Thesis (MScEng)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The focus of this project was on the potential application of waste heat recovery and utilisation (WHR&U) systems in pebble bed modular reactor (PBMR) technology. The background theory provided in the literature survey showed that WHR&U systems have attracted the attention of many researchers over the past two decades, as using waste heat improves the system overall efficiency, notwithstanding the cost of extra plant. PBMR waste heat streams were identified and investigated based on the amount of heat rejected to the environment. WHR&U systems require specially designed heat recovery equipment, and as such the used and/or spent PBMR fuel tanks were considered by the way of example. An appropriately scaled system was designed, built and tested, to demonstrate the functioning of such a cooling system. Two separate and independent cooling lines, using natural circulation flow in a particular form of heat pipes called thermosyphon loops were used to ensure that the fuel tank is cooled when the power conversion unit has to be switched off for maintenance, or if it fails. A theoretical model that simulates the heat transfer process in the as-designed WHR&U system was developed. It is a one-dimensional flow model assuming quasi-static and incompressible liquid and vapour flow. An experimental investigation of the WHR&U system was performed in order to validate the theoretical model results. The experimental results were then used to modify the theoretical heat transfer coefficients so that they simulate the experiments more accurately. Three energy conversion devices, the dual-function absorption cycle (DFAC), the organic Rankine cycle (ORC) and the Stirling engine (SE), were identified as suitable for transforming the recovered heat into a useful form, depending on the source temperatures from 60 ºC to 800 ºC. This project focuses on a free-piston SE with emphasis on the thermo-dynamic performance of a SE heat exchanger. It was found that a heat exchanger with a copper woven wire mesh configuration has a relatively large gas-to-metal and metal-to-liquid heat transfer area. Tube-in-shell heat exchanger configurations were tested, with the working fluid flowing in ten copper inner pipes, while a coolant flows through the shell tube. A lumped parameter model was used to describe the thermo-fluid dynamic behaviour of the SE heat exchanger. In order to validate the theoretical results, a uni-directional flow experimental investigation was performed. The theoretical model was adjusted so that it simulated the SE heat exchanger. It was found that after this correction the theoretical model accurately predicts the experiment. Finally, a dynamic analysis of the SE heat exchanger experimental set-up was undertaken to show that, although vibrating, the heat exchanger setup assembly was indeed acceptable from a vibrational and fatigue point of view. / AFRIKAANSE OPSOMMING: Die hoofoogmerk met hierdie projek was die moontlike aanwending van afvalhitteherwinningen- benutting-(WHR&U-) stelsels in modulêre-gruisbedreaktor-(PBMR-) tegnologie. Agtergrondteorie in die literatuurondersoek toon dat WHR&U-stelsels al menige navorser se belangstelling geprikkel het, hetsy vanweë die moontlike ekonomiese voordele wat dit inhou óf vir besoedelingsvoorkoming, bo-en-behalwe die koste van bykomende toerusting. Die PBMRafvalhittestrome is ondersoek en bepaal op grond van die hoeveelheid hitte wat dit na die omgewing vrystel. Om in die prosesbehoeftes van WHR&U-stelsels te voorsien, moet goed ontwerpte, doelgemaakte hitteherwinningstoerusting in ʼn verkoelings- en/of verhittingsproses gebruik word, dus is die PBMR as voorbeeld gebruik vir die konsep. ʼn Toepaslik geskaleerde WHR&U-stelsel is dus ontwerp, gebou en getoets om die geldigheid van die stelselontwerp te toon. Twee onafhanklike verkoelingslyne, wat van natuurlike konveksie gebruik maak, in die vorm van hitte-pype of termoheuwel lusse, was gebruik om te verseker dat verkoeling verskaf word wanneer die hoof lus breek of instandhouding nodig hê. ʼn Teoretiese model is ontwikkel wat die hitteoordragproses in die ontwerpte WHR&U-stelsel simuleer. Dié model was ʼn eendimensionele vloeimodel wat kwasistatiese en onsamedrukbare vloeistof- en dampvloei in die WHR&U-stelsel-lusse veronderstel. ʼn Eksperimentele ondersoek is op die WHR&U-stelsel uitgevoer ten einde die teoretiese model se resultate te bevestig. Die eksperimentele resultate was dus geneem om die teoretiese hitteoordragkoëffisiënte aan te pas sodat dit die eksperimente kon simuleer. Drie energieomsettingstoestelle, naamlik die dubbel funksie absorpsie siklus (DFAC), die organiese Rankine siklus (ORC) en die Stirling enjin (SE), is as geskikte toestelle uitgewys om die herwonne hitte op grond van brontemperature tussen 60 ºC en 800 ºC in ʼn bruikbare vorm om te sit. Hierdie tesis het op vryesuier-SE’s gekonsentreer, met klem op die hitteruiler. Meer bepaald is die termodinamiese werkverrigting van ʼn SE-hitteruiler ondersoek. Daar is bevind dat ʼn hitteruiler met ʼn geweefde koperdraadmaas-samestelling oor ʼn betreklik groot gas-totmetaal- en metaal-tot-vloeistof-oordragoppervlakte beskik. Die verhitter en verkoeler is in ʼn buis-in-mantel-vorm ontwerp, met die werksvloeistof wat deur tien koperbinnepype vloei en ʼn koelmiddel deur die mantelbuis. ʼn Saamgevoegde-parameter-model is gebruik om die termodinamiese gedrag van die SEhitteruiler te beskryf. Ten einde die teoretiese resultate te bevestig, is ʼn eenrigtingvloeiproefondersoek uitgevoer. Die teoretiese model is aangepas sodat dit die SE-hitteruiler kon simuleer. Ná die nodige verstellings is daar bevind dat die teoretiese model die proefneming akkuraat voorspel. Laastens was ʼn dinamiese ontleding van die SE-hitteruiler ook onderneem om te toon dat, hoewel dit vibreer, die hitteruiler proef samestel inderdaad veilig is.

Thesis (MScEng (Mechanical and Mechatronic Engineering))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: A reactor cavity cooling system (RCCS) is used in the PBMR to protect the concrete citadel surrounding the reactor from direct nuclear radiation impingement and heat. The speci ed maximum operating temperature of the concrete structure is 65 ±C for normal operating conditions and 125 ±C for emergency shut-down conditions. A conceptual design of an entirely passive RCCS suitable for the PBMR was done by using closed loop thermosyphon heat pipes (CLTHPs) to remove heat from a radiation heat shield over a horizontal distance to an annular cooling dam placed around the PBMR. The radiation shield is placed in the air space between the Reactor Pressure Vessel (RPV) and the concrete citadel, 180 mm from the concrete citadel. A theoretical heat transfer model of the RCCS was created. The theoretical model was used to develop a computer program to simulate the transient RCCS response during normal reactor operation, when the RCCS must remove the excess generated heat from the reactor cavity and during emergency shut-down conditions, when the RCCS must remove the decay heat from the reactor cavity. The main purpose of the theoretical model is to predict the surface temperature of the concrete citadel for di erent heat generation modes in the reactor core and ambient conditions. The theoretical model assumes a 1D geometry of the RCCS. Heat transfer by both radiation and convection from the RPV to the radiation heat shield (HS) is calculated. The heat shield is modelled as a n. The n e ciency was determined with the experimental work. Conduction through the n is considered in the horizontal direction only. The concrete structure surface is heated by radiation from the outer surface of the heat shield as well as by convection heat transfer from the air between the heat shield and the concrete structure surface. The modelling of the natural convection closed loop thermosyphon heat pipes in the RCCS is done by using the Boussinesq approximation and the homogeneous ow model. An experiment was built to verify the theoretical model. The experiment is a full scale model of the PBMR in the horizontal, or main heat transfer, direction, but is only a 2 m high section. The experiments showed that the convection heat transfer between the RPV and the HS cannot be modelled with simple natural convection theory. A Nusselt number correlation developed especially for natural convection in enclosed rectangles found in literature was used to model the convection heat transfer. The Nusselt number was approximately 3 times higher than that which classic convection theory suggested. An optimisation procedure was developed where 121 di erent combinations of n sizes and heat pipe sizes could be used to construct a RCCS once a cooling dam size was chosen. The purpose of the optimisation was to nd the RCCS with the lowest total mass. A cooling dam with a diameter of 50 m was chosen. The optimal RCCS radiation heat shield that operates with the working uid only in single phase has 243 closed loop thermosyphon heat pipes constructed from 62.72 mm ID pipes and 25 mm wide atbar ns. The total mass of the single phase RCCS is 225 tons. The maximum concrete structure temperature is 62.5 ±C under normal operating conditions, 65.8 ±C during a PLOFC emergency shut-down condition and 80.9 ±C during a DLOFC emergency shut-down condition. In the case where one CLTHP fails and the adjacent two must compensate for the loss of cooling capacity, the maximum concrete structure temperature for a DLOFC emergency shut-down will be 87.4 ±C. This is 37.6 ±C below the speci ed maximum temperature of 125 ±C. The RCCS design is further improved when boiling of the working uid is induced in the CLTHP. The optimal RCCS radiation heat shield that operates with the working uid in a liquid-vapour mixture, or two phase ow, has 338 closed loop thermosyphon heat pipes constructed from 38.1 mm ID pipes and 20 mm wide atbar ns. The total mass of the two phase RCCS is 198 tons, 27 tons less than the single phase RCCS. The maximum concrete structure temperature is 60 ±C under normal operating conditions, 2.5 ±C below that of the single phase RCCS. During a PLOFC emergency shut-down condition, the maximum concrete structure temperature is 62.3 ±C, 3.5 ±C below that of the single phase RCCS and still below the normal operating temperature of the single phase RCCS. By inducing two phase ow in the CLTHP, the maximum temperature of the working uid is xed equal to the saturation temperature of the working uid at the vacuum pressure. This property of water is used to limit the concrete structure temperature. This e ect is seen in the transient response of the RCCS where the concrete structure temperature increases until boiling of the working uid starts and then the concrete structure temperature becomes constant irrespective of the heat load on the RCCS. An increased heat load increases the quality of the working uid liquid-vapour mixture. Working uid qualities approaching unity causes numerical instabilities in the theoretical model. The theoretical model cannot capture the heat transfer to a control volume with a density lower than approximately 20 kg/m3. This limits the extent to which the two phase RCCS can be optimised. Recommendations are made relating to future work on how to improve the theoretical model in particular the convection modelling in the reactor cavities as well as the two phase ow of the working uid. Further recommendations are made on how to improve the basic design of the heat shield as well as the cooling section of the CLTHPs. / AFRIKAANSE OPSOMMING: 'n Reaktor lug spasie verkoelingstelsel (RLSVS) word in die PBMR gebruik om die beton wat die reaktor omring te beskerm teen direkte stralingskade en hitte. Die gespesi seerde maksimum temperatuur van die beton is 65 ±C onder normale bedryfstoestande en 125 ±C gedurende die noodtoestand afskakeling van die reaktor. 'n Konseptuele ontwerp van 'n geheel en al passiewe RLSVS geskik vir die PBMR is gedoen deur gebruik te maak van geslote lus termo-sifon (GLTSe) om hitte van die stralingskerm te verwyder oor a horisontale afstand na 'n ringvormige verkoelingsdam wat rondom die reaktor geposisioneer is. Die stralingskerm word in die lug spasie tussen die reaktor drukvat (RDV) en die beton geplaas, 180 mm vanaf die beton. 'n Teoretiese hitteoordrag model van die RLSVS was geskep. Die teoretiese model was gebruik vir die ontwikkeling van 'n rekenaar program wat die transiënte gedrag van die RLSVS sal simuleer gedurende normale bedryfstoestande, waar die oorskot gegenereerde hitte verwyder moet word vanuit die reaktor lug spasie, asook gedurende noodtoestand afskakeling van die reaktor, waar die afnemingshitte verwyder moet word. Die primêre doel van die teoretiese model is om the oppervlak temperatuur van die beton te voorspel onder verskillende bedryfstoestande asook verskillende omgewingstoestande. Die teoretiese model aanvaar 'n 1D geometrie van die RLSVS. Hitte oordrag d.m.v. straling asook konveksie vanaf die RDV na die stralingskerm word bereken. The stralingskerm word gemodelleer as 'n vin. Die vin doeltre endheid was bepaal met die eksperimente wat gedoen was. Hitte geleiding in die vin was slegs bereken in die horisontale rigting. Die beton word verhit deur straling vanaf die agterkant van die stralingskerm asook deur konveksie vanaf die lug tussen die stralingskerm en die beton. The modellering van die natuurlike konveksie GLTS hitte pype word gedoen deur om gebruik te maak van die Boussinesq benadering en die homogene vloei model. 'n Eksperiment was vervaardig om the teoretiese model te veri eer. Die eksperiment is 'n volskaal model van die PBMR in die horisontale, of hoof hitteoordrag, rigting, maar is net 'n 2 m hoë snit. Die eksperimente het gewys dat die konveksie hitte oordrag tussen die RDV en die stralingskerm nie met gewone konveksie teorie gemodelleer kan word nie. 'n Nusselt getal uitdrukking wat spesi ek ontwikkel is vir natuurlike konveksie in geslote, reghoekige luggapings wat in die literatuur gevind was, was gebruik om die konveksie hitteoordrag te modelleer. Die Nusselt getal was ongeveer 3 maal groter as wat klassieke konveksie teorie voorspel het. 'n Optimeringsprosedure was ontwikkel waar 121 verskillende kombinasies van vin breedtes en pyp groottes wat gebruik kan word om 'n RLSVS te vervaardig nadat 'n toepaslike verkoelingsdam diameter gekies is. Die doel van die optimering was om die RLSVS te ontwerp wat die laagste totale massa het. 'n Verkoelingsdam diameter van 50 m was gekies. Die optimale RLSVS stralingskerm, waarvan die vloeier slegs in die vloeistof fase bly, bestaan uit 243 GLTSe wat van 62.72 mm binne diameter pype vervaardig is met 25 mm breë vinne. The totale massa van die enkel fase RLSVS is 225 ton. Die maksimum beton temperatuur is 62.5 ±C vir normale bedryfstoestande, 65.8 ±C vir 'n PLOFC noodtoestand afskakeling en is 80.9 ±C vir 'n DLOFC noodtoestand afskakeling. In die geval waar een GLTS faal gedurende 'n DLOFC noodtoestand afskakeling en die twee naasgeleë GLTSe moet kompenseer vir die vermindering in verkoelings kapasiteit, is die maksimum beton temperatuur 87.4 ±C. Dit is 37.6 ±C laer as die gespesi seerde maksimum temperatuur van 125 ±C. Die RLSVS ontwerp kan verder verbeter word wanneer die vloeier in die GLTSe kook. Die optimale RLSVS stralingskerm met die vloeier wat kook, of in twee fase vloei is, bestaan uit 338 GLTSe wat van 38.1 mm binne diameter pype vervaardig is met 20 mm breë vinne. The totale massa van die twee fase vloei RLSVS is 198 ton, 27 ton ligter as die enkel fase RLSVS. Die maksimum beton temperatuur is 60 ±C vir normale bedryfstoestande, 2.5 ±C laer as die enkel fase RLSVS. Gedurende 'n PLOFC noodtoestand afskakeling is die maksimum beton temperatuur 62.3 ±C, 3.5 ±C laer as die enkel fase RLSVS en nogtans onder die maksimum beton temperatuur van die enkel fase RLSVS vir normale bedryfstoestande. Deur om koking te veroorsaak in die GLTS word die maksimum temperatuur van die vloeier vasgepen gelyk aan die versadigings temperatuur van die vloeier by die vakuüm druk. Hierdie einskap van water word gebruik om 'n limiet te sit op die maksimum temperatuur van die beton. Hierdie e ek kan gesien word in die transiënte gedrag van die RLSVS waar die beton temperatuur styg tot en met koking plaasvind en dan konstant raak ongeag van die hitte belasting op die RLSVS. 'n Toename in die hitte belasting veroorsaak net 'n toename in die kwaliteit van die vloeistof-gas mengsel. Mengsel kwaliteite van 1 nader veroorsaak numeriese onstabiliteite in die teoretiese model. The teoretiese model kan nie die hitteoordrag beskryf na 'n kontrole volume wat 'n digtheid het laer as ongeveer 20 kg/m3. Hierdie plaas 'n limiet op die optimering van die twee fase RLSVS. Aanbevelings was gemaak met betrekking tot toekomstige werk aangaande die verbetering van die teoretiese model met spesi eke klem op die modellering van konveksie in die reaktor asook die modellering van twee fase vloei. Verdere aanbevelings was gemaak aangaande die verbetering van die stralingskerm ontwerp asook die ontwerp van die verkoeling van die GLTSe.

Thesis (MScEng (Mechanical and Mechatronic Engineering))--University of Stellenbosch, 2011. / ENGLISH ABSTRACT: The feasibility of a closed loop thermosyphon for the Reactor Cavity Cooling System of the Pebble Bed Modular Reactor has been the subject of many research projects. Difficulties identified by previous studies include the hypothetical inaccuracies of heat transfer coefficient correlations available in literature. The aim of the research presented here is to develop inside-pipe heat transfer correlations that are specific to the current design of the RCCS. In order to achieve this, a literature review is performed which identifies reactors which employ closed loop thermosyphons and natural circulation. The literature review also explains the general one-dimensional two-fluid conservation equations that form the basis for numerical modelling of natural circulation loops. The literature review lastly discusses available heat transfer coefficient correlations with the aim of identifying over which ranges and under which circumstances these correlations are considered accurate. The review includes correlations commonly used in natural circulation modelling in the nuclear industry in aims of identifying correlations applicable to the modelling of the proposed RCCS. One of the objectives of this project is to design and build a one-third-height-scale model of the RCCS. Shortcomings of previous experimental models were assessed and, as far as possible, compensated for in the design of the model. Copper piping is used, eliminating material and surface property uncertainties. Several sight glasses are incorporated in the model, allowing for the visual identification of two-phase flow regimes. An orifice plate is used allowing for bidirectional flow measurement. The orifice plate, thermocouples and pipe-in-pipe heat exchangers are calibrated in-situ to minimize experimental error and aid repeatability. Twelve experiments are performed with data logging occurring every ten seconds. The results presented here are limited to selected single and two-phase flow operating mode results. Error analyses and repeatability of experimental measurements for single and two-phase operating modes as well as cooling water mass flow rates are performed, to show repeatability of experimental results. These results are used to mathematically determine the experimental inside-pipe heat transfer coefficients for both the evaporator and condenser sections. Trends in the heat transfer coefficient profiles are identified and the general behaviour of the profiles is thoroughly explained. The RCCS is modelled as a one-dimensional system. Correlations for the friction factor, heat transfer coefficient, void fraction and two-phase frictional multiplier are identified. The theoretical heat transfer coefficients are calculated using the mathematical model and correlations identified in the literature review. Fluid parameters are evaluated using experimentally determined temperatures and mass flow rates. The resulting heat transfer coefficient profiles are compared to experimentally determined profiles, to confirm the hypothesis that existing correlations do not accurately predict the inside-pipe heat transfer coefficients. The experimentally determined coefficients are correlated to 99% confidence intervals. These generated correlations, along with identified and established twophase heat transfer coefficient correlations, are used in a mathematical model to generate theoretical coefficient profiles. These are compared to the experimentally determined coefficients to show prediction accuracy. / AFRIKAANSE OPSOMMING: Die haalbaarheid van ‘n natuurlike sirkulasie geslote lus vir die Reaktor Holte Verkoeling Stelsel (RHVS) van die Korrelbed Modulêre Kern-Reaktor (KMKR) is die onderwerp van talle navorsings projekte. Probleme geïdentifiseer in vorige studies sluit in die hipotetiese onakkuraatheid van hitte-oordrag koëffisiënt korrelasies beskikbaar in literatuur. Die doel van die navorsing aangebied is om binne-pyp hitte-oordrag koëffisiënt korrelasies te ontwikkel spesifiek vir die huidige ontwerp van die RHVS. Ten einde dit te bereik, word ‘n literatuurstudie uitgevoer wat kern-reaktors identifiseer wat gebruik maak van natuurlike sirkulasie lusse. Die literatuurstudie verduidelik ook die algemene een-dimensionele twee-vloeistof behoud vergelykings wat die basis vorm vir numeriese modellering van natuurlike sirkulasie lusse. Die literatuurstudie bespreek laastens beskikbare hitte-oordrag koëffisiënt korrelasies met die doel om te identifiseer vir welke massavloei tempo waardes en onder watter omstandighede hierdie korrelasies as korrek beskou is. Die ontleding sluit korrelasies in wat algemeen gebruik word in die modellering van natuurlike sirkulasie in die kern industrie met die hoop om korrelasies vir gebruik in die modellering van die voorgestelde RHVS te identifiseer. Een van die doelwitte van die projek is om ‘n een-derde-hoogte-skaal model van die RHVS te ontwerp en te bou. Tekortkominge van vorige eksperimentele modelle is geidentifiseer en, so ver as moonlik, voor vergoed in die ontwerp van die model. Koper pype word gebruik wat die onsekerhede van materiaal en opperkvlak eindomme voorkom. Verkseie deursigtige polikarbonaat segmente is ingesluit wat visuele identifikasie van twee-fase vloei regimes toelaat. ‘n Opening plaat word gebruik om voorwaartse en terugwaartse vloeimeting toe te laat. Die opening plaat, termokoppels en hitte uitruilers is gekalibreer in plek om eksperimentele foute te verminder en om herhaalbaarheid te verseker. Twaalf eksperimente word uitgevoer en data word elke tien sekondes aangeteken. Die resultate wat hier aangebied word, is beperk tot geselekteerde enkel- en tweefase vloei meganismes van werking. Fout ontleding en herhaalbaarheid van eksperimentele metings, om die herhaalbaarheid van eksperimentele resultate te toon. Hierdie is gebruik om wiskundig te bepaal wat die eksperimentele binne-pyp hitte-oordrag koëffisiënte is vir beide die verdamper en kondenseerder afdelings. Tendense in die hitte-oordrag koëffisiënt profiele word geïdentifiseer en die algemene gedrag van die profiles is deeglik verduidelik. Die RHVS is gemodelleer as 'n een-dimensionele stelsel. Korrelasies vir die wrywing faktor, hitte-oordrag koëffisiënte, leegte-breuk en twee-fase wrywings vermenigvuldiger word geïdentifiseer. Die teoretiese hitte-oordrag koëffisiënte word bereken deur middle van die wiskundige model en korrelasies wat in literatuur geidentifiseer is. Vloeistof parameters is geëvalueer met eksperimenteel bepaalde temperature en massa-vloei tempos. Die gevolglike hitte-oordrag koëffisiënt profiles is vergelyk met eksperimentele profiele om die hipotese dat die bestaande korrelasies nie die binne-pyp hitte-oordrag koëffisiënte akkuraat voorspel nie, te bevestig. Die eksperimenteel bepaalde koëffisiënte is gekorreleer en die gegenereerde korrelasies, saam met geïdentifiseerde twee-fase hitte-oordrag koëffisiënt korrelasies, word gebruik in 'n wiskundige model om teoretiese koëffisiënt profiele te genereer. Dit word dan vergelyk met die eksperimenteel bepaalde hitteoordrag koëffisiënte om die akkuraatheid van voorspelling te toon. Tekortkominge in die teoretiese en eksperimentele model word geïdentifiseer en aanbevelings gemaak om hulle aan te spreek in die toekoms.

Thesis (MScEng)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: A high temperature reactor (HTR) generates heat inside of the reactor core through nuclear fission, from where the heat is transferred through the core and heats up the reactor pressure vessel (RPV). The heat from the RPV is transported passively through the reactor cavity, where it is cooled by the reactor cavity cooling system (RCCS), through the concrete confinement structure and ultimately into the environment. The concrete confinement structure can withstand temperatures of up to 65°C for normal operating conditions and temperatures of up to 125°C during an emergency. This project endeavours to research the heat transfer between an HTR’s RPV and the outside of the concrete confinement structure by utilising three investigative approaches: experimental, computational fluid dynamics (CFD) and analytical. The first approach, an experimental analysis, required the development of an experi- mental model. The model was used to perform experiments and gather temperature data that could be used to verify the accuracy of the CFD simulations. The second approach was a CFD analysis of the experimental model, and the external concrete temperatures from the simulation were compared with the temperatures measured with the experimen- tal model. Finally, an analytical analysis was performed in order to better understand CFD and how CFD solves natural convection-type problems. The experiments were performed successfully and the measurements taken were com- pared with the CFD results. The CFD results are in good agreement with the Dry experiments, but not with the Charged experiments. It was identified that the inaccurate results for the CFD simulations of the Charged experiments arose due to convective heat leakage through gaps in the heat shield and between the heat shield and the sides of the experimental model. A computer program was developed for the analytical analysis and it was established that the program could successfully solve the natural convection in a square cavity - as required. / AFRIKAANSE OPSOMMING: ’n Hoë temperatuur reaktor (HTR) genereer hitte binne die reaktor kern deur kernsplyting en die hitte word dan deur die kern versprei en verhit die reaktor se drukvat. Die hitte van die reaktor drukvat word dan passief deur die reaktorholte versprei, waar dit deur die reaktorholte se verkoelingstelsel afgekoel word, en deur die beton beskermingstruktuur gelei word en uiteindelik die omgewing bereik. Die beton beskermingstruktuur kan temperature van tot 65°C onder normale operasietoestande van die reaktor weerstaan, en temperature van tot 125°C tydens ’n noodgeval. Hierdie projek poog om die hitte-oordrag tussen ’n HTR-reaktor drukvat en die buitekant van die beton beskermingstruktuur te on- dersoek deur gebruik te maak van drie ondersoekbenaderings: eksperimenteel, numeriese vloei dinamika (NVD) en analities. Die eerste benadering, ’n eksperimentele analise, het die ontwikkeling van ’n eksper- imentele model vereis. Die model is gebruik om eksperimente uit te voer en temperatu- urmetings te neem wat gebruik kon word om die akkuraatheid van die NVD simulasies te bevestig. Die tweede benadering was ’n NVD-analise van die eksperimentele model, en die eksterne betontemperature verkry van die simulasies is vergelyk met die gemete temperature van die eksperimente. Uiteindelik is ’n analitiese analise uitgevoer ten einde NVD beter te verstaan en hoe NVD natuurlike konveksie-tipe probleme sal oplos. Die eksperimente is suksesvol uitgevoer en die metings is gebruik om die NVD resultate mee te vergelyk. Die NVD resultate van die Droë eksperimente het goeie akkuraatheid getoon. Dit was nie die geval vir die Gelaaide eksperimente nie. Daar is geïdentifiseer dat die verskille in resultate tussen die NVD en die eksperimente aan natuurlike konveksie hitte verliese deur gapings in die hitteskuld en tussen die hitteskuld en die kante van die eksperimentele model toegeskryf kan word. ’n Rekenaarprogram is geskryf vir die analitiese ontleding en die program kon suksesvol die natuurlike konveksie in ’n vierkantige ruimte oplos.

Thesis (MBA)--Stellenbosch University, 2002. / ENGLISH ABSTRACT: The Pebble Bed Modular Reactor is a new and inherently safe concept for a nuclear power generation plant. In order to obtain the necessary licenses to build and operate this reactor, numerous design and safety analyses need to be performed. The results of these analyses must be supported with substantial proof to provide the nuclear authorities with a sufficient level of confidence in these results to be able to supply the required licences. Beside the obvious need for a sufficient level of confidence in the safety analyses, the analyses concerned with investment protection also need to be reliable from the investors’ point of view. The process to be followed to provide confidence in these analyses is the verification and validation process. It is aimed at presenting reliable material against which to compare the results from the simulations. This material for comparison will consist of a combination of results from experimental data, extracts from actual plant data, analytical solutions and independently developed solutions for the simulation of the event to be analysed. Besides comparison with these alternative sources of information, confidence in the results will also be built by providing validated statements on the accuracy of the results and the boundary conditions with which the simulations need to comply. Numerous standards exist that address the verification and validation of computer software, for instance by organisations such as the American Society of Mechanical Engineers (ASME) and the Institute of Electrical and Electronics Engineers (IEEE). The focal points of the verification and validation of the design and safety analyses performed on typical PBMR modes and states, and the requirements imposed by both the local and overseas nuclear regulators, are not entirely enveloped by these standards. For this reason, PBMR developed a systematic and disciplined approach for the preparation of the Verification and Validation Plan, aimed at capturing the essence of the analyses. This approach aims to make a definite division between software development and the development of technical analyses, while still using similar processes for the verification and validation. The reasoning behind this is that technical analyses are performed by engineers and scientists who should only be responsible for the verification and validation of the models and data they use, but not for the software they are dependent on. Software engineers should be concerned with the delivery of qualified software to be used in the technical analyses. The PBMR verification and validation process is applicable to both hand calculations and computer-aided analyses, addressing specific requirements in clearly defined stages of the software and Technical Analysis life cycle. The verification and validation effort of the Technical Analysis activity is divided into the verification and validation of models and data, the review of calculational tasks, and the verification and validation of software, with the applicable information to be validated, captured in registers or databases. The resulting processes are as simple as possible, concise and practical. Effective use of resources is ensured and internationally accepted standards have been incorporated, aiding in faith in the process by all stakeholders, including investors, nuclear regulators and the public. / AFRIKAASE OPSOMMING: Die Modulêre Korrelbedreaktor is ’n nuwe konsep vir ’n kernkragsentrale wat inherent veilig is. Dit word deur PBMR (Edms.) Bpk. ontwikkel. Om die nodige vergunnings om so ’n reaktor te kan bou en bedryf, te bekom, moet ’n aansienlike hoeveelheid ontwerp- en veiligheidsondersoeke gedoen word. Die resultate wat hierdie ondersoeke oplewer, moet deur onweerlegbare bewyse ondersteun word om vir die owerhede ’n voldoende vlak van vertroue in die resultate te gee, sodat hulle die nodigde vergunnings kan maak. Benewens die ooglopende noodsaak om ’n voldoende vlak van vertroue in die resultate van die veiligheidsondersoeke te hê, moet die ondersoeke wat met die beskerming van die beleggers se beleggings gepaard gaan, net so betroubaar wees. Die proses wat gevolg word om vertroue in die resultate van die ondersoeke op te bou, is die proses van verifikasie en validasie. Dié proses is daarop gerig om betroubare vergelykingsmateriaal vir simulasies voor te lê. Hierdie vergelykingsmateriaal vir die gebeurtenis wat ondersoek word, sal bestaan uit enige kombinasie van inligting wat in toetsopstellings bekom is, wat in bestaande installasies gemeet is, wat analities bereken is; asook dit wat deur ’n derde party onafhanklik van die oorspronklike ontwikkelaars bekom is. Vertroue in die resultate van die ondersoeke sal, behalwe deur vergelyking met hierdie alternatiewe bronne van inligting, ook opgebou word deur die resultate te voorsien van ’n gevalideerde verklaring wat die akkuraatheid van die resultate aantoon en wat die grensvoorwaardes waaraan die simulasies ook moet voldoen, opsom. Daar bestaan ’n aansienlike hoeveelheid internasionaal aanvaarde standaarde wat die verifikasie en validasie van rekenaarsagteware aanspreek. Die standaarde kom van instansies soos die Amerikaanse Vereniging vir Meganiese Ingenieurs (ASME) en die Instituut vir Elektriese en Elektroniese Ingenieurs (IEEE) – ook van Amerika. Die aandag wat deur die Suid-Afrikaanse en oorsese kernkragreguleerders vereis word vir die toestande wat spesifiek geld vir korrelbedreaktors, word egter nie geheel en al deur daardie standaarde aangespreek nie. Daarom het die PBMR maatskappy ’n stelselmatige benadering ontwikkel om verifikasie- en validasieplanne voor te berei wat die essensie van die ondersoeke kan ondervang. Hierdie benadering is daarop gemik om ’n duidelike onderskeid te maak tussen die ontwikkeling van sagteware en die ontwikkeling van tegniese ondersoeke, terwyl steeds gelyksoortige prosesse in die verifikasie en validasie gebruik sal word. Die rede hiervoor is dat tegniese ondersoeke uitgevoer word deur ingenieurs en wetenskaplikes wat net vir verifikasie en validasie van hulle eie modelle en die gegewens verantwoordelik gehou kan word, maar nie vir die verifikasie en validasie van die sagteware wat hulle gebruik nie. Ingenieurs wat spesialiseer in sagteware-ontwikkeling behoort verantwoordelik te wees vir die daarstelling van sagteware wat deur die reguleerders gekwalifiseer kan word, sodat dit in tegniese ondersoeke op veiligheidsgebied gebruik kan word. Die verifikasie- en validasieproses van die PBMR is sowel vir handberekeninge as vir rekenaarondersteunde-ondersoek geskik. Hierdie proses spreek spesifieke vereistes in onderskeie stadiums gedurende die lewenssiklusse van die ontwikkeling van sagteware en van tegniese ondersoeke aan. Die verifikasie- en validasiewerk vir tegniese ondersoeksaktiwiteite is verdeel in die verifikasie en validasie van modelle en gegewens, die nasien van berekeninge en die verifikasie en validasie van sagteware, waarby die betrokke inligting wat gevalideer moet word, versamel word in registers of databasisse. Die prosesse wat hieruit voortgevloei het, is so eenvoudig as moontlik, beknop en prakties gehou. Hierdeur is ’n effektiewe benutting van bronne verseker. Internasionaal aanvaarde standaarde is gebruik wat die vertroue in die proses deur alle betrokkenes, insluitende beleggers, die owerhede en die publiek, sal bevorder.

Om man ser på de bästa nu kända algoritmerna för att avgöra satisfierbarhet hos logiska formler så är de allra flesta baserade på den så kallade DPLL-metoden utökad med klausulinlärning. De två viktigaste gränssättande faktorerna för sådana algoritmer är hur mycket tid och minne de använder, och att förstå sig på detta är därför en fråga som har stor praktisk betydelse. Inom området beviskomplexitet svarar tids- och minnesåtgång mot längd och minne hos resolutionsbevis för formler i konjunktiv normalform (CNF-formler). En lång rad arbeten har studerat dessa mått och även jämfört dem med bredden av bevis, ett annat mått som visat sig höra nära samman med både längd och minne. Mer formellt är längden hos ett bevis antalet rader, dvs. klausuler, bredden är storleken av den största klausulen, och minnet är maximala antalet klausuler som man behöver komma ihåg samtidigt om man under bevisets gång bara får dra nya slutsatser från klausuler som finns sparade. För längd och bredd har man lyckats visa en rad starka resultat men förståelsen av måttet minne har lämnat mycket i övrigt att önska. Till exempel så är det känt att minnet som behövs för att bevisa en formel är minst lika stort som den nödvändiga bredden, men det har varit en öppen fråga om minne och bredd kan separeras eller om de två måtten mäter "samma sak" i den meningen att de alltid är asymptotiskt lika stora för en formel. Det har också varit okänt om det faktum att det finns ett kort bevis för en formel medför att formeln också kan bevisas i litet minne (motsvarande påstående är sant för längd jämfört med bredd) eller om det tvärtom kan vara så att längd och minne är "helt orelaterade" på så sätt att även korta bevis kan kräva maximal mängd minne. I denna avhandling presenterar vi först ett förenklat bevis av trade-off-resultatet för längd jämfört med minne i (Hertel och Pitassi 2007) och visar hur samma idéer kan användas för att visa ett par andra exponentiella avvägningar i relationerna mellan olika beviskomplexitetsmått för resolution. Sedan visar vi att det finns formler som kan bevisas i linjär längd och konstant bredd men som kräver en mängd minne som växer logaritmiskt i formelstorleken, vilket vi senare förbättrar till kvadratroten av formelstorleken. Dessa resultat separerar således minne och bredd. Genom att använda andra men besläktade idéer besvarar vi därefter frågan om hur minne och längd förhåller sig till varandra genom att separera dem på starkast möjliga sätt. Mer precist visar vi att det finns CNF-formler av storlek O(n) som har resolutionbevis i längd O(n) och bredd O(1) men som kräver minne minst Omega(n/log n). Det gemensamma temat för dessa resultat är att vi studerar formler som beskriver stenläggningsspel, eller pebblingspel, på riktade acykliska grafer. Vi bevisar undre gränser för det minne som behövs för den så kallade pebblingformeln över en graf uttryckt i det svart-vita pebblingpriset för grafen i fråga. Slutligen observerar vi att vår optimala separation av minne och längd i själva verket är ett specialfall av en mer generell sats. Låt F vara en CNF-formel och f:{0,1}^d->{0,1} en boolesk funktion. Ersätt varje variabel x i F med f(x_1, ..., x_d) och skriv om denna nya formel på naturligt sätt som en CNF-formel F[f]. Då gäller, givet att F och f har rätt egenskaper, att F[f] kan bevisas i resolution i väsentligen samma längd och bredd som F, men att den minimala mängd minne som behövs för F[f] är åtminstone lika stor som det minimala antalet variabler som måste förekomma samtidigt i ett bevis för F. / Most state-of-the-art satisfiability algorithms today are variants of the DPLL procedure augmented with clause learning. The two main bottlenecks for such algorithms are the amounts of time and memory used. Thus, understanding time and memory requirements for clause learning algorithms, and how these requirements are related to one another, is a question of considerable practical importance. In the field of proof complexity, these resources correspond to the length and space of resolution proofs for formulas in conjunctive normal form (CNF). There has been a long line of research investigating these proof complexity measures and relating them to the width of proofs, another measure which has turned out to be intimately connected with both length and space. Formally, the length of a resolution proof is the number of lines, i.e., clauses, the width of a proof is the maximal size of any clause in it, and the space is the maximal number of clauses kept in memory simultaneously if the proof is only allowed to infer new clauses from clauses currently in memory. While strong results have been established for length and width, our understanding of space has been quite poor. For instance, the space required to prove a formula is known to be at least as large as the needed width, but it has remained open whether space can be separated from width or whether the two measures coincide asymptotically. It has also been unknown whether the fact that a formula is provable in short length implies that it is also provable in small space (which is the case for length versus width), or whether on the contrary these measures are "completely unrelated" in the sense that short proofs can be maximally complex with respect to space. In this thesis, as an easy first observation we present a simplified proof of the recent length-space trade-off result for resolution in (Hertel and Pitassi 2007) and show how our ideas can be used to prove a couple of other exponential trade-offs in resolution. Next, we prove that there are families of CNF formulas that can be proven in linear length and constant width but require space growing logarithmically in the formula size, later improving this exponentially to the square root of the size. These results thus separate space and width. Using a related but different approach, we then resolve the question about the relation between space and length by proving an optimal separation between them. More precisely, we show that there are families of CNF formulas of size O(n) that have resolution proofs of length O(n) and width O(1) but for which any proof requires space Omega(n/log n). All of these results are achieved by studying so-called pebbling formulas defined in terms of pebble games over directed acyclic graphs (DAGs) and proving lower bounds on the space requirements for such formulas in terms of the black-white pebbling price of the underlying DAGs. Finally, we observe that our optimal separation of space and length is in fact a special case of a more general phenomenon. Namely, for any CNF formula F and any Boolean function f:{0,1}^d->{0,1}, replace every variable x in F by f(x_1, ..., x_d) and rewrite this new formula in CNF in the natural way, denoting the resulting formula F[f]. Then if F and f have the right properties, F[f] can be proven in resolution in essentially the same length and width as F but the minimal space needed for F[f] is lower-bounded by the number of variables that have to be mentioned simultaneously in any proof for F. / QC 20100831

Turbulent flows and coherent structures emerging within turbulent flow fields have been extensively studied for the past few decades and a wide variety of experimental and numerical techniques have been developed for measurement and analysis of turbulent flows. The complex nature of turbulence requires methods that can accurately estimate its highly chaotic spatial and temporal behavior. Some of the classical cases of turbulent flows with simpler geometries have been well characterized by means of the existing experimental techniques and numerical models. Nevertheless, since most turbulent fields are of complex geometries; there is an increasing interest in the study of turbulent flows through models with more complicated geometries. In this dissertation, characteristics of turbulent flows through two different facilities with complex geometries are studied applying two different experimental methods. The first study involves the investigation of turbulent impinging jets through a staggered array of rods with or without crossflow. Such flows are crucial in various engineering disciplines. This experiment aimed at modeling the coolant flow behavior and mixing phenomena within the lower plenum of a Very High Temperature Reactor (VHTR). Dynamic Particle Image Velocimetry (PIV) and Matched Index of Refraction (MIR) techniques were applied to acquire the turbulent velocity fields within the model. Some key flow features that may significantly enhance the flow mixing within the test section or actively affect some of the structural components were identified in the velocity fields. The evolution of coherent structures within the flow field is further investigated using a Snapshot Proper Orthogonal Decomposition (POD) technique. Furthermore, a comparative POD method is proposed and successfully implemented for identification of the smaller but highly influential coherent structures which may not be captured in the full-field POD analysis. The second experimental study portrays the coolant flow through the core of an annular pebble bed VHTR. The complex geometry of the core and the highly turbulent nature of the coolant flow passing through the gaps of fuel pebbles make this case quite challenging. In this experiment, a high frequency Hot Wire Anemometry (HWA) system is applied for velocity measurements and investigation of the bypass flow phenomena within the near wall gaps of the core. The velocity profiles within the gaps verify the presence of an area of increased velocity close to the outer reflector wall; however, the characteristics of the coolant flow profile is highly dependent on the gap geometry and to a less extent on the Reynolds number of the flow. The time histories of the velocity are further analyzed using a Power Spectra Density (PSD) technique to acquire information about the energy content and energy transfer between eddies of different sizes at each point within the gaps.

The effect of water ingress in two pebble bed high temperature gas-cooled reactors i.e. the PBMR-200 MWthermal and the PBMR-400 MWthermal were simulated and compared using the VSOP 99/05 suite of codes. To investigate the effect of this event on reactivity, power profiles and thermal neutron flux profiles, the addition of partial steam vapour pressures in stages up to 400 bar into the primary circuit for the PBMR-400 and up to 300 bar for the PBMR- 200 was simulated for both reactors. During the simulation, three scenarios were simulated, i.e. water ingress into the core only, water ingress into the reflectors only and water ingress into both the core and reflectors. The induced reactivity change effects were compared for these reactors. An in-depth analysis was also carried out to study the mechanisms that drive the reactivity changes for each reactor caused by water ingress into the fuel core only, the riser tubes in the reflectors only and ingress into both the fuel core and the riser tubes in the reflectors. The knowledge gained of these mechanisms and effects was used in order to propose design changes aimed at mitigating the reactivity increases, caused by realistic water ingress scenarios. Past results from simulations of water ingress into Pebble Bed Reactors were used to validate and verify the present simulation approach and results. The reactivity increase results for both reactors were in agreement with the German HTR-Modul calculations. / Thesis (MSc (Engineering Sciences in Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013

The effect of water ingress in two pebble bed high temperature gas-cooled reactors i.e. the PBMR-200 MWthermal and the PBMR-400 MWthermal were simulated and compared using the VSOP 99/05 suite of codes. To investigate the effect of this event on reactivity, power profiles and thermal neutron flux profiles, the addition of partial steam vapour pressures in stages up to 400 bar into the primary circuit for the PBMR-400 and up to 300 bar for the PBMR- 200 was simulated for both reactors. During the simulation, three scenarios were simulated, i.e. water ingress into the core only, water ingress into the reflectors only and water ingress into both the core and reflectors. The induced reactivity change effects were compared for these reactors. An in-depth analysis was also carried out to study the mechanisms that drive the reactivity changes for each reactor caused by water ingress into the fuel core only, the riser tubes in the reflectors only and ingress into both the fuel core and the riser tubes in the reflectors. The knowledge gained of these mechanisms and effects was used in order to propose design changes aimed at mitigating the reactivity increases, caused by realistic water ingress scenarios. Past results from simulations of water ingress into Pebble Bed Reactors were used to validate and verify the present simulation approach and results. The reactivity increase results for both reactors were in agreement with the German HTR-Modul calculations. / Thesis (MSc (Engineering Sciences in Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013

Through the years different models have been proposed to calculate the total effective thermal conductivity in packed beds. The purpose amongst others of these models is to calculate the temperature distribution and heat flux in high temperature pebble bed reactors. Recently a new model has been developed at the North–West University in South Africa and is called the Multi–Sphere Unit Cell (MSUC) model. The unique contribution of this model is that it manages to also predict the effective thermal conductivity in the near wall region by taking into account the local variation in the porosity. Within the MSUC model the thermal radiation has been separated into two components. The first component is the thermal radiation exchange between spheres in contact with one another, which for the purpose of this study is called the short range radiation. The second, which is defined as the longrange radiation, is the thermal radiation between spheres further than one sphere diameter apart and therefore not in contact with each other. Currently a few shortcomings exist in the modelling of the long–range radiation heat transfer in the MSUC model. It was the purpose of this study to address these shortcomings. Recently, work has been done by Pitso (2011) where Computational Fluid Dynamics (CFD) was used to characterise the long–range radiation in a packed bed. From this work the Spherical Unit Nodalisation (SUN) model has been developed. This study introduces a method where the SUN model has been modified in order to model the long–range radiation heat transfer in an annular reactor packed with uniform spheres. The proposed solution has been named the Cylindrical Spherical Unit Nodalisation (CSUN, pronounced see–sun) model. For validation of the CSUN model, a computer program was written to simulate the bulk region of the High Temperature Test Unit (HTTU). The simulated results were compared with the measured temperatures and the associated heat flux of the HTTU experiments. The simulated results from the CSUN model correlated well with these experimental values. Other thermal radiation models were also used for comparison. When compared with the other radiation models, the CSUN model was shown to predict results with comparable accuracy. Further research is however required by comparing the new model to experimental values at high temperatures. Once the model has been validated at high temperatures, it can be expanded to near wall regions where the packing is different from that in the bulk region. / Thesis (M.Ing. (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2012.