Thesis (PhD (Mechanical and Mechatronic Engineering))--University of Stellenbosch, 1992. / The effect of cross-winds on the performance of natural draft dry-cooling towers is studied by means of isothermal model tests, a numerical simulation and full scale measurements. The action of the wind on such towers is found to be complex and is influenced by a number of different parameters including the wind speed, the shape of the approaching wind profile, the inlet diameter to the inlet height ratio of the tower, the tower height, the shape of the tower shell, the pressure loss coefficient of the heat exchangers and the amount of heat rejected by the tower. For a horizontal arrangement of the heat exchangers the wind effect on the tower is shown to be strongly dependent on both the shape and pressure loss coefficient of the tower supports. In practical cooling towers the heat exchangers are either arranged horizontally in the inlet cross-section of the tower or vertically around the circumference of the tower and the wind effect is found to be dependent on the particular layout. The wind effect on a tower is furthermore found to increase if the heat exchangers are arranged in the form of A-frames. Additional reductions in the heat rejection rate of the tower are caused by a non-uniform air temperature distribution inside the tower and flow distortions through the heat exchanger. Significant reductions in the wind effect on a cooling tower can be achieved by installing windbreak walls below the heat exchangers if the latter are arranged horizontally in the tower inlet.

Thesis (PhD (Mechanical and Mechatronic Engineering))--University of Stellenbosch, 2009. / The main research objective of this dissertation was to determine the performance parameters of particle dampers (PDs) under centrifugal loads. A test bench was developed consisting of a rotating cantilever beam with a PD at the tip. Equal mass containers with di erent depths, filled with a range of uniform sized steel ball bearings, were used as PDs. For all the tests, the total PD mass was identical. During operation the tip of the beam was displaced, and after release, the beam could vibrate freely. The decay in the vibratory motion of the tip of the beam was measured over a range of centrifugal loads. The experiments were duplicated numerically with a discrete element method (DEM) model, calibrated against the experimental data. This model could then be used for a more in-depth investigation of phenomena occurring when PDs are under centrifugal loads. From the data analysis, it can be concluded that there are two zones of damping, one with a high and one with a low damping factor. These damping zones depend on the ratio between the peak vibration acceleration and the centrifugal loading. Each zone has a limit in terms of the centrifugal loading beyond which the PD cannot function if the vibration amplitude is fixed. In the high damping zone, it was found that the excitation state of the particles was high enough for the system vibration frequency to change. In the low damping zone, there is only limited motion between the particles. The main parameters that influence the performance of the PDs are the friction between the particles themselves and with the container, the PD length/diameter aspect ratio, and the particle size. An important finding is that a PD with less layers (increase in particle size) will still function at a higher centrifugal load compared to one with a smaller number number of layers.

Thesis (PhD (Mechanical and Mechatronic Engineering)--University of Stellenbosch, 1990. / 260 leaves printed single pages, preliminary pages i-xxi and numbered pages Chapter 1/1.1-1.3, Chapter 2/2.1-2.17, Chapter 3/3.1.1-3.10, Chapter 4/4.1-4.18, Chapter 5/5.1-5.3, References pages R.1-R.7, Appendix A pages A.1-A.34, Appendix B pages B.1-B.34, Appendix C pages C.1-C.26, Appendix D pages D.1-D.16, Appendix E pages E.1-E.30, Appendix F pages F.1-F.39. Includes bibliography, list of tables, figures and symbols. / Digitized at 600 dpi grayscale to pdf format (OCR), using a Bizhub 250 Konica Minolta Scanner. / ENGLISH ABSTRACT: The ultimate goal of this project is to ensure a better understanding of the governing mechanisms present when flow distorting components are installed in close proximity of an axial flow fan. The effect of different parameters on the operation of axial flow fans is investigated. These parameters are divided into flow enhancing and flow reduction effects. The performance of an axial flow fan can be enhanced by changing the tip clearance, by adding a solid disc to the hub of the fan or by varying the number of fan blades. Flow reductions are caused by components such as inlet grids, walkways and their supporting structures, heat exchangers and windwalls. The effects of flow enhancing components are measured and compared to the results of other authors. The sensitivity of these effects to parameters such as the type of fan rotor and the specific system in which the rotor is installed is highlighted. The system effect (the interaction between the fan rotor and flow resistances in close proximity of each other) of individual components, as well as the combination of different components, is predicted both theoretically and experimentally. These predictions are compared to measured data relevant to the components in an installation where the system effects are present. The results are correlated to the kinetic energy flux coefficient of the flow at different locations within the installation. Experimental data obtained from a full scale unit (inlet shroud diameter of 9,216 m) are used to compare to scaled data from the model (inlet shroud diameter of 1,542 m). The hub to tip ratio of the axial flow fans investigated is 0,15. The most important conclusions are that the performance of the type of axial flow fan under investigation can be improved by reducing its tip clearance and by installing a solid disc to the downstream side of the rotor. An increase in the number of blades of the fan leads to only marginal improvements in the fan performance. The overall performance of the system can also be improved by removing some of the flow resisting components, or by changing their relative positions. All these conclusions are based on the assumption that the power input to the fan rotor remains constant. / AFRIKAANSE OPSOMMING: Die uiteindelike doel van hierdie projek is om te verseker dat die beherende meganismes wat teenwoordig is wanneer vloeiversteurende komponente in die nabyheid van 'n aksiaalwaaier geinstalleer word, beter verstaan word. Die effek van verskillende parameters op die werkverrigting van aksiaalwaaiers word ondersoek. Hierdie parameters word verdeel in vloeiverbeterings- en vloeiverminderingseffekte. Die werkverrigting van 'n aksiaalwaaier kan verbeter word deur die lempuntspeling te verstel, deur 'n soliede skyf aan die naaf van die waaierrotor te installeer, of deur die aantal lemme te verander. Die vloeiverminderings word veroorsaak deur inlaatsiwwe, loopvlakke en hul ondersteuningsstrukture, warmteruilers en windwande. Die effekte van vloeiverbeteringskomponente word gemeet en vergelyk met die resultate van ander outeurs. Die sensitiwiteit van hierdie effekte op parameters soos die tipe rotor en die spesifieke stelsel waarin die rotor geinstalleer is, word uitgelig. Die stelseleffek (die interaksie tussen die rotor van die waaier en vloei weerstande wat naby mekaar geinstalleer is) van individuele, sowel as 'n kombinasie van verskillende komponente, word teoreties en eksperimenteel voorspel. Hierdie voorspellings word dan vergelyk met eksperimentele data wat van toepassing is op die komponente in 'n installasie waar stelseleffekte voorkom. Die resultate word gekoppel aan die kinetiese energievloedkoeffisient van die vloei by verskillende posisies binne die installasie. Eksperimentele data, verkry vanaf 'n volskaaleenheid (inlaatmondstukdiameter van 9,216 m), word met die geskaleerde data van die model (inlaatmondstukdiameter van 1,542 m) vcrgelyk. Die naaf- tot hulsverhouding van die aksiaalwaaiers wat ondersoek word is 0,15. Die belangrikste gevolgtrekkings is dat die werkverrigting van die tipe aksiaalwaaier wat ondersoek word verbeter kan word deur die lempuntspeling te verminder en deur 'n soliede skyf te installeer by die stroomaf kant van die rotor. 'n Toename in die aantal lemme van die waaier lei slegs tot marginale verbeterings in die werkverrigting van die waaier. Die totale werkverrigting van die stesel kan ook verbeter word deur sommige vloeiweerstandskomponente te verwyder, of deur hulle relatiewe posisies te verander. Al hierdie gevolgtrekkings is gebasseer op die aanname dat die drywingsinset na die waaierrotor konstant bly.

Thesis (PhD)--University of Stellenbosch, 2004. / ENGLISH ABSTRACT:This work is concerned with the numerical simulation of the aeolian snow transportation process (drifting or wind blown snow) and especially the snow deposition and erosion phenomenon (snow drift). The research work is interested in modelling the atmospheric boundary layer wind flow and its associated snow drifting processes around threedimensional obstacles by means of computational fluid dynamics (CFD). A modelling method is required to predict and evaluate the snow drifting phenomenon surrounding the SANAE IV research station in Antarctica. This station is of an elevated design to ensure that wind blown snow may travel around the structure relatively undisturbed and without deposition near the structure. This design is partly successful but localised drifts are formed especially leeward of the interconnecting structures that join the main building sections together. The theoretical and numerical description to describe the turbulent transport of the two-phase mixture of air and snow particles is investigated. This theory is subsequently employed to describe the snow deposition and erosion process and two models are developed to determine the deposition flux onto the snow surface. These models presented and discussed are a threshold based approach and a conservative based approach. The first model is dependent on a threshold shear velocity to determine the onset of either erosion or deposition. The second model determines the deposition or erosion flux based on the conservation of the snow mass transport in the near surface control volume. A numerical scheme that evaluates the snow deposition flux at the surface and forces a temporal surface adaptation during the simulation is established and implemented in a commercial CFD software code by means of user subroutines. Various test cases for which observed snow drift data are available are numerically modelled to validate the snow drift schemes presented in this work. These tests include the wind driven snow accumulation around a three-dimensional cube, around two adjacent three-dimensional cubes and near a typical porous snow fence. The results indicate that both methods can predict realistic snow drifts for a variety of wind flow conditions but also show that the conservative approach is superior to the threshold based approach in describing the snow drift process around obstacles. This model allows drifts to form not only in areas of low flow velocities but also under high shear conditions. The theoretical investigation and the development and validation of the conservatively based snow drift scheme shows that drift formation depends strongly on the near surface flow divergence and secondary flow structures. To resolve the snow drift formation under a variety of flow conditions a three-dimensional field solution is required to determine velocity and snow concentration gradients and include the effects of near surface convective and turbulent entrainment. The model is applied to numerically simulate and predict snow drifting around the SANAE IV base for a moderate as well as a high wind speed event. The predicted snow drift around the base agrees favourably with the observed drifts at the station. Further numerical simulations are carried out to evaluate the effects a few design modifications may have on the snow deposition. These results suggest that a simple baffle plate installation near the bottom of the interconnecting link structures may minimise the snow accumulation leeward of that area. This study shows that to achieve realistic numerical snow drift predictions around, on or near obstacles, a conservative based snow drift scheme should be considered using some form of temporal terrain adaptation strategy. Only then does one include a sufficient level of important flow effects such as deposition along near surface boundaries of strong flow divergence which plays as an important role as vertical settling and entrainment in determining deposition rates. / AFRIKAANSE OPSOMMING:Hierdie studie behels die numeriese simulasie van windgedrewe sneeubeweging asook die daarmee gepaardgaande sneeu neerslag en erosie eienskappe. Die navorsing het verder belang in die berekening van die atmosferiese grenslaag vloei en die simulasie van sneeu neerslag naby drie-dimensionele strukture deur gebruik te maak van berekeningsvloeimeganika (BVM). ‘n Berekeningsmetodiek is nodig om die eienskappe van die sneeu neerslag rondom die SANAE IV navorsingsstasie in Antarktika te voorspel en te evalueer. Die bogrondse struktuur is spesifiek so ontwerp om te verseker dat wind gedrewe sneeu hoofsaaklik onversteurd verby die struktuur kan beweeg sonder neerslag teenaan die struktuur. Die ontwerp is grotendeels suksesvol alhoewel sneeu neerslag wel lokaal plaasvind, wind af vanaf die aansluitings strukture tussen die hoof geboue. Die teoretiese en numeriese beskrywing van die twee-fase lug- en sneeumengsel beweging word ondersoek en gebruik om die sneeu neerslag en erosie einskappe te beskryf. Twee modelle wat hierdie verskynsel beskryf word beskryf en bespreek naamlik ‘n drumpel gebaseerde benadering en ‘n konserwatief gebaseerde benadering. Die eerste model is afhanklik van ‘n drumpel skuifsnelheid om die aanvang van of erosie of neerslag te bereken. Die tweede model bereken die neerslag eerder gebaseer op die behoud van die sneeu massa vloei in die kontrole volume naby aan die oppervlak. ‘n Numeriese metode is ontwikkel en geimplementeer in ‘n kommersiële BVM sagteware pakket deur van gebruikerssubroetines gebruik te maak. Die ontwikkelde kode evalueer die sneeu neerslag vloed by die oppervlak en forseer ‘n tydafhanklike oppervlak aanpassing gedurende die simulasie. Die sneeu neerslag metode wat beskryf word in hierdie studie word ge-evalueer teen verskeie toetsgevalle waarvoor daar waargenome sneeu neerslag resultate beskikbaar is. Hierdie toetse sluit in die wind gedrewe sneeu neerslag rondom ‘n drie-dimensionele kubus, rondom twee naby geleë kubusse en naby ‘n tipiese poruese sneeu heining. Die resultate dui aan dat beide die metodes realistiese sneeu neerslag voorspel vir verskeie wind toestande. Die studie wys ook dat die konserwatief gebaseerde benadering vir die beskrywing van die sneeu neerslag proses meer akkuraat is as die drumpel gebaseerde benadering aangesien die neerslagvoorspel kan word nie net alleenlik in gebiede met lae vloeisnelhede nie, maar ook in gebiede waar hoë skuifsnelhede teenwoordig is. Die teoretiese ondersoek, ontwikkeling en toepassing van die konserwatief gebaseerde model dui daarop dat die neerslag afhanklik is van die divergensie van die vloeiveld asook van die sekondêre vloei patrone naby die oppervlak. Ten einde die sneeu neerslag vir verskeie toestande op te los is dit nodig om snelheids- en sneeukonsentrasie gradiënte te kan bereken in ‘n drie-dimensionele vloei veld om sodoende die invloed van naby-oppervlak konveksie en turbulente verspreiding in ag te neem. Die metode word toegepas deur die sneeu neerslag rondom die SANAE IV navorsingsstasie te voorspel vir ‘n gematigde asook ‘n hoë wind snelheid toestand. Die sneeu neerslag voorspelling stem gunstig ooreen met die waargenome neerslag by die struktuur. Verdere numeriese simulasies is uitgevoer om die invloed van ontwerpsverandering op die neerslag te evalueer. Uit hierdie resultate blyk dit dat ‘n eenvoudige plaat struktuur onder die aansluitingsstrukture die sneeu neerslag wind af mag verminder. Hierdie navorsingsstudie dui daarop dat ‘n tydafhanklike terrein aanpassing strategie saam met die konserwatiewe neerslag model noodsaaklik is ten einde realistiese resultate te behaal vir die sneeu opbou rondom of naby strukture. Sodoende word genoegsame vlakke van belangrike vloei verskynsels, soos die invloed van vloei divergensie, in ag geneem wat net so ‘n belangrik rol in neerslag speel soos vertikale afsetting.

Thesis (PhD)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: Natural draught wet-cooling tower rain zone performance can be significantly enhanced by reducing the mean drop size in the rain zone with the installation of specially designed grids below the cooling tower fill. Drops enter the rain zone in the form of a polydisperse drop distribution, dripping from below the cooling tower fill, comprising relatively large drops. In order to design and optimize a grid for breaking up these drops, the mechanisms of drop break-up after impingement on the grid surface, referred to as splashing, straddling and dripping, need to be clearly understood. Two of these mechanisms, splashing and straddling, are therefore investigated experimentally using high speed video cameras to measure initial drop sizes, mass fractions and drop size distributions after impingement on different horizontal slats covered with a thin layer of water. The following parameters are varied independently for these experiments: drop fall distance, initial drop size, slat width and the water film thickness on the slats. Dripping from below the grid, is investigated theoretically. The effect of drop interaction on the drop size distribution in the rain zone is also investigated experimentally by measuring the drop distributions at the top and bottom of rain zones with a height of approximately 7.05 m to 7.65 m for different inlet distributions. The experimental drop break-up data, numerically obtained splash drop trajectory data and drop interaction data found in literature are used to develop a theoretical model of a purely counter flow cooling tower rain zone with and without installed grids. The model is compared to experimental data and theoretical data from literature and the predicted thermal and dynamic behaviour of the rain zone are generally found to be in good agreement with these results. Ultimately, this model is used for the optimization of the grid layout in terms of variables such as distance between the grid and the fill, slat width, slat spacing and slat height. It is found that the best drop break-up is achieved for grids comprising narrower slats with lower grid porosities as opposed to grids comprising wider slats. For the determined optimal grid layout it is found that a significant improvement in cooling tower performance can be achieved. / AFRIKAANSE OPSOMMING: Nat-koeltoringreënsonevermoë kan aansienlik verhoog word deur die druppelgrootte in hierdie gebied te verklein deur roosters, wat spesifiek vir hierdie doel ontwerp is, onder die pakkingsmateriaal te installeer. Die inlaatdruppelverdeling aan die bokant van die reënsone bestaan uit ‘n verdeling van relatief groot druppels wat drip van die onderkant van die pakkingsmateriaal. Ten einde ‘n rooster te ontwerp en te optimeer wat hierdie druppels kan opbreek moet die meganismes van druppelopbreking, bekend as spatting, vurking en drip goed verstaan word. Spatting en vurking is om hierdie rede eksperimenteel ondersoek, met behulp van hoëspoed videokameras. Die volgende veranderlikes is onafhanklik verander tydens hierdie eksperimente: valafstand van die druppel, aanvanklike druppelgrootte, latwydte en die dikte van die lagie water bo-op die lat. Die dripmeganisme aan die onderkant van die rooster is slegs teoreties ondersoek. Die effek wat druppelinteraksie in die reënsone het op die druppelgrootte is ondersoek deur die druppelgroottes aan die bo- en onderkant van ‘n 7.05 m tot 7.65 m reënsone te meet vir verskillende druppelinlaatverdelings. Die eksperimentele druppeldata, sowel as numeries berekende data wat die snelheid en trajek van spatdruppels beskryf, tesame met data vir druppelinteraksies wat uit die literatuur verkry is word gebruik om ‘n teoretiese model te ontwikkel vir ‘n suiwer teenvloei koeltoringreënsone met en sonder roosters. Hierdie model word vergelyk met eksperimentele data en data wat uit die literatuur verkry is en daar is gevind dat daar oor die algemeen ‘n goeie ooreenstemming is tussen die voorspelde en gemete termiese en dinamiese gedrag van die reënsone. Uiteindelik word die model gebruik vir die optimering van die rooster in terme van die volgende veranderlikes: afstand tussen rooster en pakkingsmateriaal, latwydte, latspasiëring en lathoogte. Daar word gevind dat beter druppelopbreking verkry word deur gebruik te maak van smaller latte en ‘n laer roosterporeusiteit. Daar is gevind dat die bepaalde optimale roosteruitleg in die reënsone van ‘n koeltoring ‘n wesenlike verbetering in koeltoringvermoë tot gevolg kan hê.

Thesis (PhD)--Stellenbosch University, 1997 / ENGLISH ABSTRACT: An experimental investigation on gas-liquid counterflow in inclined rectangular ducts is conducted. The pressure drop across the sharp-edged gas inlet and the pressure gradient inside the duct are measured. Combinations of water, methanol, propanol, air, argon, helium and hydrogen are tested. The duct height and width are varied from 50 mm to 150 mm and 10 mm to 20 mm respectively. The emphasis is on high void fraction flow, i.e. low liquid flow rates as encountered in air-cooled reflux condensers. At low to moderate gas flow rates the pressure gradient is gas Reynolds number related while it becomes dependent on the superficial densimetric gas Froude number as the gas flow is increased. According to experiment the hydraulic diameter is the required length dimension in the gas Reynolds number while the duct height becomes the characteristic dimension in the Froude number regime. Flooding curves are generated for duct inclinations from close to the horizontal to the vertical. The data correlate in terms of the phase Froude numbers and a dimensionless liquid property parameter containing the hydraulic diameter, density, surface tension and the viscosity. The flooding gas velocity is found to be strongly dependent on the duct height, the phase densities and the duct inclination. The liquid viscosity has a stronger effect than the surface tension. Both these properties however playa secondary role. Flooding is not related to the gas Reynolds number. A theoretical model, based on the phenomenological findings of the adiabatic counterflow investigation, is derived to evaluate the performance of an air-cooled reflux condenser. Field tests are conducted on a full scale reflux condenser and the measured performance is compared to the model prediction. The reflux condenser is found to achieve only 60% of the predicted heat rejection rate due to the existence of so-called cold or dead zones. Indications are that excessive entraiment in the bottom header and the subsequent accumulation of condensate in the finned tubes causes a maldistribution of the steamside flow. In the process noncondensable gases accumulate and form dead zones, causing ineffective performance. Flooding as found in single-ducts does not appear to contribute to the formation of the dead zones. / AFRIKAANSE OPSOMMING: Die teenvloei van gas en vloeistof in reghoekige skuins buise is eksperimenteel ondersoek. Die drukverlies oor die skerp gasinlaat en die drukval in die buis is gemeet vir verskillende kombinasies van water, propanol, metanol, lug, argon, helium en waterstof. Buishoogtes en breedtes van 50 mm tot 150 mm en 10 mm tot 20 mm respektiewelik is getoets. Die klem van die ondersoek is op lae vloeistofvloeitempos soos teenwoordig tydens kondensasie van stoom in lugverkoelde teenvloeikondensors. Vir lae tot matige gasvloeitempos is die drukval afhanklik van die gas Reynolds-getal terwyl die densimetriese gas Froude-getal die heersende parameter word soos die gasvloei toeneem. Die hidrouliese diameter verteenwoordig die dimensie in die Reynolds-getal maar die buishoogte word die karakteristieke dirnensie in die Froude-getal gebied. Vloedingskurwes is vir 'n reeks van buishoeke gegenereer. Die vloedingdata korreleer in terme van die Froude-getal en 'n dimensielose parameter bestaande uit die hidrouliese diameter, oppervlakspanning, vloeistofdigtheid en die vloeistofviskositeit. Die vloeidingsnelheid is primêr van die buishoogte, vloeierdigthede en die buishoek afhanklik. Die vloeistofviskositeit-effek is sterker as die van die oppervlakspanning. Beide die eienskappe speel egter 'n sêkondere rol. Die gas Reynolds-getal beïnvloed nie die vloeidingsproses nie. Die fundamentele bevindinge van die teenvloeiondersoek is toegepas om die werkverigting van 'n lugverkoelde teenvloeikondenser teoreties te modelleer. Werkverigtingstoetse is uitgevoer op 'n volskaal teenvloeikondenser. Die toetsresultate word vergelyk met die teoretiese voorspelling. Die teenvloeikondensor behaal slegs sowat 600% van die voorspelde warmteoordrag omdat van die gevinde buise gedeeltelik by omgewingstemperatuur is. Hierdie verskynsel heet koue of dooie sones. Dit blyk dat die kondensaat in die onderste spruitstuk nie vrylik kan dreineer nie en in die vorm van druppels deur die stoom opgesleur word. Gevolglik versamel kondensaat binne die buise en sodoende kan nie-kondenseerbare gasse nie effektief uit die teenvloeikondensor verwyder word nie. Soos die gasse versamel word koue sones gevorm. Dit blyk dat vloeding soos waargeneem in enkelbuise nie tot die vorming van koue sones bydra nie.

Thesis (PhD)--Stellenbosch University, 2012 / ENGLISH ABSTRACT: This dissertation addresses a number of topics that arise from the use of a dual method of sequential approximate optimisation (SAO) to solve structural optimisation problems. Said approach is widely used because it allows relatively large problems to be solved efficiently by minimising the number of expensive structural analyses required. Some extensions to traditional implementations are suggested that can serve to increase the efficacy of such algorithms. The work presented herein is concerned primarily with three topics: the use of nonconvex functions in the definition of SAO subproblems, the global convergence of the method, and the application of the dual SAO approach to large-scale problems. Additionally, a chapter is presented that focuses on the interpretation of Sigmund’s mesh independence sensitivity filter in topology optimisation. It is standard practice to formulate the approximate subproblems as strictly convex, since strict convexity is a sufficient condition to ensure that the solution of the dual problem corresponds with the unique stationary point of the primal. The incorporation of nonconvex functions in the definition of the subproblems is rarely attempted. However, many problems exhibit nonconvex behaviour that is easily represented by simple nonconvex functions. It is demonstrated herein that, under certain conditions, such functions can be fruitfully incorporated into the definition of the approximate subproblems without destroying the correspondence or uniqueness of the primal and dual solutions. Global convergence of dual SAO algorithms is examined within the context of the CCSA method, which relies on the use and manipulation of conservative convex and separable approximations. This method currently requires that a given problem and each of its subproblems be relaxed to ensure that the sequence of iterates that is produced remains feasible. A novel method, called the bounded dual, is presented as an alternative to relaxation. Infeasibility is catered for in the solution of the dual, and no relaxation-like modification is required. It is shown that when infeasibility is encountered, maximising the dual subproblem is equivalent to minimising a penalised linear combination of its constraint infeasibilities. Upon iteration, a restorative series of iterates is produced that gains feasibility, after which convergence to a feasible local minimum is assured. Two instances of the dual SAO solution of large-scale problems are addressed herein. The first is a discrete problem regarding the selection of the point-wise optimal fibre orientation in the two-dimensional minimum compliance design for fibre-reinforced composite plates. It is solved by means of the discrete dual approach, and the formulation employed gives rise to a partially separable dual problem. The second instance involves the solution of planar material distribution problems subject to local stress constraints. These are solved in a continuous sense using a sparse solver. The complexity and dimensionality of the dual is controlled by employing a constraint selection strategy in tandem with a mechanism by which inconsequential elements of the Jacobian of the active constraints are omitted. In this way, both the size of the dual and the amount of information that needs to be stored in order to define the dual are reduced. / AFRIKAANSE OPSOMMING: Hierdie proefskrif spreek ’n aantal onderwerpe aan wat spruit uit die gebruik van ’n duale metode van sekwensi¨ele benaderde optimering (SBO; sequential approximate optimisation (SAO)) om strukturele optimeringsprobleme op te los. Hierdie benadering word breedvoerig gebruik omdat dit die moontlikheid skep dat relatief groot probleme doeltreffend opgelos kan word deur die aantal duur strukturele analises wat vereis word, te minimeer. Sommige uitbreidings op tradisionele implementerings word voorgestel wat kan dien om die doeltreffendheid van sulke algoritmes te verhoog. Die werk wat hierin aangebied word, het hoofsaaklik betrekking op drie onderwerpe: die gebruik van nie-konvekse funksies in die defini¨ering van SBO-subprobleme, die globale konvergensie van die metode, en die toepassing van die duale SBO-benadering op grootskaalse probleme. Daarbenewens word ’n hoofstuk aangebied wat fokus op die interpretasie van Sigmund se maasonafhanklike sensitiwiteitsfilter (mesh independence sensitivity filter) in topologie-optimering. Dit is standaard praktyk om die benaderde subprobleme as streng konveks te formuleer, aangesien streng konveksiteit ’n voldoende voorwaarde is om te verseker dat die oplossing van die duale probleem ooreenstem met die unieke stasionˆere punt van die primaal. Die insluiting van niekonvekse funksies in die definisie van die subprobleme word selde gepoog. Baie probleme toon egter nie-konvekse gedrag wat maklik deur eenvoudige nie-konvekse funksies voorgestel kan word. In hierdie werk word daar gedemonstreer dat sulke funksies onder sekere voorwaardes met vrug in die definisie van die benaderde subprobleme inkorporeer kan word sonder om die korrespondensie of uniekheid van die primale en duale oplossings te vernietig. Globale konvergensie van duale SBO-algoritmes word ondersoek binne die konteks van die CCSAmetode, wat afhanklik is van die gebruik en manipulering van konserwatiewe konvekse en skeibare benaderings. Hierdie metode vereis tans dat ’n gegewe probleem en elk van sy subprobleme verslap word om te verseker dat die sekwensie van iterasies wat geproduseer word, toelaatbaar bly. ’n Nuwe metode, wat die begrensde duaal genoem word, word aangebied as ’n alternatief tot verslapping. Daar word vir ontoelaatbaarheid voorsiening gemaak in die oplossing van die duaal, en geen verslappings-tipe wysiging word benodig nie. Daar word gewys dat wanneer ontoelaatbaarheid te¨engekom word, maksimering van die duaal-subprobleem ekwivalent is aan minimering van sy begrensingsontoelaatbaarhede (constraint infeasibilities). Met iterasie word ’n herstellende reeks iterasies geproduseer wat toelaatbaarheid bereik, waarna konvergensie tot ’n plaaslike KKT-punt verseker word. Twee gevalle van die duale SBO-oplossing van grootskaalse probleme word hierin aangespreek. Die eerste geval is ’n diskrete probleem betreffende die seleksie van die puntsgewyse optimale veselori¨entasie in die tweedimensionele minimum meegeefbaarheidsontwerp vir veselversterkte saamgestelde plate. Dit word opgelos deur middel van die diskrete duale benadering, en die formulering wat gebruik word, gee aanleiding tot ’n gedeeltelik skeibare duale probleem. Die tweede geval behels die oplossing van in-vlak materiaalverspredingsprobleme onderworpe aan plaaslike spanningsbegrensings. Hulle word in ’n kontinue sin opgelos met die gebruik van ’n yl oplosser. Die kompleksiteit en dimensionaliteit van die duaal word beheer deur gebruik te maak van ’n strategie om begrensings te selekteer tesame met ’n meganisme waardeur onbelangrike elemente van die Jacobiaan van die aktiewe begrensings uitgelaat word. Op hierdie wyse word beide die grootte van die duaal en die hoeveelheid inligting wat gestoor moet word om die duaal te definieer, verminder.

Thesis (PhD (Mechanical and Mechatronic Engineering))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: A methodology to facilitate analysis of dynamic subject-specific patellofemoral function is presented. An enhanced understanding of patellofemoral biomechanics will enable orthopaedic surgeons to identify the mechanisms responsible for imbalances in the joint stabilisers, while also providing objective information on which to base treatment methods. Dynamic patellofemoral function of three volunteers was simulated with a musculoskeletal computational model. The individuals underwent scans from which three-dimensional models of their patellofemoral joints were constructed. Skeletal muscles and soft tissue stabilisers were added to the skeletal models, after which subject-specific motion was simulated. After trochlear engagement, the patellae of the volunteers followed a lateral path, whereas patella tilt was subject-specific. Comparison of the predicted tilt and mediolateral position values at 30 degrees knee flexion to in-vivo MRI values showed a mean accuracy of 62.1 % and 96.9 % respectively. The patellofemoral contact load . quadriceps tendon load ratio varied between 0.7 and 1.3, whereas the mediolateral load component . resultant load ratio ranged between 0 and 0.4. Both parameters. values were similar to previous findings. The medial patellofemoral ligament tension decreased with knee flexion, while the patellar tendon-quadriceps tendon ratio followed a similar trend to that of previous findings (varied between 0.4 and 1.2). After induction of a tubercle osteotomy in the coronal plane, Volunteer One.s patella engaged the trochlear groove at an earlier knee flexion angle, while the patella of Volunteer Two only underwent a small medial displacement. Finite element analyses were employed to investigate the influence of the osteotomy on the patellofemoral pressure distribution. The mean pressure in Volunteer One.s patellofemoral joint was alleviated (17 % smaller) at all angles of flexion with the exception of 60 degrees (12 % greater). Pressure in Volunteer Two.s joint was alleviated at 30 and 45 degrees knee flexion (6 % smaller), while it was elevated (9.1 % greater) at other angles of flexion. Two commercial patellofemoral prostheses were tested on the three Volunteers. joints in the virtual environment. Prosthesis Two delivered patella shift and tilt patterns similar to the baseline values. Patellar tendon tension was slightly greater after resurfacing, with the tensions elevated most with Prosthesis Two. Medial patellofemoral ligament tension was reduced most with Prosthesis Two, while lateral retinaculum tension was increased slightly. Prosthesis Two was the best candidate to reproduce patella kinematics, while the patellofemoral kinetics was largely independent from the type of prosthesis used. The prostheses performed worse for Volunteer Three, supporting the need for the development of patient-specific prostheses. Three validated subject-specific musculoskeletal models facilitated the analysis of the individuals. patellofemoral biomechanics. The technique can potentially be employed by orthopaedic surgeons to visualise the change that an osteotomy or patellofemoral arthroplasty might induce on an individual.s patellofemoral joint. This technique might aid in the development of a tool to assist biomedical engineers in the development of new patellofemoral prostheses. Most importantly, the outcome of surgical intervention may be predicted beforehand, and a treatment procedure may be tailored to optimally fit the patellofemoral biomechanics of that individual. / AFRIKAANSE OPSOMMING: 'n Ondersoekmetode van die dinamiese gedrag van pasiënt-spesifieke patellofemorale gewrigte word beskryf. Indien die patellofemorale biomeganika beter verstaan word, kan ortopediese chirurge die meganismes wat verantwoordelik is vir oneffektiewe stabiliseerders identifiseer en behandeling op objektiewe bevindinge baseer. Die dinamiese patellofemorale funksie van drie vrywilligers is gesimuleer m.b.v. `n spier-skelet rekenaarmodel. Drie-dimensionele modelle van die individue se patellofemorale gewrig is gekonstrueer m.b.v. skanderings. Die skeletspiere en sagte ondersteuningsweefsel is tot die model toegevoeg, voordat vrywilliger-spesifieke beweging gesimuleer is. Die knieskywe van die vrywilligers het `n laterale pad gevolg nadat dit die groef binnegetree het, met die tiltwaardes uniek vir elke vrywilliger. Vergelyking van die beraamde knieskyf mediolaterale tilt en posisies by 30 grade fleksie met in-vivo magnetiese resonansieskandering waardes het `n akkuraatheid van 62.1 % en 96.9 % respektiewelik getoon. Die patellofemorale kontaklas-kwadriseps seningspanning verhouding het gewissel tussen 0.7 en 1.3; asook die mediale komponent – resultante komponent patellofemorale kontaklas wat gewissel het tussen 0 en 0.4. Beide parameters se waardes was soortgelyk aan voorheen-gepubliseerde data. Die mediale patellofemorale ligamentspanning het afgeneem met fleksie. Die patella sening-kwadriseps seningspanning verhouding was soortgelyk aan vorige gepubliseerde waardes en het gewissel tussen 0.4 en 1.2. Nadat 'n tuberkel-osteotomie in die koronale vlak aangebring is, het Vrywilliger Een se patella die femorale groef vroeër binnegetree. Vrywilliger Twee se patella het slegs `n mediale verskuiwing ondergaan. Eindige element analises is ingespan om die effek van die osteotomie op die spanningsverspreiding in die patellofemorale gewrig te ondersoek. Die gemiddelde spanning in Vrywilliger Een se gewrig was minder by alle hoeke van fleksie (17 % minder), met uitsondering van die spanning by 60 grade (12 % meer). Die spanning in Vrywilliger Twee se gewrig was minder by 30 en 45 grade (6 % minder), maar hoër by ander hoeke (9.1 % meer). Twee kommersiële patellofemorale prosteses is getoets op die drie Vrywilligers d.m.v. die model. Prostese Twee het die knieskyf-kinematika die beste nageboots. Die patella-seningspanning was effens groter na die vervanging. Prostese Twee het gesorg vir die grootste toename. Die mediale patellofemorale ligamentspanning was die kleinste toe Prostese Twee gebruik is, maar dit het gesorg vir effense hoër laterale retinakulumlaste. Die analises het getoon dat Prostese Twee die beste kandidaat is om die korrekte kinematika te herbewerkstellig. Die kinetika daarteenoor was onafhanklik van die tipe prostese wat gebruik is. Geeneen van die twee prosteses was geskik vir Vrywilliger Drie nie, wat as motivering vir die ontwikkeling van pasiënt-spesifieke prosteses dien. Drie bekragtigde vrywilliger-spesifieke spier-skelet modelle het die analise van patellofemorale biomeganika bewerkstellig. Die tegniek het die potensiaal om ortopediste in staat te stel om die effek van `n osteotomie of patellofemorale vervanging te visualiseer. Die tegniek kan verder gebruik word deur biomediese ingenieurs in die vervaardiging van nuwe patellofemorale prosteses. Meer belangrik is die feit dat die resultaat van chirurgiese ingryping voorspel kan word en optimale behandelingsprosedures beplan kan word vir die patellofemorale biomeganika van `n individu.

Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: This dissertation is basically a summary, with some interpretation, of published research by the author. The scope is limited to the fields of turbo-machinery, computational fluid dynamics and solar chimney power plants. The main contribution in the field of turbo-machinery in general is in the development of a through-flow method that automatically satisfies mass conservation. Concerning fan design, the contributions are the realization of the importance of the exit kinetic energy in the determination of the efficiency of rotor-only axial flow fans, and the quantification of the effect of off-axis inflow into cooling system fans on their performance. In the field of centrifugal fans and compressors an original, unifying model for the prediction of slip factor was developed. To investigate accident scenarios in closed cycle gas turbine nuclear reactors, all possible operational modes of multi-stage axial compressor operation caused by flow and rotation direction were investigated experimentally and computationally. Spanning the fields of turbo-machinery and solar chimneys, the basic theory of solar chimney turbines was developed, showing that high turbine efficiency was possible. In the field of solar chimneys, an original thermodynamic approach was developed to predict the main relationships that govern solar chimney performance, and to solve the through-flow equations for non-ideal systems with losses. Equations for the accurate determination of all the thermodynamic variables in a solar chimney as dependent on chimney height, wall friction, additional losses, internal drag and area change were derived and solved. Coefficients of wall friction, bracing wheel loss and exit kinetic energy were determined experimentally, and empirical equations were developed to predict the loss coefficient of the collector to turbine transition section and and the turbine inlet flow angle. A simple power law approach allowed the calculation of the optimal turbine pressure drop in solar chimney power plants. A comparison of two sets of equations used to calculate the heat fluxes into, inside and leaving the solar collector, resulted in similar air temperature rises in the collector, and similar produced power. It turned out however that the optimal flow for minimal turbine pressure drop was dependent on the heat transfer models. Investigation of the performance of various solar chimney turbo-generator layouts using analytical models and optimisation techniques showed that the optimal number of turbines varies with plant size, but the individual turbine size, the number of blades and even the efficiency remains close to constant. It was found that the cost of a turbogenerator system, however, varies significantly with size. A joint paper with several German universities and institutions did a comparative cost analysis of solar chimney power plants / AFRIKAANSE OPSOMMING: Hierdie verhandeling is basies ’n opsomming, met interpretasie, van gepubliseerde navorsing deur die outeur. Die omvang is beperk tot die gebiede van turbomasjinerie, berekeningsvloeidinamika en sonskoorsteenkragstasies. Die hoof bydrae op die gebied van turbomasjinerie in die algemeen is in die ontwikkeling van ’n deurvloeimetode wat outomaties massabehoud bevredig. Wat waaierontwerp betref is die bydrae die besef van die belangrikheid van die uitlaat kinetiese energie in die bepaling van waaierbenuttingsgraad, en die kwantifisering van die effek van af-as invloei in verkoelingswaaiers op hulle gedrag. Op die gebied van sentrifugaalwaaiers en -kompressors is ’n oorspronklike, samevattende model vir die voorspelling van glipfaktor ontwikkel. Om ongeluk-scenario’s in geslote kringloop gasturbine kenreaktors te ondersoek is al die moontlike werksmodusse veroorsaak deur vloei en rotasie rigting van ’n multistadium aksiaalkompressor eksperimenteel en numeries ondersoek. As brug tussen turbomasjinerie en sonskoorstene is die basiese teorie van sonskoorsteenturbines ontwikkel met die aanduiding dat hoë turbine benuttingsgraad moontlik is. Op die gebied van sonskoorstene is ’n oorspronklike termodinamies benadering ontwikkel om die hoofverwantskappe te voorspel wat sonskoorsteen gedrag bepaal, en om die deurvloei vergelykings op te los vir nie-ideale stelsels met verliese. Vergelykings vir die akkurate bepaling van al die termodinamiese veranderlikes in ’n sonskoorsteen soos afhanklik van skoorsteenhoogte, wandwrywing, bykomstige verliese, interne sleur en oppervlakte verandering is afgelei en opgelos. Koëffisiënte vir wandwrywing, verstywingswiel-verlies en uitlaat kinetiese energie is eksperimenteel bepaal, en empiriese vergelykings is ontwikkel om die verlieskoëffisiënt van die kollektor-tot-skoorsteen oorgang en die turbine inlaatvloeihoek te bepaal. ’n Eenvoudige magswet benadering het dit mootlik gemaak om die optimum turbine-drukval in sonskoorsteen aanlegte te bepaal. ’n Verglyking van twee stelle vergelykings om warmtevloede in, binne en uit die sonkollektor te bereken het gelei na soortgelyke temperatuurstygings en gelewerde drywing. Die optimale vloei vir maksimum drywing was egter afhanklik van die warmteoordrag modelle. Ondersoek van die gedrag van verskeie turbo-generator uitlegte, deur gebruik van analitiese modelle en optimeringstegnieke het getoon dat die optimale aantal turbines wissel met aanleg grootte, maar die individuele turbine grootte, die aantal lemme en selfs die benuttingsgraad bly feitlik konstant. Daar is egter gevind dat die koste van ’n turbogenerator stelsel beduidend wissel met grootte. ’n Gesamentlike artikel met verskeie Duitse universiteite en instansies het ’n vergelykende koste analise van sonskoorstene gedoen.

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