Magistro darbe analizuotos vakuuminių saulės kolektorių, skirtų vandeniui šildyti sistemos energetiniai parametrai, rodikliai ir konstrukcijos. Taip pat šiame darbe nagrinėjama vakuuminio saulės kolektoriaus energetinės charakteristikos. Darbą sudaro dvi dedamosios dalys: analitinė ir praktinė darbo dalys. Analitinėje dalyje apžvelgtos skirtingų tipų saulės kolektorių charakteristikos, saulės kolektorinių vandens šildymo sistemų veikimo principas ir panaudojimo galimybės. Trumpai apžvelgta perteklinės energijos panaudojimo galimybės ir saulės kolektorių sistemos projektavimo principas. Praktinėje darbo dalyje tirta saulės kolektorinė vandens šildymo sistema gamybinėmis sąlygomis. Atskleistas sistemos veikimo mechanizmas, ištirtas kolektorių našumas skirtingomis darbinėmis sąlygomis. Darbo pabaigoje suformuluotos atlikto tyrimo išvados. Pateiktos rekomendacijos tirtos saulės kolektorinės vandens šildymo sistemos administraciniam personalui. / Master's thesis analyses vacuum solar collectors for water heating system energy parameters, indicators and construction. Also vacuum solar collector system energy characteristics. The work consists of two component parts: the analytical and practical parts of the research. In the analytical part is an overview of the different types of solar collector performance, solar water heating systems operation and utilization. Short overview of surplus energy utilization possibilities and solar system design principle. In the practical part of the thesis is investigated solar collector water heating system under production conditions. Revealed mechanism of the system, investigated thermal performance under different operating conditions. In the end of research thesis conclusions are formulated. Recommendations were given for tested solar collector water heating system administrative personnel.

The development of new types of offshore wind turbine on floating platforms requires the development of new approaches to modelling the combined platform-turbine system. In this thesis a linearised frequency-domain approach is developed which gives fast but approximate results: linearised models of the structural dynamics, hydrodynamics, aerodynamics and control system dynamics are brought together to find the overall response of the floating wind turbine to harmonic wind and wave loading. Initially, a nonlinear flexible multibody dynamics code is developed and verified, which is then used to provide reference nonlinear simulation results. The structural dynamics of a wind turbine on a moving platform are shown to be nonlinear, but for realistic conditions the effects are small. An approximate analysis of the second-order response of floating cylinders to hydrodynamic loads suggests slow drift motion may be relatively small for floating wind turbines, compared to other floating offshore structures. The aerodynamic loads are linearised using both harmonic and tangent linearisation approaches; the harmonic linearisation gives improved results when stall occurs. The wake dynamics can also be included. The control system behaviour is linearised using the same method, which works well when the wind speed is far from the rated wind speed; close to the rated wind speed the nonlinearity is stronger, but further improvement should be possible. These sub-models are combined to give a simple but complete model of a floating wind turbine, with flexible blades and a flexible tower, but neglecting the control system behaviour, wake dynamics and nonlinear hydrodynamic loads. For the OC3-Hywind turbine, the accuracy of the results is assessed by comparison to nonlinear time-domain simulations using the commercial code Bladed. Peak-peak errors of less than 5 % are achievable for many harmonic wind and wave inputs, but certain conditions lead to larger errors. The effect of including linearised control system behaviour is demonstrated for a subset of conditions. Overall, the results are promising but more work is needed for practical application.

<p>  </p> <p>As aviation fuel costs and consumption have continued to rise over recent decades, gas turbine engine manufacturers have sought methods to reduce fuel burn. Manufacturers plan to achieve this by reducing the specific fuel consumption of the machine by increasing the bypass ratio through a reduction of the diameter of the engine core. This presents an opportunity for implementing a centrifugal compressor as the final stage of the high-pressure compressor. The vaned diffuser in a centrifugal compressor stage maintains an integral role in determining the extents of the operating range as well as conditioning the flow for the downstream combustor. Thus, it is critical to understand the aerodynamics and performance of the vaned diffuser across the entire compressor operating range.</p> <p>This investigation focused on seven compressor operating points at the stage’s design corrected speed, which ranged from choked flow to the minimum mass flow rate before rotating stall. Steady-state and unsteady performance data were acquired to study the aerodynamics at each operating point as well as the steady-state performance of the vaned diffuser. Laser Doppler velocimetry, high-frequency pressure transducers, and additive manufacturing techniques were all implemented to acquire data in the research compressor.</p> <p>Unsteady velocity measurements were acquired in the vaneless space and were used to quantify the change in diffuser inlet incidence as the stage mass flow rate changes. The impeller exit jet and wake were compared at each operating point to understand the effect of these flow structures on the spanwise incidence profile. Steady-state performance metrics for the vaned diffuser were compared with the change in incidence to assess the effect of incidence on performance. Maximum static pressure recovery and minimum total pressure loss occurred at the maximum incidence operating point. </p> <p>The chordwise static pressure distribution is critical for health monitoring of the polymer, additive manufactured diffuser vanes. Steady-state and unsteady pressure measurements were acquired along the diffuser vane surface to assess the change in the aerodynamic lift force across the compressor operating range as well as the static pressure differential across the vane leading edge. The maximum unsteady lift on the diffuser vanes was up to 34% greater than the steady-state lift force. Unsteady static pressure differentials across the diffuser vane leading edge were similar to the steady-state values, but they were marginally greater across the entire examined operating range. These unsteady pressure measurements were acquired with high-frequency response pressure transducers installed along the diffuser vane surfaces. These transducers were also used to study the rotating stall and surge behavior of the investigated centrifugal compressor stage. This centrifugal compressor stage exhibits a spike-type rotating stall pattern at the onset of stage instability, which rapidly evolves into full flow reversal with several surge cycles. During these surge cycles, the diffuser vane leading edges are subject to a 20 psid static pressure differential. </p> <p>A computational model was used to predict the compressor flow at three different operating points. This model utilized the BSL-EARSM turbulence model, and it included surface roughness and an experimentally measured shroud thermal profile. The model accurately predicted the diffuser inlet flow angles near the shroud, but it predicted more radial flow near midspan. The diffuser vane leading edge static pressure differential was predicted within 1 psid at higher aerodynamic loading conditions. The differences between the computationally predicted and experimentally measured flow are attributed to difficulties associated with modelling the rate of mixing within the flow.</p>

<p>Advancements in future technologies such as artificial intelligence, electric vehicles, and renewable energy create a consistent need for more powerful and smaller electronic devices and systems. As a result, thermal management components such as heat sinks need to remove higher heat loads from more compact spaces to keep electronics within their operational temperature limits. Constraints imposed by conventional manufacturing processes restrict the design of heat sinks to simple geometries with limited cooling performance. Recent widespread commercialization of metal additive manufacturing (AM) tools offers new potential for leveraging the design freedom of these manufacturing technologies to design and fabricate heat sinks with improved performance. </p> <p>In AM, three dimensional parts are created through layer-by-layer depositing of materials, which allows fabrication of complex geometries that would be impossible or too costly using conventional subtractive methods. Many novel heat sink geometries have been proposed in literature which incorporate features such as manifolds, flow mixers, and curved channels using engineering intuition to reduce pressure drop or enhance heat transfer. Although such designs have been shown to offer improved performance, mathematical design algorithms such as topology optimization (TO) have been shown to outperform engineering intuition. Topology optimization optimizes the material distribution within a given design space, guided by physics-based simulations, to achieve a user-defined objective such as minimization of thermal resistance. Previous TO approaches have used penalization methods to ensure the final designs are composed of macroscopic and non-porous features due to the past precedent of fabrication capabilities. This traditional penalization approach is well-suited to the constraints of conventional manufacturing methods; however, microstructures and porous features are easily fabricable with additive manufacturing. There is a need to develop TO approaches that are better suited for leveraging AM for the design of heat sinks. In this thesis, a homogenization approach to topology optimization is proposed wherein the material distribution is represented as parametrized microstructures. This formulation allows design of thermal management components that have sub-grid features and leverages AM for fabrication. The focus of this thesis is the development of the homogenization approach for TO of heat sinks, as well as the exploration of the design problems it can address, the performance benefits made available, and the two-phase flow physics that it uniquely allows to be incorporated into the topology optimization process.</p> <p>A topology optimization algorithm using the homogenization approach is developed by representing the material distribution as arrays of pin fins with varying gap sizes. To this end, the pin fins are modeled as a porous medium with volume-averaged effective properties. Height-averaged two-dimensional flow and non-equilibrium thermal models for porous media are developed for transport in the pin fin array. Through multi-objective optimization, TO designs are generated for an example case involving a hotspot over a uniform background heat input. The resulting topologies have porous-membrane-like designs where the liquid is transported through a fractal network of open, low-hydraulic-resistance manifold pathways and then forced across tightly spaced arrays of pin fins for effective heat transfer. The TO designs are revealed to offer significant performance improvements relative to the benchmark straight microchannel (SMC) heat sink with features optimized under the same multi-objective cost function. A series of microchannel heat sinks are fabricated using direct metal laser sintering to investigate the printing capabilities and to experimentally demonstrate the performance of topology optimized designs. Advantages of the homogenization approach over the penalization approach can be summarized as follows: (1) reduced computational costs due to its ability to create sub-resolution features, (2) intrinsically fabricable parts using available metal AM tools, and (3) easier to use due to significantly reduced number of hyperparameters (e.g., penalization factors) that are controlled by the user. </p> <p>Topology optimization has been applied to thermal management methods involving single-phase flows such as natural convection, forced air cooling, and pumped liquid cooling. Compared to these conventional heat sink technologies, flow boiling offers very high heat transfer coefficients and effective heat capacities, making it a promising candidate for future cooling electronics applications. The final goal of this thesis is to enable topology optimization of flow boiling heat sinks. However, TO of flow boiling heat sinks has been avoided due to difficulties in modeling the boiling phenomena; of note, there are no examples of TO being applied to the design of heat sink under flow boiling throughout the literature. Multi-dimensional two-phase flow models require prior knowledge of friction factor and heat transfer coefficients. Correlations are available in literature but are not universal and depend significantly on channel/fin geometries, surface roughness, and operating conditions. Given that traditional penalization-based TO approach results in fin and channel geometries with unknown shapes, dimensions, and alignment before the optimization is completed, this prohibits their use for optimization of flow boiling heat sinks. However, the homogenization approach to topology optimization developed in this thesis enables the optimization of flow boiling heat sinks. As it relies on user-defined microstructures with known shapes, alignments, and ranges of geometric dimensions, a universal correlation for flow boiling in microchannels is not needed. Instead, correlations for the user-defined microstructures are sufficient to simulate flow boiling in TO designs generated using the homogenization approach. To this end, a predefined microstructure geometry is chosen for which two-phase flow correlations exist and therefore topology optimization can be performed. Topology optimized heat sink designs under flow-boiling are generated and investigated at various heat inputs, topology optimization grid sizes, and maximum vapor quality constraints. Topology optimized heat sinks designed for single-phase versus two-phase flow are compared.  There are significant differences in hydraulic and thermal responses of the single-phase and two-phase designs due to high effective heat capacity rates and high heat transfer coefficients of flow boiling. The algorithm demonstrated in this work extends the capabilities of topology optimization to two-phase flow physics, and thereby enables the design of various two-phase flow components such as evaporators, condensers, heat sinks, and cold plates.</p> <p>The flow and heat transfer of the TO algorithm for microchannel heat sinks under flow boiling use a two-phase mixture model featuring an effective porous medium formulation. However, closure of the governing equations requires empirical correlations for pressure drop and heat transfer that are specific to the operating conditions, microstructure geometry, and surface finish. Therefore, it must be demonstrated these available correlations can be successfully calibrated over a range of microstructural variations present within the homogenization framework, so as to attain the required prediction generality and accuracy needed to ensure the resulting designs achieve Pareto-optimality. To this end, a set of uniform pin fin calibration samples are additively manufactured and experimentally tested under flow boiling at various flow rates and heat inputs for model calibration. All of the unknown/free coefficients in the adopted correlations are determined by minimizing the error between the model predictions and the experimental measurements using gradient-based optimization. The calibrated topology optimization algorithm is then used to generate a Pareto-optimal set of heat sinks optimized for minimum pressure drop and thermal resistance during flow boiling. Experimental characterization of these additively manufactured heat sinks, unseen during the model coefficient calibration process, reveals that the measured Pareto optimality curve matches that predicted by the topology optimization algorithm. Lastly, a heat sink design is generated for a design space involving multiple hot spots and background heating to showcase the capability of the experimentally calibrated two-phase topology optimization algorithm at handling complex boundary conditions. The optimized heat sink intelligently distributes an adequate amount of coolant flow to each of the heated regions to avoid local dry-out. This work demonstrates a complete framework for two-phase topology optimization of heat sinks through experimental calibration of flow boiling correlations to the porous medium used by the homogenization approach. </p> <p>The major contribution of this thesis is the development of a homogenization approach for TO of additively manufactured microchannel heat sinks under single- and two-phase flows. Not only does the homogenization approach provide several advantages over the traditional penalization approaches such as reduced computational costs, intrinsic fabricability using AM, and ease of use, but it also enables TO of heat sinks under flow boiling and potentially TO of other two-phase thermal management components. The work discussed in this thesis serves a comprehensive end-to-end guide on TO of microchannel heat sinks using the homogenization approach with experimental demonstrations for validation.</p>

<p>Purdue University is facing an increasing undergraduate student enrollment every year. Laboratory courses in fluid mechanics at the School of Aeronautics and Astronautics and the School of Mechanical Engineering are facing challenges due to increased enrollments. On the other hand, the internet and computer technology have made education more conveniently delivered in recent years. The onset of these technologies has made way for innovative forms of teaching. One such application is virtual laboratories. This document will describe the challenges in the current method of teaching and learning fluid mechanics laboratory courses, explain how a virtual lab is a potential solution to supplement the current learning methods, and discuss its development. This document will discuss the virtual fluid mechanics laboratory development from the fluid mechanics perspective- generating flow data and designing realistic measurement probes. The use of CFD to generate flow data sets, along with their post-processing for virtual labs, will be discussed. Furthermore, simulation results for flow around cylinders and through pipes will be presented. And finally, design ideas conceptualized for developing a virtual pitot-static probe and a virtual hot-wire anemometer will also be presented. Finally, this document summarizes the work done till now and presents conclusions on what has been achieved along with recommendations that could be completed in the future.</p>

Pagrindinės šiame darbe sprendžiamos problemos yra susijusios su efektyviu ilgalaikiu šilumos siurblių eksploatavimu. Šilumos siurblio sistemos kintamuoju priimamas gruntinis šilumokaitis. Tai reiškia, kad šilumos siurblio efektyvumas priklausys nuo šilumnešio temperatūros gruntiniame šilumokaityje. Pirmoje darbo dalyje pateikiama informacija apie geoterminę energiją bei jos naudojimo būdus. Apibrėžiama seklioji geoterminė energija. Pateikiamos šilumos siurblių šilumokaičių schemos. Praktinėje darbo dalyje pateikiama gruntinių šilumokaičių modeliavimo metodų analizė bei pasirenkamas metodas tolimesniam modeliavimui. Modeliuojami trijų skirtingų tipų vertikalūs gruntiniai šilumokaičiai. Modeliavimo rezultatas: šilumnešio vidutinės mėnesinės temperatūros 25 metų laikotarpiui. Pagal temperatūras nustatomas šilumos siurblio vidutinis mėnesinis efektyvumo koeficientas. Naudojant efektyvumo koeficientus apskaičiuojamas elektros energijos poreikis. Atliekama ekonominė analizė. Analizės rezultatai parodė, kad efektyviausias vertikalus gruntinis šilumokaitis, prie darbe priimtų modeliavimo sąlygų, yra viengubas gruntinis šilumokaitis su dviem U-formos vamzdžiais. / The main problems that are solved in this thesis are tailored with heat pumps longtime efficiency. The borehole heat exchanger was selected as a variable of a heat pump system. This means that efficiency of the heat pump depends from the temperature of heat carrier inside soil heat exchanger. First part of this thesis represents information about geothermal energy and ways of using it. Definition about shallow geothermal energy is made. The examples of heat pump heat exchangers are given. The practical part of the thesis contains analysis of the simulation models for soil heat exchangers. According to this analysis, selection of the simulation tool is made for further modeling. The simulations of three different heat exchangers types are made. Modeling results show heat carrier’s mean monthly temperatures during time period of 25 years. Using these temperatures the heat pump’s mean monthly coefficient of performance is defined. Using coefficients of performance the calculation of electric power demand is made. Economic analysis is made. The analysis results showed that the most efficient vertical borehole heat exchanger is one heat exchanger with two U-pipes, in terms of conditions that had been used in this thesis.

Baigiamajame magistro darbe nagrinėjama problema – dideli energijos poreikiai vėsinimui biurų pastatuose, dėl vis didėjančių mikroklimato kokybės reikalavimų, didesnių šilumos pritekėjimų į patalpas ir šilumos išsiskyrimų dėl naudojamos įrangos. Problemos sprendimui darbe suprojektuotos keturios oro kondicionavimo sistemos su skirtingais šilumnešiais: oru, vandeniu ir freonu. Atsižvelgiant į šilumnešio tipą suprojektuotos ventiliatorinių konvektorių, aktyviųjų šalčio sijų, freoninė ir orinė vėsinimo sistemos. Oro kondicionavimo sistemos analizuojamos remiantis realaus tipinio administracinio pastato pavyzdžiu. Lyginamoms sistemoms buvo atlikti hidrauliniai ir aerodinaminiai skaičiavimai, įvertintos sistemų pradinės investicijos, apskaičiuotos energijos sąnaudos ir eksploatacijos išlaidos. Ekonominio skaičiavimo metu buvo įvertintas sistemų atsipirkimo laikas ir atlikta elektros kainų jautrumo analizė. Šio tyrimo rezultatai parodo, kokia sistema iš visų darbe nagrinėtųjų sistemų yra tinkamiausia biurų pastatams, pagal efektyvų elektros energijos naudojimą ir pradines investicijas. / The final master's work deals with the problem of high energy needs for cooling in office buildings, due to the growing of higher quality requirements for microclimate, higher heat gains in premises and equipment heat emissions used in. To solve the problem four different types of cooling systems with different coolants: air, water and refrigerant are designed at work. Depending on the type of coolant were designed fan coil units, active chilled beams, variable refrigerant volume system and air cooling systems. Air conditioning systems are analyzed on the basis of an example of the real typical office building. The hydraulic and aerodynamic calculations were made, initial investments, energy expenditures and operating costs were estimated for the compared systems. The pay-back time of the systems was assessed and the sensitivity analysis of electricity prices was carried out by economic calculations. The results of this investigation show, which system of all analysed systems at work is the most appropriate for office buildings, according to the efficient use of electricity and the initial investments.

<p>Detta är ett examensarbete som genomförts hos Göteborg Energi AB och syftar till att utreda omkryogen uppgradering av biogas med fördel kan ske genom att producera nödvändig kyla medvärmedriven absorptionskylmaskin. Göteborg Energi är en av tre parter som tillsammans ska bygga enbiogasanläggning i Lidköping som ska vara i drift 2010. Anläggningen ska producera 30 GWhflytande biogas per år.</p><p>Arbetet utreder om det är fördelaktigt ur ekonomiskt, energimässigt och miljömässigt perspektiv attuppgradera biogas med kryogen teknik med värmeproducerad kyla. En jämförelse görs först medkryogen teknik där kylan är producerad med el och sen med andra uppgraderingstekniker. Som stödhar två olika processimuleringsprogram används, Hysys och DESIGN II.</p><p>Resultatet visar att energianvändningen ökar då värmedriven kyla används i jämförelse med kylaproducerad med el. 0,47 kW/Nm3 rågas för kryo med absorptionskyla och 0,29 kW/Nm3 rågas medel. Om det finns avsättning för spillvärmen kan energianvändningen i uppgraderingen minska till 0,29kW/Nm3 rågas och 0,15 kW/Nm3 rågas för systemet med värmedriven respektive eldriven kyla. Ijämförelse med andra uppgraderingstekniker ligger 0,47 kW/Nm3 bland de teknikerna med högstenergianvändning medans 0,29 kW/Nm3 placerar sig bland de teknikerna med lägstenergianvändning.</p><p>Resultat visar att klimatpåverkan från uppgraderingen, som kommer av metanslip och elanvändningen,minskar marginellt om kylan produceras med värme istället för el. Resultatet varierar mycket beroendepå hur koldioxidutsläppen från marginalelen beräknas. I jämförelse med andra uppgraderingsteknikerligger kryo lägre än de flesta andra. Undantaget är COOAB-tekniken som är överlägset bäst tack varalågt metanslip och liten elanvändning.</p><p>Ekonomisk jämförelse med andra uppgraderingstekniker visar att kostnaden för energianvändningenligger i samma nivå som övriga uppgraderingstekniker i jämförelsen, ca 0,03 kr/kWh uppgraderad gas.Om det finns avsättning för spillvärmen sjunker kostnaden till 0,024 och 0,02 kr/kWh uppgraderad gasför kryoteknik med kyla ifrån värme respektive el.</p><p>Min slutsats är att utnyttjande av spillvärmen är av stor vikt för att få god ekonomi och lågenergianvändning med kryogen uppgradering. En marginellt förbättrad miljöprestanda kan erhållas omnödvändig kyla produceras med värme istället för el då kryogen uppgradering används. Annars är detalltid mer fördelaktigt att använda el för att producera nödvändig kyla.</p> / <p>This is a master thesis that has been carried out at Göteborg Energi AB. It refers to investigate ifcryogenic upgrading of biogas with advantage can be done by producing necessary cold with a heatdriven absorption cooling machine. Göteborg Energi is one of three actors that together will build abiogas plant in Lidköping that will be up and running in 2010. The plant will produce 30 GWhliquefied biogas annually.</p><p>This thesis investigastes whether it is advantageous, to upgrade biogas with heat driven cooling, in aperspective of economy, energy use and environment. It compares cryogenic upgrading with coldproduced by electricity, but also by other techniques. Two different process simulation softwares havebeen used as support to this thesis; Hysys and DESIGN II.</p><p>The result shows that energy usage increases when the necessary cold is produced with heat instead ofelectricity; 0,47 kW/Nm3 rawgas for cryo upgrade with absorptions cooling and 0,29 kW/Nm3 rawgaswith cold produced by electricity. If it’s possible to use the waste heat to warm the digester, the energyconsumption for the upgrading can be reduced to 0,29 kW/Nm3 for the system with heat-driven cold,and 0,15 kW/Nm3 rawgas for cold produced by electricity. In comparison with other techniques forupgrading, 0,47 kW/Nm3 rawgas is a high value while 0,29 kW/Nm3 rawgas is among the lowestvalues for energy use.</p><p>The impact on the climate emerges from the use of electricity and when methane slips out from theupgrading plant. The result shows that the impact on the climate is slightly decreased for cryogenicupgrading when the cold is produced with a heat driven absorption machine instead of electricity. Theresult varies a lot due to how one calculate the emission of carbon dioxide from the electricity on themargin. In comparison with other upgrading techniques, the climate impact from cryogenic upgradingis less, other than the COOAB-technique that is superior because of its low methane slip and lowdemand of electricity.</p><p>An economical comparison shows that the cost for energy usage is about the same for cryogenic as forother techniques; approximately 0,03 SEK/kWh upgraded gas. If one can utilize the waste heat, thecost would be decreased to 0,024 and 0,02 SEK/kWh upgraded gas for the system with cryogenicupgrading with cooling from absorption machine respectively cooling produced with electricity.</p><p>My conclusion is that the utilization of the waste heat is essential if one wishes to get good economyand low energy use for the upgrading of biogas with cryogenic methods. A slightly increasedenvironmental improvement can be received if one change the cold production from electricity to heat,otherwise it is always more advantageous to use electricity for cryogenic methods.</p>

<p>This project is a preliminary study in order to build a small power plant, located beside to Gavleån River. It has been designed with the aim of cooling a district of Gävle city, Sweden. That big project is carried out by the international consulting engineering company SWECO. The mentioned plant contains a thermodynamic cycle that takes water from the river and afterwards, it is returned back warmer. It will attempt to study the temperature raise downstream along the river due to the spill of hot water. In addition, it will try to quantify and weight which may be the importance of the increment of temperature compared to the entire river. This work could be vital for an environmental impact study. The thermo and fluid dynamic problem is going to be solved using typical procedure for numerical simulations. To do this, it will be used Computer Aided Design (CAD) to model Gavleån River path and Computational Fluent Dynamics (CFD) to predict the distribution of temperatures. Finally the results of the simulations will be analyzed and discussed to draw conclusions about the final temperature raise in Gavleån River.</p>

<p>Flerfasestrømning er av betydning i en lang rekke anvendelser, blant annet i olje- og gassindustrien, i den kjemiske og i prosessindustrien, inkludert i varmepumpende systemer, samt i sikkerhetsanalyse av kjernekraftverk. Denne avhandlingen analyserer modeller for tofasestrømning, og metoder for numerisk løsning av disse modellene. Den er derfor ett bidrag til å utvikle pålitelige ingeniørverktøy for flerfase-anvendelser. Slike verktøy trengs og forventes av ingeniører i industrien.</p><p>Den tilnærmede Riemann-løseren framsatt av Roe har blitt studert. Roe-skjema for tre ulike modeller for tofasestrømning har blitt implementert i rammen av en standard numerisk algoritme for løsning av hyperbolske bevaringslover. Disse skjemaene har blitt analysert ved hjelp av referanse-regnestykker fra litteraturen, og ved sammenlikning med hverandre.</p><p>Et Roe-skjema for den fire-liknings ettrykks tofluid-modellen har blitt implementert, og det har blitt vist at en andreordens utvidelse basert på bølge-dekomponering og fluksdifferanse-splitting virker godt, og gir forbedrede resultater sammenliknet med det førsteordens skjemaet.</p><p>Det har blitt foreslått et Roe-skjema for en fem-liknings totrykks tofluid-modell med trykkrelaksering. Bruken av analoge numeriske metoder for fire-liknings- og fem-liknings-modellene gjorde det mulig med en direkte sammenlikning av en metode med og uten trykkrelaksering. Numeriske eksperiment demonstrerte at de to framgangsmåtene konvergerte til samme resultat, men at den fem-liknings trykkrelakserings-metoden var betydelig mer dissipativ, særlig for kontakt-diskontinuiteter. Videre viste beregninger at selv om fem-liknings-modellen har reelle egenverdier, så produserte den oscillasjoner for tilfeller der fire-liknings-modellen hadde komplekse egenverdier.</p><p>Et Roe-skjema har blitt konstruert for driftfluks-modellen med generelle lukningslover. Roe-matrisen er helt analytisk for det tilfellet at man kan anvende Zuber-Findlay-slipp-loven som beskriver boblestrømning. Dermed er dette Roe-skjemaet mer effektivt enn tidligere fullt numeriske Roe-skjema for driftfluks-modellen.</p><p>En isentropisk diskret-nivå-flerfasemodell har blitt presentert. En diskusjon av hvordan man kan ta hensyn til ulike interfase-trykkmodeller har blitt gitt. Med de passende modellene for interfase-trykk og -fart, var samsvaret svært godt mellom diskret-nivå-modellen og det fem-liknings Roe-skjemaet.</p><p>Multi-steg- (MUSTA) metoden har som siktemål å komme nær oppstrøms-metodene i nøyaktighet, samtidig som den bevarer enkelheten til sentrerte skjema. Her har metoden blitt brukt på driftfluks-modellen. Når antallet steg økes, nærmer resultatene fra MUSTA-metoden seg det man får med Roe-metoden. De gode resultatene til MUSTA-metoden er avhengige av at man bruker et stort nok lokalt grid. Derfor er hovedfordelen med MUSTA-metoden at den er enkel, snarere enn at man sparer regnetid.</p><p>En karakteristikk-basert metode for å spesifisere grensebetinglser for flerfase-modeller har blitt testet, og funnet å virke godt for transiente problem.</p> / <p>This thesis analyses models for two-phase flows and methods for the numerical resolution of these models. It is therefore one contribution to the development of reliable design tools for multiphase applications. Such tools are needed and expected by engineers in a range of fields, including in the oil and gas industry.</p><p>The approximate Riemann solver of Roe has been studied. Roe schemes for three different two-phase flow models have been implemented in the framework of a standard numerical algorithm for the solution of hyperbolic conservation laws. The schemes have been analysed by calculation of benchmark tests from the literature, and by comparison with each other.</p><p>A Roe scheme for the four-equation one-pressure two-fluid model has been implemented, and a second-order extension based on wave decomposition and flux-difference splitting was shown to work well and to give improved results compared to the first-order scheme. The convergence properties of the scheme were tested on smooth and discontinuous solutions.</p><p>A Roe scheme has been proposed for a five-equation two-pressure two-fluid model with pressure relaxation. The use of analogous numerical methods for the five-equation and four-equation models allowed for a direct comparison of a method with and without pressure relaxation. Numerical experiments demonstrated that the two approaches converged to the same results, but that the five-equation pressure-relaxation method was significantly more dissipative, particularly for contact discontinuities. Furthermore, even though the five-equation model with instantaneous pressure relaxation has real eigenvalues, the calculations showed that it produced oscillations for cases where the four-equation model had complex eigenvalues.</p><p>A Roe scheme has been constructed for the drift-flux model with general closure laws. For the case of the Zuber-Findlay slip law describing bubbly flows, the Roe matrix is completely analytical. Hence the present Roe scheme is more efficient than previous fully numerical Roe schemes for the drift-flux model.</p><p>An isentropic discrete-equation multiphase model has been presented. The incorporation of different interfacial-pressure models was discussed, and examples were given. With the adequate models for the interfacial pressure and velocity, the agreement was very good between the discrete-equation model and the five-equation Roe scheme.</p><p>The flux-limiter centred (FLIC) scheme was tested for the four-equation two-fluid model. Only the first-order version (FORCE) of the scheme was found to work well, but it was rather diffusive. The purpose of the multi-stage (MUSTA) method is to come close to the accuracy of upwind schemes while retaining the simplicity of centred schemes. Here it has been applied to the drift-flux model. As the number of stages was increased, the results of the MUSTA scheme approached those of the Roe method. The good results of the MUSTA scheme were dependent on the use of a large-enough local grid. Hence, the main advantage of the MUSTA scheme is its simplicity.</p><p>A multiphase characteristic-based boundary-condition method has been tested, and it was shown to be workable for transient problems.</p>