekeninge. Dit word bereik deur die nuwe kombinasie van
’n hoë-resolusie skema, wat gebruik word om die volumefraksie te interpoleer, met
die samevoeging van ’n kunsmatige term in die volume-van-vloeistof vergelyking
om die resolusie te verfyn. Verder is die doeltreffendheid van die skema verbeter
deur die genormaliseerde veranderlikes benadering te herformuleer en deur die
ontwikkeling van ’n nuwe hoë-resolusie vermengingsfunksie.
Verskeie toetsgevalle is uitgevoer met die doel om die nuwe modelle te evalueer.
Daar word aangetoon dat die nuwe skema vir die modellering van die vloeistofoppervlak
’n meetbare verbetering bied, veral by hoër Courant-Friedrichs-Lewy getalle.
Die nuwe formulering bied dus hoër akkuraatheid vir ’n wye verskeidenheid
van toestande. Vir die swak samedrukbare formulering is daar ’n goeie korrelasie
tussen die numeriese resultate en die analitiese oplossing. In ’n toegepassingsgeval
word die noodsaaklikheid om die samedrukbaarheid van die gas in ag te neem gedemonstreer.
Die addisionele berekening-kostes van die nuwe formulering is weglaatbaar
en in sommige gevalle verhoog die tempo waarteen die oplossing konvergeer
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/71934 |
| Date | 12 1900 |
| Creators | Heyns, Johan Adam |
| Contributors | Harms, T. M., Malan, A. G., Stellenbosch University. Faculty of Engineering. Dept. of Mechanical and Mechatronic Engineering. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
| Format | 92 p. : ill. |
| Rights | Stellenbosch University |
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