Thesis (MScIng)--University of Stellenbosch, 2008. / ENGLISH ABSTRACT: The focus of this project was the application of a passive device in the form of a loop thermosyphon as a reactor cavity cooling system (RCCS) for a Pebble Bed Modular Reactor. An extensive literature review showed that loop thermosyphons have been widely researched, both theoretically and experimentally. In the review attention has specifically been given to matters such as safety, instability, control and mathematical modelling. One of the objectives of the project was to build one of the axially symmetric sections of Dobson’s (2006) proposed full scale RCCS using a scaled down version consisting of a single loop heated by a section of the reactor pressure vessel and cooled by a tank of water. The second objective was to derive a theoretical model that could be used in a computer code to simulate the experiment. The theory and experiment would then be compared in order to verify the code. The mathematical model created used the following three major assumptions: quasistatic flow, incompressible liquid and vapour and one dimensionality. The conservation equations in the form of a set of difference equations with the appropriate closure equations were then solved explicitly. It was found that the theoretical results were heavily influenced by the surface optical properties as well as the heat transfer coefficients. The emissivity influenced the transition point from single to two-phase flow as well as the condenser outlet temperature. The single phase heat transfer coefficients influenced the condenser outlet temperature significantly while it was found that for two phase flow the combination of the available boiling and condensation heat transfer coefficients had only minor effects on the end results. A stainless steel and aluminium thermosyphon loop was built using water as the working fluid. A stainless steel heater plate provided the heat input while a 200 L water tank was the heat sink. Temperature and flow rate measurements were recorded as a function of time with various heating/cooling transients from start-up to steady state for three operating modes. The three operating modes were single phase, two-phase and heat pipe mode. It was found that the theoretical temperatures correspond reasonably well with the experimental temperatures. The time predicted by the theoretical model to reach the operating temperature was however somewhat longer than for the experimental. This is to be expected when considering that there is some uncertainty pertaining to the heat transfer coefficients as well as surface emissive properties. The correspondence of the theoretical and experimental fin temperatures was poor due to significant thermal stratification of the air separating the heater plate and fins. Several shortcomings in the theoretical model as well as the experimental setup were identified and discussed. The conclusion was reached that this exploratory study showed that the loop thermosyphon is a viable option for the RCCS and that the mathematical model is a viable theoretical simulation tool. Several recommendations were made for further study to address and overcome the shortcomings identified in the theoretical and experimental models in order to prove this conclusion. Amongst these is the determination of better material surface properties and heat transfer coefficients and improved mass flow rate measurement. Investigating scaling issues, natural convection outside the loop and updating of the computer program is also recommended. / AFRIKAANSE OPSOMMING: Die fokus van hierdie projek was die toepassing van passiewe apparatuur, in die vorm van ‘n geslote lus termoheuwel, as ‘n reaktor kamer verkoellings stelsel vir die korrel bed modulêre reaktor. Die literatuur studie wys dat hierdie tegnologie reeds breedvoerig ondersoek is teoreties sowel as eksperimenteel. In die literatuur oorsig word aandag spesifiek gegee aan veiligheid, onstabiliteit, beheer en modelleering. Een van die doelwitte van die projek was om ‘n klein skaalse model te bou van een van die aksiaal simmetriese seksies van Dobson (2006) se voorgestelde volskaalse reaktor kamer verkoellings stelsel. Die model bestaan uit n enkele lus verhit deur ‘n seksie van die reaktor drukvat en verkoel deur ‘n tenk vol water. Die tweede doelwit was die afleiding van ‘n teoretiese model wat in ‘n rekenaar program gebruik kan word om die eksperiment te simuleer. Die teoretiese en eksperimentele data kan dan vergelyk word om die geldigheid van die program te toets. Die volgende aanames is gemaak tydens die afleiding van die wiskundige model: kwasi-statiese vloei, onsamedrukbare vloeistof en gas en een dimensionalitiet. Die behouds wette is in die vorm van ‘n stel differensie vergelykings met die toepasbare sluitings vergelykings eksplisiet opgelos. Dit is bevind dat die teoretiese resultate swaar beinvloed is deur die materiaal oppervlak eienskappe sowel as die warmteoordrag koëffisiënte. Die emisiviteit beinvloed die oorgangs punt van enkel na twee fase vloei sowel as die kondenser uitlaat temperatuur. Die enkel fase warmteoordrag koëffisiënt het n beduidende invloed op die kondenser uitlaat temperatuur terwyl dit voorkom asof die spesifieke kombinasie van die koking en kondensasie warmteoordrag koëffisiënte minimale invloed op die resultate het in die twee fase gebied. Vlekvrye staal en aluminium is gebruik om die lus te bou met water as die verkoelings middel. Warmte is toegevoeg tot die stelsel deur ’n vlekvrye staal verhittings plaat terwyl ‘n 200 L water tenk die warmte onttrek het. Temperatuur en massa vloei tempo is aangeteken as ‘n funksie van tyd vir verskeie verhitting/verkoellings oorgangs gedragte vanaf begin tot bestendige toestand vir drie bedryfs modusse. Die drie bedryfs modusse was enkel fase, twee fase en hitte pyp modus. Dit is bevind dat die teoretiese temperature redelik goed ooreengekom het met die eksperimentele waardes. Die tyd wat dit neem om by die bedryfs temperatuur te kom soos voorspel deur die teorie is egter langer as wat in die eksperiment gevind is. Dit is te verstane wanneer die onsekerheid in die warmteoordrag koëffisiënte en materiaal oppervlak eienskappe in ag geneem word. Die fin temperature het ‘n swakker ooreenkoms getoon as gevolg van beduidende termiese stratifikasie van die lug tussen die fin en verhittings plaat. Verskeie tekortkominge in die teoretiese model en eksperimentele opstelling is geïdentifiseer en bespreek. Die gevolgtrekking is gemaak dat die ondersoek bewys dat geslote lus termoheuwels ‘n lewensvatbare opsie is vir ‘n reaktor kamer verkoellings stelsel en dat die wiskundige model lewensvatbaar is vir teoretiese simulasie. Verskeie aanbevelings word egter gemaak om die tekortkominge in die teoretiese en eksperimentele modelle aan te spreek om so doende die gevolgtrekking te staaf. Dit word aanbeveel dat beter waardes vir die materiaal oppervlak eienskappe en warmteoordrag koëffisiënte gevind word en verbeterde massa vloei meetings gedoen word. Dit word verder aanbeveel om skaleering asook natuurlike konveksie buite die lus te ondersoek en om die rekenaar program by te werk.

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.