Dissertationen zum Thema „Thermal CFT“

In this thesis we study the time evolution of Rényi and entanglement entropies of thermal states in Conformal Field Theory (CFT). These quantities are usually hard to compute but Ryu-Takayanagi (RT) and Hubeny-Rangamani-Takayanagi (HRT) proposals allow us to find the same quantities using calculations in general relativity. We will introduce main concepts of holography, quantum information and conformal field theory that will be used to derive the results of this thesis. In the first part of the thesis, we explicitly compute entanglement entropy of the rotating BTZ black hole by directly applying HRT proposal and finding lengths of spacelike geodesics. Rényi entropy of thermal state perturbed by a local quantum quench is computed by mapping correlators on two glued cylinders to the plane for field theory containing a single free boson and for 2d CFTs in the large c limit. We consider Thermofield Double State (TFD) which is an entangled state in direct product of two 2D CFTs. It is conjectured to be holographically equivalent to the eternal BTZ black hole. TFD state is perturbed by a local quench in one CFT and mutual information between two intervals in two CFTs is computed. We find when mutual information vanishes and interpret this as scrambling time, i.e. time scale required for the system to thermalize. This field theory result is modelled with a massive free falling particle in the BTZ black hole. We have computed the back-reaction of the particle on the metric of BTZ and used RT proposal to find holographic entanglement entropy. Finally, we generalize this calculation to the case of rotating BTZ with inner and outer horizons. It is dual to the CFT with different temperatures for left and right moving modes. We calculate mutual information and scrambling time and find exact agreement between results in the gravity and those in the CFT.

Le travail que nous présentons dans cette thèse est structuré autour de la notion de théorie des champs et de géométrie, qui sont appliquées à la gravité et la thermalisation.En gravité, notre travail donne un éclairage nouveau sur la structure asymptotique du champ gravitationnel dans le contexte des espace-temps asymptotiquement plats, ceci en utilisant l'information codée sur leur bord conforme. Ce dernier est une hypersurface de genre lumière sur laquelle émerge la physique carrollienne au lieu de la physique relativiste. Une structure carrollienne sur une variété est constituée une métrique dégénérée et un champ de vecteurs couvrant le noyau de cette dernière. Ce vecteur sélectionne une direction particulière qui peut être le point de départ de la description des structures carrolliennes dans un cadre séparé. Nous développons d'abord la géométrie carrollienne, y compris une étude complète des connexions et isométries (conformes). Des actions effectives peuvent vivre sur un arrière-plan carrollien. Les moments canoniques conjugués à la géométrie ou à la connexion peuvent être définis, et la variation de l'action donnera leurs équations de conservation, à partir desquelles les charges isométriques peuvent être bâties.La physique carrollienne émerge également lorsque la vitesse de la lumière tend vers zéro. Cette limite donne généralement plus de descendants carrolliens que ce qui est attendu après une analyse intrinsèque, comme le montrent les exemples explicites des fluides carrolliens, des champs scalaires carrolliens (pour lesquels deux actions, électrique et magnétique, apparaissent dans la limite) et du tenseur de Cotton carrollien. La richesse de la limite est due à sa possibilité de décrire plus de degrés de liberté, ce qui s'avère être un outil fondamental dans l'étude de la relation entre les espace-temps asymptotiquement anti de Sitter et plats.Les espace-temps asymptotiquement plats peuvent être écrits comme une expansion infinie dans une jauge covariante par rapport à leur bord nul. Cette légère extension de la jauge de Newman-Unti est également valable dans AdS, ce qui permet de prendre la limite plate dans le bulk, équivalente à la limite carrollienne sur le bord. Nous démontrons que l'espace des solutions infini des espace-temps Ricci-plat provient en fait du développement en série de Laurent du tenseur énergie-impulsion d'AdS. Ces répliques obéissent à chaque ordre une dynamique carrollienne (lois de flux). Dans le cadre des espaces algébriquement spéciaux de Petrov (pour lesquels le développement infinie se resomme), nous utilisons les lois de flux carrolliennes ainsi que la conservation des tenseurs énergie-impulsion et de Cotton pour construire, du point de vue du bord, deux tours duales de charges du bulk. Parmi elles, nous retrouvons l'expansion mutipolaire de la masse et du moment angulaire pour la famille Kerr-Taub-NUT. La jauge covariante est également le cadre approprié pour dévoiler l'action des symétries cachées de la gravité sur le bord nul. Dans ce travail, nous étudions le cas de la symétrie SL(2,R) d'Ehlers.Du côté de la théorie thermique des champs, nous travaillons sur l'ensemble minimal de données nécessaires pour les décrire à température finie. Alors qu'à température infinie toutes les valeurs moyennes des opérateurs primaires s’annulent, leurs valeurs non nulle dans le cas thermique constituent les données supplémentaires qu'il faut calculer pour caractériser la théorie. Les simulations numériques, la dualité avec un trou noir dans AdS ou une analyse spectrale sont généralement les méthodes employées pour trouver la valeur de ces coefficients. Notre travail propose une nouvelle approche à ce problème en montrant, à partir de deux oscillateurs harmoniques couplés, que ces coefficients sont en fait liés à des graphes conformes de théories de type fishnet. A partir de cette observation, nous avons établi une correspondance entre les fonctions de partition thermique et ces graphes
The work we present in this thesis is structured around the concepts of field theories and geometry, which are applied to gravity and thermalisation.On the gravity side, our work aims at shedding new light on the asymptotic structure of the gravitational field in the context of asymptotically flat spacetimes, using information encoded on the conformal boundary. The latter is a null hypersurface on which Carrollian physics instead of relativistic physics is at work. A Carroll structure on a manifold is a degenerate metric and a vector field spanning the kernel of the latter. This vector selects a particular direction which can be the starting point for describing Carroll structures in a split frame. We first elaborate on the geometry one can construct on such a manifold in this frame, including a comprehensive study of connections and (conformal isometries). Effective actions can be defined on a Carrollian background. Canonical momenta conjugate to the geometry or the connection are introduced, and the variation of the action shall give their conservation equations, upon which isometric charges can be reached.Carrollian physics is also known to emerge as the vanishing speed of light of relativistic physics. This limit usually exhibits more Carrollian descendants than what might be expected from a naive intrinsic analysis, as shown in the explicit examples of Carrollian fluids, Carrollian scalar fields (for which two actions, electric and magnetic arise in the limit) and the Carrollian Chern-Simons action. The richness of the limiting procedure is due to this versatility in describing a palette of degrees of freedom. This turns out to be an awesome tool in studying the relationship between asymptotically anti de Sitter (AdS) and flat spacetimes.Metrics on asymptotically flat spacetimes can be expressed as an infinite expansion in a gauge, covariant with respect to their null boundaries. This slight extension of the Newman-Unti gauge is shown to be valid also in AdS, which allows to take the flat limit in the bulk i.e. the Carrollian limit on the boundary, while preserving this covariance feature. We demonstrate that the infinite solution space of Ricci-flat spacetimes actually arises from the Laurent expansion of the AdS boundary energy-momentum tensor. These replicas obey at each order Carrollian dynamics (flux/balance laws). Focusing our attention to Petrov algebraically special spacetimes (for which the infinite expansion resums), we use the Carrollian flux/balance laws together with the conservation of the energy-momentum and Cotton tensors to build two dual towers of bulk charges from a purely boundary perspective. Among them we recover the mass and angular momentum mutipolar moments for the Kerr-Taub-NUT family. The covariant gauge is also the appropriate framework to unveil the action of hidden symmetries of gravity on the null boundary. In this thesis we study exhaustively the case of Ehlers' $SL(2,mathbb{R})$ symmetry.On the side of thermal field theory we see that while at infinite temperature a CFT is described by its spectrum and the OPE coefficients, additional data is needed in the thermal case. These are the average values of primary operators, completely determined up to a constant coefficient. Numerical simulations, duality with black-hole states in AdS or spectral analyses are the methods usually employed to uncover the latter. Our work features a new breadth. Starting from two coupled harmonic oscillators, we show that they are related to conformal ladder graphs of fishnet theories. This observation is the first step for setting a new correspondence between thermal partition functions and graphs

Buildings expend vast quantities of energy, which has a detrimental impact on the environment. Buildings systems are often oversized to cope with possible extreme environmental conditions. Building simulation provides an opportunity to improve building thermal design, but the available tools are typically used in combination in order to overcome their individual deficiencies. Two such tools, often used in tandem are computational fluid dynamics (CFD) and dynamic thermal modelling (DTM). DTM provides a coarse analysis, by considering external and internal thermal conditions over a building (including its fabric) over time. CFD is usually used to provide steady state analysis. Boundary conditions typically in the form of surface temperatures are manually input from DTM into CFD. CFD can model buildings dynamically, but is not commonly used, since solving for hugely different time constants of solid and air pose significant limitations, due to data generated and time consumed. A technique is developed in this study to tackle these limitations. There are two main strands to the research. DTM techniques had to be incorporated into CFD, starting from first principles of modelling heat transfer through solid materials. These were developed into employing the use of functions such as the 'freeze flow' function (FEF) and the 'boundary freeze' function (BFF) in combination with a time-varying grid schedule to model solids and air simultaneously. The FFF pauses the solution of all governing equations of fluid flow, except temperature. The BFF can be applied to solid boundaries to lock their temperatures whilst all other equations are solved. After extensive research the established DTM-CFD Procedure eventually used the FEF and BFF with transient periods and steady state updates, respectively. The second strand of research involved the application of the DTM-CFD Procedure to a typical office space over a period of 24-hours. Through inter-model comparisons with a fully transient simulation, the DTM-CFD Procedure proved to be capable of providing dynamic thermal simulations 16.4% more efficiently than a typical CFD code and more accurately than a typical DTM code. Additional research is recommended for the further improvement of the DTM-CFD Procedure.

This dissertation examines the suitability of Computational Fluid Dynamics (CFD) modelling for the production of realistic flowfields and temperature fields within a series of vortex combustion chambers of differing geometries and operating under various conditions. Initial validation of the CFD predictions was obtained through modelling of a series of isothermal vortex chambers for which a comprehensive set of experimental data was available. It was observed that CFD did indeed produce representative flowfield predictions for chambers of various geometries and operating conditions. A vortex unit used for the incineration of sewage sludge (US Navy Waste Incinerator) was subsequently investigated, and it was shown that due to the high moisture content of the waste material used, temperature profiles obtained with a modified coal combustion model were similar to those obtained with a more straightforward and computationally less expensive spray drier model. Results from both models were similar to experimentally observed conditions. However, comprehensive validation was not possible. In order that full validation could be provided for a CFD model of a vortex combustion unit, a model was developed of a commercial thermal oxidiser used for the incineration of liquid and gaseous wastes. CFD temperature predictions for the BASF Thermal Oxidiser were validated by a series of experimental measurements obtained from the operating unit. In general, it was found that the Reynolds Stress Model for turbulence produced the most representative velocity flowfields, with the less computationally demanding k-e model being applicable only under certain limited circumstances. Furthermore, insufficient grid refinement resulted in significantly distorted velocity profiles.

This thesis is about problematics of creating Computational Fluid Dynamics (CFD) model suited for analysis of airflow around sitting passive person. Thesis includes analysis of velocity field distribution, thermal distribution and thermal losses in the surroundings of sitting thermal dummy (computational model) and comparison of these values with experimental measurements. Thesis is a part of large experimental research (this research is not included here) focused on creating of functional method used for person-surrounding airflow analysis in future commercial use.

In this study, the thermal management system of a notebook computer is investigated by using a commercial finite volume Computational Fluid Dynamics (CFD) software. After taking the computer apart, all dimensions are measured and all major components are modeled as accurately as possible. Heat dissipation values and necessary characteristics of the components are obtained from the manufacturer'
s specifications. The different heat dissipation paths that are utilized in the design are investigated. Two active fans and aluminum heat dissipation plates as well as the heat pipe system are modeled according to their specifications. The first and second order discretization schemes as well as two different mesh densities are investigated as modeling choices. Under different operating powers, adequacy of the existing thermal management system is observed. Average and maximum temperatures of the internal components are reported in the form of tables. Thermal resistance networks for five different operating conditions are obtained from the analysis of the CFD simulation results. Temperature distributions on the top surface of the chassis where the keyboard and touchpad are located are investigated considering the user comfort.

Energy consumption in buildings contributes more greenhouse gas emissions than either the industrial or transportation sectors, primarily due to space cooling and heating energy use, driven by the basic human need for thermal comfort and good indoor air quality. In recent years, there has been a proliferation of air conditioning in both residential and commercial buildings especially in the developing economic areas of the world, and, due to the warming climate and the growing disposable income in several densely populated developing countries, the energy demand for space cooling is dramatically increasing. Although several previous studies focused on thermal comfort, there are only a few works on asymmetrical environments or transient conditions, such as those expected when mixed mode ventilation or other low energy techniques such as elevated air movement generated by ceiling fans are adopted in the residential sector. Moreover, even fewer studies addressed the accuracy of computer predictions of human thermal comfort in non-uniform environmental conditions. However, focusing on non-uniform thermal environments is important because the space conditioning systems that generate them are often likely to be less energy consuming than those which provide more homogeneous conditions. This is due to the fact that these less energy-intensive space conditioning systems tend to condition the occupants, and not the entire room. The aim of this research was to investigate human thermal comfort in non-uniform transient environmental conditions, focusing in particular on the capability of predicting human thermal comfort in such conditions in residential buildings. Furthermore, this research investigated the energy savings that can be achieved in residential buildings when the same level of thermal comfort is delivered using less conventional, but lower-energy, approaches. In this research, a combination of computer based modelling, experimental work in controlled environments, and data from field studies was used. Computer modelling comprised CFD coupled with a model of human thermal physiology and human thermal comfort, and dynamic thermal modelling. In the experimental work, environmental chambers were used to collect data to validate the coupled CFD model. The data from field studies on real domestic buildings in India and in the UK was used to identify the most relevant configurations to be modelled using the coupled system. This research led to three main conclusions concerning thermal comfort in non-uniform environments: (i) the coupled model is able to predict human thermal comfort in complex non-uniform indoor configurations, as long as the environment around the human body is accurately modelled in CFD, and is superior to the traditional PMV model as both temporal and spatial variation and non-uniform conditions can be taken into account; (ii) dynamic thermal simulation completed using a dynamic cooling set-point showed that the energy demand for space cooling can be reduced by as much as 90% in mixed mode buildings by using ceiling fans, without jeopardising occupants' thermal comfort; and (iii) the accurate and validated transient three-dimensional CFD model of a typical Indian ceiling fan developed in this research can be used for any study that requires the air flow generated by a ceiling fan to be modelled in CFD.

Thermal stripping is a major safety challenge in nuclear power generation and propulsion systems. It arises as a consequence of the heat transfer from fluid to surrounding solid components varying in time and typically occurs in regions where the mixing of hot and cold fluids results in turbulent temperature fluctuations. It can occur in a range of components in reactors and thermal-hydraulics systems and may lead to structural failure by high-cycle thermal fatigue. Cases of cooling system pipes failing by this mechanism have been reported at the French Civaux and the Japanese Tsuruga-2 & Tomari-2 pressurised water reactor plants. CFD has great potential to provide predictions for flow fields in the pipe bends and junctions of nuclear plant thermal-hydraulics systems. The current project aims to use CFD to explore the physics of thermal mixing in plant components, and to develop \& validate CFD techniques for studying such problems in industry. Firstly, wall-resolved LES is used to demonstrate the importance of including nearby upstream pipe bends in CFD studies of thermal mixing in T-junctions. Swirl-switching of the Dean vortices generated at an upstream bend can give rise to an unsteady secondary flow about the pipe axis. This provides an additional mechanism for low-frequency near-wall temperature fluctuations downstream of the T-junction, over those that would be produced by mixing in the same T-junction with straight inlets. Wall-resolved LES is however currently computationally unaffordable for studying plant components in industry. Wall-functions offer a solution to this problem by imposing empirical results near walls, such that a coarser grid can be used. LES with blended wall-function predictions for flows in a 90 degree pipe bend and a simple T-junction with straight inlets are compared to experimental data. These studies highlight limitations in the predictive capabilities of the LES with wall-function approach. Predictions from a number of RANS models are also benchmarked. Finally, the consistent dual-mesh hybrid LES/RANS framework proposed by Xiao and Jenny (2012) is further developed as an alternative solution to the high computational cost of wall-resolved LES. Numerous modifications to the coupling between the two meshes are presented, which improve automation and accuracy. The approach is also extended to a passive temperature scalar field. Predictions for channel flows, a flow through periodic hills and thermal mixing in a T-junction between channel flows are all in excellent agreement with reference data.

Power transformers are key components of electric system networks; their performance inevitably influences the reliability of electricity transmission and distribution systems. To comprehend the thermal ageing of transformers, hot-spot prediction becomes of significance. As the current method to estimate the hot-spot temperature is based on empirical hot-spot factor and is over-simplified, thermal network modelling has been developed due to its well balance between computation speed and approximation details. The application of Computational Fluid Dynamics (CFD) on transformer thermal analysis could investigate detailed and fundamental phenomena of cooling oil flow, and the principle of this PhD thesis is then to develop more accurate and reliable network modelling tools by utilising CFD.In this PhD thesis the empirical equations employed in network model for Nusselt number (Nu), friction coefficient and junction pressure losses (JPL) are calibrated for a wide range of winding dimensions used by power transformer designs from 22 kV to 500 kV, 20 MVA to 500 MVA, by conducting large sets of CFD simulations. The newly calibrated Nu equation predicts a winding temperature increase as the consequence of on average 15% lower Nu values along horizontal oil ducts. The new friction coefficient equation predicts a slightly more uniform oil flow rate distribution across the ducts, and also calculates a higher pressure drop over the entire winding. The new constant values for the JPL equations shows much better match to experimental results than the currently used 'off-the-shelf' constants and also reveals that more oil will tend to flow through the upper half of a pass if at a high inlet oil flow rate. Based on a test winding model in the laboratory, the CFD calibrated network model's calculation results are compared to both CFD and experimental results. It is concluded that the deviation between the oil pressure drop over the pass calculated by the network model and the CFD and the measured values is acceptably low. It proves that network modelling could deliver quick and reliable calculation results of the oil pressure drop over windings and thereby assist to choose capable oil pumps at the thermal design stage. However the flow distribution predicted by network model deviates from the one by CFD; this is particularly obvious for the cases with high flow rates probably due to the entry eddy circulation phenomena observed in CFD. As no experiment validation has been conducted, further investigation is necessary. The CFD calibrated network model is also applied to conduct a set of sensitivity studies on various thermal design parameters as well as loads. Because the studies are on a directed oil cooling winding case, an oil pump model is incorporated. From the studies recommendations are given for optimising thermal design, e.g. narrowed horizontal ducts will reduce average winding and hot-spot temperatures, and narrowed vertical ducts will however increase the temperatures. Doubled oil block washers are found to be able to significantly reduce the disc temperatures, although there is a slight reduction of the total oil flow rate, due to the increase of winding hydraulic impedance. The impact of different loadings, 50%~150% of rated load, upon the forced oil flow rate is limited, relative change below 5%. The correlations between the average winding and hot-spot temperatures versus the load factors follow parabolic trends.

Pyrolysis is considered as a promising technology of recovering bioenergy from biomass into gas, liquid and solid fuels. A series of works have been carried out previously on the fundamentals and the decomposition mechanism of pyrolysis empirically. Based on these experimental works, numerical approaches are employed to achieve a better understanding of the pyrolysis mechanism or aid the applications in experimental and industrial area. In order to construct a systematic model of the thermochemical processes in biomass pyrolysis in a fluidized bed, the mass and heat transfer processes are investigated by two sub-subjects: modelling of the heat exchange between an immersed tube and a fluidized bed; modelling of mixing-segregation phenomena of binary mixture loaded in a fluidized bed as bed materials. Based on the finished studies, two reacting beds are represented by Eulerian approaches. The fast pyrolysis and catalytic pyrolysis of biomass is modelled by incorporating the corresponding kinetic schemes into the mass and heat transfer processes. The relevant models, coefficients and functions are tested and discussed for the sensitivity and the simulation results show qualitative consistence with the existing experimental works. The general model for thermochemical processes of biomass in the fluidised beds is built up in the present work successfully. The entire structure and methods can be introduced into other applications but not limited to biomass pyrolysis. The further optimization based on this model can be a useful tool on design of a large-scale pyrolyzor.

Methane and oxygen are a promising propellant combination in future rocket propulsion engines mainly due to its advantages like reusability and cost reduction. In order to have a comprehensive understanding of this propellant combination extensive research work is being done. Especially, for reusable rocket engines the thermal calculations become vital as an effective and efficient cooling system is crucial for extending the engine life. The design of cooling channels may significantly be influenced by radiation. Within the framework of this thesis, the gas radiation heat transfer is modelled for CFD simulation of rocket thrust chambers and analysed for the 𝐶𝐻4/𝑂2 fuel combination. The radiation is modelled within ArianeGroup’s in-house spray combustion CFD tool - Rocflam3, which is used to carry out the simulations. Radiation properties can have strong influence for certain chemical compositions, especially 𝐶𝑂2 and 𝐻2𝑂 which are the products of the 𝐶𝐻4 and 𝑂2 combustion. A simplified gas radiation transport equation is implemented along with various spectral models which compute the gas emissivity for higher temperature. Also, Rocflam-II code which has an existing gas radiation model is used to compare and validate the simplified model. Finally the combination of the convective and radiative heat transfer values are compared to the experimental test data. In contrast to the previously existing emissivity models with a certain temperature limit, the model used here enables the inclusion for the total emissivity of 𝐶𝑂2 and 𝐻2𝑂 for temperatures up to 3400 K and hence more appropriate for hydrocarbon combustion in space propulsion systems. It turns out that the gas radiation is responsible for 2-4% of the total heat flux for a 𝐶𝐻4/𝑂2 combustion chamber with maximum integrated temperature of 2700 K. The influence of gas radiation would be greater than 4% respective of the integrated temperature. Gas radiation heat flux effects are higher in stream-tube combustion zone compared to the other sections of the thrust chamber. The individual contribution of radiative heat flux by 𝐶𝑂2 was noted to be 1.5-2 times higher than that to 𝐻2𝑂. It was shown that the analytically derived simplified expression for gas radiation along with the various spectral models had reasonable approximation of the measured radiation. The estimated radiation was correct to the measured radiation from the Rocflam-II model for a temperature range of 400-3400 K.
Metan och syre är en lovande kombination av drivmedel i framtida raketframdrivningsmotorer främst på grund av dess fördelar som återanvändbarhet och kostnadsminskning. För att få en omfattande förståelse av denna drivmedelkombination görs ett omfattande forskningsarbete. Speciellt för återanvändbara raketmotorer blir värmeberäkningarna viktiga eftersom ett effektivt och effektivt kylsystem är avgörande för att förlänga livslängden på motorn. Utformningen av kylkanaler kan betydligt påverkas av strålning. Inom ramen för denna avhandling modelleras gasstrålningsvärmeöverföringen för CFD-simulering av rakettryckkamrar och analyseras för 𝐶𝐻4/𝑂2 -bränslekombinationen. Strålningen är modellerad i ArianeGroup’s egen förbränning CFD-verktyg - Rocflam3, som används för att utföra simuleringarna. Strålningsegenskaper kan ha starkt inflytande för vissa kemiska kompositioner, särskilt 𝐶𝑂2 och 𝐻2𝑂 som är produkterna från förbränningen 𝐶𝐻4 och 𝑂2. En förenklad gasstrålningstransportekvation implementeras tillsammans med olika spektralmodeller som beräknar gasemissiviteten för högre temperatur. Dessutom används Rocflam-II-kod som har en befintlig gasstrålningsmodell för att jämföra och validera den förenklade modellen. Slutligen jämförs kombinationen av konvektiva och strålningsvärmeöverföringsvärden med de experimentella testdata. Till skillnad från de tidigare existerande utsläppsmodellerna med en viss temperaturgräns möjliggör modellen som används här att inkludera den totala emissiviteten för 𝐶𝑂2 och 𝐻2𝑂 för temperaturer upp till 3400 K och därmed mer lämplig för kolväteförbränning i rymdframdrivningssystem. Det visar sig att gasstrålningen svarar för 2-4% av det totala värmeflödet för en 𝐶𝐻4/𝑂2 förbränningskammare med maximal integrerad temperatur på 2700 K. Påverkan av gasstrålning skulle vara större än 4% av den integrerade temperaturen. Effekter på värmeströmning av gasstrålning är högre i strömrörs förbränningszon jämfört med de andra sektionerna av tryckkammaren. Det individuella bidraget från strålningsvärmeflöde med 𝐶𝑂2 noterades vara 1.5-2 gånger högre än det 𝐻2𝑂. Det visades att det analytiskt härledda förenklade uttrycket för gasstrålning tillsammans med de olika spektralmodellerna hade en rimlig tillnärmning av det uppmätta strålning. Den uppskattade strålningen var korrekt den uppmätta strålningen från Rocflam-II-modellen för ett temperaturintervall på 400-3400 K.

Methane and oxygen are a promising propellant combination in future rocket propulsion engines mainly due to its advantages like reusability and cost reduction. In order to have a comprehensive understanding of this propellant combination extensive research work is being done. Especially, for reusable rocket engines the thermal calculations become vital as an effective and efficient cooling system is crucial for extending the engine life. The design of cooling channels may significantly be influenced by radiation. Within the framework of this thesis, the gas radiation heat transfer is modelled for CFD simulation of rocket thrust chambers and analysed for the 𝐶𝐻4/𝑂2 fuel combination. The radiation is modelled within ArianeGroup’s in-house spray combustion CFD tool - Rocflam3, which is used to carry out the simulations. Radiation properties can have strong influence for certain chemical compositions, especially 𝐶𝑂2 and 𝐻2𝑂 which are the products of the 𝐶𝐻4 and 𝑂2 combustion. A simplified gas radiation transport equation is implemented along with various spectral models which compute the gas emissivity for higher temperature. Also, Rocflam-II code which has an existing gas radiation model is used to compare and validate the simplified model. Finally the combination of the convective and radiative heat transfer values are compared to the experimental test data. In contrast to the previously existing emissivity models with a certain temperature limit, the model used here enables the inclusion for the total emissivity of 𝐶𝑂2 and 𝐻2𝑂 for temperatures up to 3400 K and hence more appropriate for hydrocarbon combustion in space propulsion systems. It turns out that the gas radiation is responsible for 2-4% of the total heat flux for a 𝐶𝐻4/𝑂2 combustion chamber with maximum integrated temperature of 2700 K. The influence of gas radiation would be greater than 4% respective of the integrated temperature. Gas radiation heat flux effects are higher in stream-tube combustion zone compared to the other sections of the thrust chamber. The individual contribution of radiative heat flux by 𝐶𝑂2 was noted to be 1.5-2 times higher than that to 𝐻2𝑂. It was shown that the analytically derived simplified expression for gas radiation along with the various spectral models had reasonable approximation of the measured radiation. The estimated radiation was correct to the measured radiation from the Rocflam-II model for a temperature range of 400-3400 K.
Metan och syre är en lovande kombination av drivmedel i framtida raketframdrivningsmotorer främst på grund av dess fördelar som återanvändbarhet och kostnadsminskning. För att få en omfattande förståelse av denna drivmedelkombination görs ett omfattande forskningsarbete. Speciellt för återanvändbara raketmotorer blir värmeberäkningarna viktiga eftersom ett effektivt och effektivt kylsystem är avgörande för att förlänga livslängden på motorn. Utformningen av kylkanaler kan betydligt påverkas av strålning. Inom ramen för denna avhandling modelleras gasstrålningsvärmeöverföringen för CFD-simulering av rakettryckkamrar och analyseras för 𝐶𝐻4/𝑂2 -bränslekombinationen. Strålningen är modellerad i ArianeGroup’s egen förbränning CFD-verktyg - Rocflam3, som används för att utföra simuleringarna. Strålningsegenskaper kan ha starkt inflytande för vissa kemiska kompositioner, särskilt 𝐶𝑂2 och 𝐻2𝑂 som är produkterna från förbränningen 𝐶𝐻4 och 𝑂2. En förenklad gasstrålningstransportekvation implementeras tillsammans med olika spektralmodeller som beräknar gasemissiviteten för högre temperatur. Dessutom används Rocflam-II-kod som har en befintlig gasstrålningsmodell för att jämföra och validera den förenklade modellen. Slutligen jämförs kombinationen av konvektiva och strålningsvärmeöverföringsvärden med de experimentella testdata. Till skillnad från de tidigare existerande utsläppsmodellerna med en viss temperaturgräns möjliggör modellen som används här att inkludera den totala emissiviteten för 𝐶𝑂2 och 𝐻2𝑂 för temperaturer upp till 3400 K och därmed mer lämplig för kolväteförbränning i rymdframdrivningssystem. Det visar sig att gasstrålningen svarar för 2-4% av det totala värmeflödet för en 𝐶𝐻4/𝑂2 förbränningskammare med maximal integrerad temperatur på 2700 K. Påverkan av gasstrålning skulle vara större än 4% av den integrerade temperaturen. Effekter på värmeströmning av gasstrålning är högre i strömrörs förbränningszon jämfört med de andra sektionerna av tryckkammaren. Det individuella bidraget från strålningsvärmeflöde med 𝐶𝑂2 noterades vara 1.5-2 gånger högre än det 𝐻2𝑂. Det visades att det analytiskt härledda förenklade uttrycket för gasstrålning tillsammans med de olika spektralmodellerna hade en rimlig tillnärmning av det uppmätta strålning. Den uppskattade strålningen var korrekt den uppmätta strålningen från Rocflam-II-modellen för ett temperaturintervall på 400-3400 K.

Thesis (MScEng)--Stellenbosch University, 2013.
ENGLISH ABSTRACT: An accurate description of the atmospheric boundary layer (ABL) is a prerequisite for computational fluid dynamic (CFD) wind studies. This includes taking into account the thermal stability of the atmosphere, which can be stable, neutral or unstable, depending on the nature of the surface fluxes of momentum and heat. The diurnal variation between stable and unstable conditions in the Namib Desert interdune was measured and quantified using the wind velocity and temperature profiles that describe the thermally stratified atmosphere, as derived by Monin- Obukhov similarity theory. The implementation of this thermally stratified atmosphere into CFD has been examined in this study by using Reynoldsaveraged Navier-Stokes (RANS) turbulence models. The maintenance of the temperature, velocity and turbulence profiles along an extensive computational domain length was required, while simultaneously allowing for full variation in pressure and density through the ideal gas law. This included the implementation of zero heat transfer from the surface, through the boundary layer, under neutral conditions so that the adiabatic lapse rate could be sustained. Buoyancy effects were included by adding weight to the fluid, leading to the emergence of the hydrostatic pressure field and the resultant density changes expected in the real atmosphere. The CFD model was validated against measured data, from literature, for the flow over a cosine hill in a wind tunnel. The standard k-ε and SST k-ω turbulence models, modified for gravity effects, represented the data most accurately. The flow over an idealised transverse dune immersed in the thermally stratified ABL was also investigated. It was found that the flow recovery was enhanced and re-attachment occurred earlier in unstable conditions, while flow recovery and re-attachment took longer in stable conditions. It was also found that flow acceleration over the crest of the dune was greater under unstable conditions. The effect of the dune on the flow higher up in the atmosphere was also felt at much higher distances for unstable conditions, through enhanced vertical velocities. Under stable conditions, vertical velocities were reduced, and the influence on the flow higher up in the atmosphere was much less than for unstable or neutral conditions. This showed that the assumption of neutral conditions could lead to an incomplete picture of the flow conditions that influence any particular case of interest.
AFRIKAANSE OPSOMMING: 'n Akkurate beskrywing van die atmosferiese grenslaag (ABL) is 'n voorvereiste vir wind studies met berekenings-vloeimeganika (CFD). Dit sluit in die inagneming van die termiese stabiliteit van die atmosfeer, wat stabiel, neutraal of onstabiel kan wees, afhangende van die aard van die oppervlak vloed van momentum en warmte. Die daaglikse variasie tussen stabiele en onstabiele toestande in die Namib Woestyn interduin is gemeet en gekwantifiseer deur gebruik te maak van die wind snelheid en temperatuur profiele wat die termies gestratifiseerde atmosfeer, soos afgelei deur Monin-Obukhov teorie, beskryf. Die implementering van hierdie termies gestratifiseerde atmosfeer in CFD is in hierdie studie aangespreek deur gebruik te maak van RANS turbulensie modelle. Die handhawing van die temperatuur, snelheid en turbulensie profiele in die lengte van 'n uitgebreide berekenings domein is nodig, en terselfdertyd moet toegelaat word vir volledige variasie in die druk en digtheid, deur die ideale gaswet. Dit sluit in die implementering van zero hitte-oordrag vanaf die grond onder neutrale toestande sodat die adiabatiese vervaltempo volgehou kan word. Drykrag effekte is ingesluit deur die toevoeging van gewig na die vloeistof, wat lei tot die ontwikkeling van die hidrostatiese druk veld, en die gevolglike digtheid veranderinge, wat in die werklike atmosfeer verwag word. Die CFD-model is gevalideer teen gemete data, vanaf die literatuur, vir die vloei oor 'n kosinus heuwel in 'n windtonnel. Die standaard k-ε en SST k-ω turbulensie modelle, met veranderinge vir swaartekrag effekte, het die data mees akkuraat voorgestel. Die vloei oor 'n geïdealiseerde transversale duin gedompel in die termies gestratifiseerde ABL is ook ondersoek. Daar is bevind dat die vloei herstel is versterk en terug-aanhegging het vroeër plaasgevind in onstabiele toestande, terwyl vloei herstel en terug-aanhegging langer gevat het in stabiele toestande. Daar is ook bevind dat vloei versnelling oor die kruin van die duin groter was onder onstabiele toestande. Die effek van die duin op die vloei hoër op in die atmosfeer is ook op hoër afstande onder onstabiele toestande gevoel, deur middel van verhoogte vertikale snelhede. Onder stabiele toestande, is vertikale snelhede verminder, en die invloed op die vloei hoër op in die atmosfeer was veel minder as vir onstabiel of neutrale toestande. Dit het getoon dat die aanname van neutrale toestande kan lei tot 'n onvolledige beeld van die vloei toestande wat 'n invloed op 'n bepaalde geval kan hê.

The mechanisms governing the formation and destruction of soot in turbulent combustion are intimately coupled to thermal radiation due to the strong dependence of sooting processes and radiative loss on temperature. Detailed computational fluid dynamics (CFD) predictions of the radiative and soot output from turbulent non-premixed flames are normally performed by parabolic algorithms. However, the modelling of combustion systems, such as furnaces and unwanted enclosure fires, often require a fully elliptic description of the flow field and its related physical phenomena. Thus, this thesis investigates the intimate coupling between radiative energy exchange and the mechanisms governing soot formation and destruction within a three-dimensional, general curvilinear CFD code. Thermal radiation is modelled by the discrete transfer radiation model (DTRM). Special emphasis is given to approximate solutions to the radiative transfer equation encompassing various models for the radiative properties of gases and soot. A new algorithm is presented, entitled the differential total absorptivity (DTA) solution, which, unlike alternative solutions, incorporates the source temperature dependence of absorption. Additionally, a weighted sum of gray gases (WSGG) solution is described which includes the treatment of gray boundaries. Whilst the DTA solution is particularly recommended for systems comprising large temperature differences, the WSGG solution is deemed most appropriate for numerical simulation of lower temperature diffusion flames, due to its significant time advantage. The coupling between radiative loss and soot concentration is investigated via a multiple laminar flamelet concept applied within the CFD simulation of confined turbulent diffusion flames burning methane in air at 1 and 3 atm. Flamelet families are employed relating individual sooting mechanisms to the level of radiative loss, which is evaluated by the DTRM formulated for emitting-absorbing mixtures of soot, C02 and H20. Combustion heat release is described by an eddy break-up concept linked to the k-c turbulence model, whilst temperature is evaluated from the solved enthalpy field. Detailed comparisons between prediction and experiment for the critical properties of mixture fraction, temperature and soot volume fraction demonstrate the effectiveness of this novel, coupled strategy within an elliptic flow field calculation.

This thesis examines the prediction of opposed flow flame spread in the Fire Dynamics Simulator version 4 (FDS4) Computational Fluid Dynamics (CFD) model by adapting the Lateral Ignition Flame Transport (LIFT) test procedure. It should be noted that FDS4 was all that was available at the time of the analysis despite FDS5 is now available for beta testing. This research follows on from previous work where LIFT experiments were conducted for various New Zealand timber and timber based products; those materials include Beech, Macrocarpa, Radiata Pine, Rimu, Hardboard, Medium Density Fibreboard (MDF), Melteca faced MDF, Plywood and Particle Board. The objective of this research is to investigate the accuracy of flame spread modelling in FDS4; where the prediction of opposed flow flame spread parameters from FDS4 were directly compared with the experimental results that were obtained experimentally. The standardised procedure for determining the material ignition and flame spread properties was followed and applied to simulate the LIFT test. The LIFT test apparatus was set up in FDS4 with a domain size of 0.9 x 0.3 x 0.3 metres in the x, y and z directions respectively. From the heat flux distribution along the calibration specimen, it indicated that calibration of the LIFT apparatus can be executed in FDS4 where the percentage error is within 1.2%. This report also provides the thermal transport properties (i.e. thermal conductivity and specific heat capacity) of the tested New Zealand timber and timber based products. These were determined using a transient plane source technique and subsequently these properties were entered as the surface identifications in FDS4. The ignition tests were not performed as part of the simulated LIFT test since a direct comparison with the results was required to give a more meaningful assessment. For this reason, the ignition parameters that were obtained from the previous experiments were employed to carry out the flame spread test. Due to the concept of a preheat time required by the standard test method and FDS4 being not able to preheat specimens, the temperature immediately after the preheat time was calculated and implemented for the specimens. The heat transfer problem was solved using an explicit method; where specimens were divided into 11 different nodes. Different scenarios were investigated to see the effect that the selected combustion model has on modelling flame spread. The two analytical models tested were (1) thermoplastic fuels and (2) charring fuels model. Furthermore, the flame spread was visualised using either the Mixture Fraction or the HRRPUV model in Smokeview; where the rate of flame spread for each specimen was obtained. And lastly, three different absorption coefficients (0.6, 0.7 and 0.8) for each specimen were examined; this parameter contributed significantly to the rate of flame spread as it determines the amount of heat flux being absorbed by the specimen during the time of preheating. A study of the grid size was also performed to investigate the accuracy of the FDS4 simulations with the grid size selected. It has been found that increasing the size of the grid cell does not greatly affect the flame spread results. Moisture content and heat of vaporisation input variables were also examined. From the flame spread data, moisture content does not have a significant role in modelling flame spread. However, it was indicated that the heat of vaporisation has an effect on the output of the flame spread parameters. It was determined from the sensitivity analysis that the most appropriate solid boundary condition to be used in predicting the flame spread would be thermoplastic fuels model with an absorption coefficient of 0.8. By using this scenario as the basis, the plot of the arrival time against the distance along the specimen exhibits a similar trend of flame spread with the experimental results at first, but later on, the extinction of flame front actually occurred at a much earlier stage than the experimental results showed. In general, the analyses showed that FDS4 cannot perform the LIFT test where the prediction of flame heating parameter and minimum heat flux for spread were out by more than 20% shown by the direct comparison between experimental results. However, the prediction of minimum heat flux required for ignition seems to agree with the experimental results where the percentage error is within 20%.

Orientadores: Rubens Maciel Filho, Andre Luiz Jardini Munhoz
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica
Made available in DSpace on 2018-08-14T19:20:20Z (GMT). No. of bitstreams: 1 Bineli_AulusRobertoRomao_M.pdf: 24103427 bytes, checksum: e0dc4ef614d43eab9b12a55f01124378 (MD5) Previous issue date: 2009
Resumo: Em tratamentos térmicos de têmpera há uma grande dificuldade em entender os diferentes perfis de resfriamento que ocorrem na superfície e no interior dos materiais, e que definem o controle da estrutura formada e das propriedades finais desejadas. A formação de diferentes tipos de estruturas no mesmo material pode ocorrer devido ao resfriamento não uniforme provocado pelas condições fluidodinâmicas do tanque e do fluido refrigerante, os quais determinam as taxas de resfriamento e o valor do coeficiente de transferência de calor. Além disso, há muito pouco na literatura sobre os critérios para a construção de tanques de têmpera. Portanto este trabalho investiga por meio da Fluidodinâmica Computacional (CFD), utilizando o software ANSYS CFX® 11, duas configurações de um sistema de agitação submerso em tanque de têmpera e o impacto das condições fluidodinâmicas e das propriedades físicas do fluido sobre a uniformidade do resfriamento e no coeficiente de transferência de calor na interface do bloco de aço. Como conseqüência as simulações permitem a verificação de alternativas de como o processo pode ser melhorado a partir deste tipo de análise. O processo físico estudado consiste no resfriamento de um bloco de aço nas dimensões 2,3m x 1,2m x 0,86m imerso em tanque com água de dimensões 8,7m x 2,8m x 4,0 m com um sistema de agitação de jato submerso distribuídos em vários bicos reguladores de saída de água. Foram realizadas duas simulações, a primeira envolvendo o sistema de agitação localizado sob o bloco. Na segunda, entretanto, foi acrescentado um sistema de agitação localizada nas laterais do material na tentativa de homogeneizar o fluxo do fluido entorno do bloco, consequentemente sobre a uniformidade do resfriamento. Os resultados deste trabalho indicam que o sistema foi suscetível a variação das propriedades físicas do fluido e do fluxo sobre o material o que levou a grandes variações na curva de resfriamento para o primeiro caso. Contudo, a implementação do sistema lateral de agitação promoveu uma melhora significativa na uniformidade da têmpera, além disso, o modelo foi capaz de predizer as curvas de resfriamento, os coeficientes de transferência de calor na interface do material, e os fluxos do fluido no tanque. A análise discutida fornece informações de como o software pode melhorar o controle do processo de resfriamento por estudos sobre a uniformidade da têmpera, o que pode auxiliar os engenheiros na concepção e desenvolvimento de novos projetos de tanque levando-se em consideração a forma e o tipo do sistema de agitação, bem como a geometria do tanque e do material, e o fluido utilizado no processo. Esta abordagem pode produzir melhorias significativas na qualidade do material enquanto simultaneamente prevê condições para redução de distorções do material durante o tratamento térmico.
Abstract: In the quenching heat treatment is a great difficulty to understand the different cooling profiles occurring at the surface and subsurface of the material, that define the structure formed and the final properties desired. The formation of different types of structures in the material can occurs due to uneven cooling caused by fluid dynamic conditions of the tank, which determine the cooling rates and the heat transfer coefficient. Moreover, there is very little literature concerning the criteria for the construction of quenching tanks. Therefore in this work was analyzed by means of Computational Fluid Dynamics (CFD), two configurations of submerged agitation system and the impact of fluid dynamic conditions and the physical properties of the fluid on the cooling uniformity and the heat transfer coefficient at the interface of the steel block. The simulations performed allow the verification of alternatives of how the process can be improved from this type of analysis. The physical process studied consist in the cooling of a steel block with dimensions 2.3m x 1.2m x 0.86m immersed in water tank with dimensions 8.7m x 2.8m x 4.0m with submerged agitation system. There were two simulations, the first involving the agitation system located under the block. In the second, however, was added agitation system located next the sides of the material in an attempt to homogenize the fluid flow around the block, consequently on the uniformity of cooling. The results indicate that the system was susceptible to variations in the fluid properties and fluid flow on the material which led to large variations in the cooling curve for the first case. The implementation of the sideway agitation system led to a significant improvement in uniformity of quenching, in addition, the model was able to predict the cooling curves, the heat transfer coefficient at the interface of the material, and fluid flow in the tank. The analysis provides information about how software can improve the control of the cooling process by studies of quench uniformity, which can help engineers in the design and development of new tank taking into account the type of agitation system, tank geometry and material, and the fluid used in the process. This approach can produce significant improvements in the quality of the material while simultaneously provide conditions to reduce distortions in the material during heat treating.
Mestrado
Mestre em Engenharia Química

Computational Fluid Dynamics (CFD) is increasingly being used in nuclear reactor safety analysis as a tool that enables safety related physical phenomena occurring in the reactor coolant system to be described in more detail and accuracy. Validation is a necessary step in improving predictive capability of a computationa code or coupled computational codes. Validation refers to the assessment of model accuracy incorporating any uncertainties (aleatory and epistemic) that may be of importance. The uncertainties must be identi ed, quanti ed and if possible, reduced. In the rst part of this thesis, a discussion on the development of an approach and experimental facility for the validation of coupled Computational Fluid Dynamics codes and System Thermal Hydraulics (STH) codes is given. The validation of a coupled code requires experiments which feature signi cant two-way feedbacks between the component (CFD sub-domain) and the system (STH sub-domain). Results of CFD analysis that are used in the development of a exible design of the TALL-3D experimental facility are presented. The facility consists of a lead-bismuth eutectic (LBE) thermal-hydraulic loop operating in forced and natural circulation regimes with a heated pool-type 3D test section. Transient analysis of the mixing and strati cation phenomena in the 3D test section under forced and natural circulation conditions in the loop show that the test section outlet temperature deviates from that predicted by analytical solution (which the 1D STH solution essentially is). Also an experimental validation test matrix according to the key physical phenomena of interest in the new experimental facility is developed. In the second part of the thesis we consider the risk related to steam generator tube leakage or rupture (SGTL/R) in a pool-type design of lead-cooled reactor (LFR). We demonstrate that there is a possibility that small steam bubbles leaking from the SGT will be dragged by the turbulent coolant ow into the core region. Voiding of the core might cause threats of reactivity insertion accident or local damage (burnout) of fuel rod cladding. Trajectories of the bubbles are determined by the bubble size and turbulent ow eld of lead coolant. The main objective of such study is to quantify likelihood of steam bubble transport to the core region in case of SGT leakage in the primary coolant system of the ELSY (European Lead-cooled SYstem) design. Coolant ow eld and bubble motion are simulated by CFD code Star-CCM+. First, we discuss drag correlations for a steam bubble moving in liquid lead. Thereafter the steady state liquid lead ow eld in the primary system is modeled according to the ELSY design parameters of nominal full power operation. Finally, the consequences of SGT leakage are modeled by injecting bubbles in the steam generator region. An assessment of the probability that bubbles can reach the core region and also accumulate in the primary system, is performed. The most dangerous leakage positions in the SG and bubble sizes are identi ed. Possible design solutions for prevention of core voiding in case of SGTL/R are discussed.

The hotspot temperature of disc windings has a close relation with the transformer age. In oil immersed transformers, oil guides are applied generally to enhance the cooling effects for disc windings. In some cases disc windings without oil guides are used. However, the lack of oil guides is expected to result in a more complicated thermal behavior of the windings, making it more difficult to predict the location and strength of the hotspot temperature (i.e. the hottest temperature in the winding). To get an improved understanding of the thermal behavior, a CFD study has been performed.  This article describes the implementation of CFD simulation for 2D axisymmetry models without oil guides, and then analyzes the results of a series of parametric studies to see the sensitive factors influencing the cooling effects. These parameters include radial disc width, inlet mass flow rate, horizontal duct height, vertical duct width and the inlet/outlet configurations. Three main characteristics, the hotspot temperature, the location of the hotspot and the number of oil flow patterns are detected to describe the thermal performance.

Attempts to identify a fundamental mechanism that increases the thermal conductivity of liquids with nanoparticle suspension (nanofluids) have not been entirely successful. Models based on the thermal conductivity of the component materials, volume fraction, and temperature have proven to predict the thermal conductivity well for larger nanoparticles. However, when the nanoparticle size becomes smaller, a large increase in thermal conductivity becomes more prominent at low volume fractions. Indicating an unknown mechanism is contributing to the thermal conductivity enhancement. This research provides a new direction for analyzing nanofluid thermal conductivity enhancements by investigating mechanisms related to the distance between suspended nanoparticles. From this study, an initial model that represents an ideal nanofluid has been developed. The ideal model can then be evolved to match Maxwell’s conductivity model by estimating particle migration with Einstein’s displacement theory coupled with thermal penetration analysis. The analytical model was also compared with a conjugate heat transfer computational fluid dynamics (CFD) simulation which provided additional insight into this phenomenon by confirming that local temperature gradients exist between sufficiently close nanoparticles. The results from the analytical model and CFD simulation indicate that particle displacement will cause significant local fluctuations in thermal conductivity for a colloidal fluid.

This thesis presents a study of the cooling process of a solid block performed by a turbulent air flow channel. The study focuses on the turbulent flow and its influence in the heat transfer of the block.

The first part of the thesis is an analysis of the different turbulent model and their adaptation on the necessities of this study. Once the turbulent model has been confirmed it makes a study of the behavior of the cooling process by CFD (Computational Fluid Dynamics), and an analysis of the numerical accuracy of this computational study.

When the procedure of the study of the cooling process is defined it proposes some different variations in the initial solution to improve this process. The study concentrates in variations of the turbulence and the geometry of the studied block.

Finally, the different improving are discussed analyzing parameters as the heat transfer, pressure drop, time consuming or energy consuming.

Although the terms "Human Thermal Comfort" and "Indoor Air Quality (IAQ)" can be highly subjective, they still dictate the indoor climate design (HVAC design) of a building. In order to evaluate human thermal comfort and IAQ, one of three main tools are used, a) direct questioning the subjects about their thermal and air quality sensation (voting, sampling etc.), b) measuring the human thermal comfort by recording the physical parameters such as relative humidity, air and radiation temperature, air velocities and concentration gradients of pollutants or c) by using numerical simulations either including or excluding detailed thermo-physiological models. The application of the first two approaches can only take place in post commissioning and/or testing phases of the building. Use of numerical techniques can however be employed at any stage of the building design. With the rapid development in computational hard- and software technology, the costs involved in numerical studies has reduced compared to detailed tests. Employing numerical modelling to investigate human thermal comfort and IAQ however demand thorough verification and validation studies. Such studies are used to understand the limitations and application of numerical modelling of human thermal comfort and IAQ in indoor climates. This PhD research is an endeavour to verify, validate and apply, numerical simulation for modelling heat transfer and respiration of occupants in indoor climates. Along with the investigations concerning convective and radiation heat transfer between the occupants and their surroundings, the work focuses on detailed respiration modelling of sedentary human occupants. The objectives of the work have been to: verify the convective and radiation numerical models; validate them for buoyancy-driven flows due to human occupants in indoor climates; and apply these validated models for investigating human thermal comfort and IAQ in a real classroom for which field study data was available. On the basis of the detailed verification, validation and application studies, the findings are summarized as a set of guidelines for simulating human thermal comfort and IAQ in indoor climates. This PhD research involves the use of detailed human body geometries and postures. Modelling radiation and investigating the effect of geometrical posture has shown that the effective radiation area varies significantly with posture. The simulation results have shown that by using an effective radiation area factor of 0.725, estimated previously (Fanger, 1972) for a standing person, can lead to an underestimation of effective radiation area by 13% for the postures considered. Numerical modelling of convective heat transfer and respiration processes for sedentary manikins have shown that the SST turbulence model (Menter, 1994) with appropriate resolution of near wall region can simulate the local air velocity, temperature and heat transfer coefficients to a level of detail required for prediction of thermal comfort and IAQ. The present PhD work has shown that in a convection dominated environment, the detailed seated manikins give rise to an asymmetrical thermal plume as compared to the thermal plumes generated by simplified manikins or point sources. Validated simulation results obtained during the present PhD work have shown that simplified manikins can be used without significant limitations while investigating IAQ of complete indoor spaces. The use of simplified manikins however does not seem appropriate when simulating detailed respiration effects in the immediate vicinity of seated humans because of the underestimation in the amount of re-inhaled CO2 and pollutants from the surroundings. Furthermore, the results have shown that due to the simplification in geometrical form of the nostrils, the CO2 concentration is much higher near the face region (direct jet along the nostrils) as compared to a detailed geometry (sideways jet). Simulating the complete respiration cycle has shown that a pause between exhalation and inhalation has a significant effect on the amount of re-inhaled CO2. Previous results have shown the amount of re-inhaled CO2 to range between 10 - 19%. The present study has shown that by considering the pause, this amount of re-inhaled CO2 falls down to values lower than 1%. A comparison between the simplified and detailed geometry has shown that a simplified geometry can cause an underestimation in the amount of re-inhaled CO2 by more than 37% as compared to a detailed geometry. The major contribution to knowledge delivered by this PhD work is the provision of a validated seated computational thermal manikin. This PhD work follows a structured verification and validation approach for conducting CFD simulations to predict human thermal comfort and indoor air quality. The work demonstrates the application of the validated model to a classroom case with multiple occupancy and compares the measured results with the simulation results. The comparison of CFD results with measured data advocates the use of CFD and visualizes the importance of modelling thermal manikins in indoor HVAC design rather than designing the HVAC by considering empty spaces as the occupancy has a strong influence on the indoor air flow. This PhD work enables the indoor climate researchers and building designers to employ simplified thermal manikin to correctly predict the mean flow characteristics in indoor surroundings. The present work clearly demonstrates the limitation of the PIV measurement technique, the importance of using detailed CFD manikin geometry when investigating the phenomena of respiration in detail and the effect of thermal plume around the seated manikin. This computational thermal manikin used in this work is valid for a seated adult female geometry.

Renewable Energies have the capability to cut down the severe impacts of energy and environmental crisis. Integrating renewable energy generation into the global energy system calls for state of the art energy storage technologies. The lithium-ion battery is introduced in this paper as a solution with a promising role in the storage sector on the grounds of high mass and volumetric energy density. Afterward, the advantages of proper thermal management, including thermal runaway prevention, optimum performance, durability, and temperature uniformity are described. In particular, this review detailedly compares the most frequently adopted battery thermal management solutions (BTMS) in the storage industry including direct and indirect liquid, air, phase-change material, and heating. In this work, four battery thermal management solutions are selected and analyzed using Computational Fluid Dynamic (CFD) simulations for accurate thermal modeling. The outcome of the simulations is compared using parameters e.g. temperature distribution in battery cells, battery module, and power consumption. Liquid cooling utilizing the direct contact higher cooling performance to the conventional air cooling methods. However, there exist some challenges being adopted in the market. Each of the methods proves to be favorable for a particular application and can be further optimized.
Integrering av förnybara energier i globala energisystem kräver enorma energilagrings teknologier. Litium jon batterier spelar en viktig roll inom denna sektor på grund av både hög vikt- och volymmässig energidensitet. Korrekt värmestyrning (Thermal management) är nödvändigt för litium jon batteriernas livslängd och operation. Dessa batterier fungerar bäst när de ligger inom intervallet 15–35 grader. dessutom har olika värmestyrsystem utvecklats för att säkerställa att batterierna arbetar optimalt i olika applikationer. I den här studien fem värmestyrningslösningar för batterier har väljas och analyseras med hjälp av beräkningsvätskedynamik (CFD) simulering. Resultaten av simuleringarna jämförs med olika parametrar som temperaturfördelning i battericeller, batterimoduler och strömförbrukning. Alla metoder visar sig vara användbara lämplig för viss tillämpning och kan vidare optimeras för detta ändamål.

In the current work the focus is on natural ventilation occurring in buildings. The first step is to discuss the potential of numerical models applied to determine building performance and air flow as part of a mixed mode building control scheme with respect to a test case. A dynamic simulation software (TRNSYS) is used to estimate the annual energy demand. An optimization program (GenOpt) changes iteratively the parameters regulating the airflow within the building model in order to minimize the whole year energy use. Elements which are considered in the analysis are outdoor climatic conditions and elements representing the building use, such as internal gains. The numerical results of this analysis have shown how a proper analysis of natural ventilation phenomena occurring in small premises can lead to energy saving while thermal comfort is not compromised. This has been tested in various Italian climates, by means of tuning different parameters handling the natural ventilation in a mixed mode office room. The natural ventilation to be effective has to be carefully designed and it may not just occur. On the other hand in large enclosures such as atria or churches, where much more complicated phenomena occur in the indoor air flow, the natural ventilation is not so straightforward to analyse. This fact pushes the application of numerical methods capable of higher resolution in order to catch the features of the streams, with the aim of achieving good levels of thermal comfort and indoor air quality. In particular, in the last years a growing attention has been paid on the analysis of building airflow, mostly due to the diffuse interest in reducing energy losses and optimizing the efficiency of heating systems. A nontrivial technical problem is the heating of churches, because nowadays they are used both for religious services and as cultural places. Such problem is still open and no solution has been so far found. In the course of the last century, with the installation of new heating systems, an increase in damage and the decay of valuable interior decoration have been noticed. Moreover in this kind of environments, because of the remarkable heights and the presence of great windows, relevant natural and mixed convection flows may show up and, on the other hand, stratification phenomena may occur, with hot air stagnation far from occupied zones. This can cause people discomfort or energy waste. Therefore it is not possible to design heating plants only to maximize energy efficiency, but the heating systems have to accomplish the best compromise between preservation of cultural property, economy, energy and comfort. For handling all these conflicting requirements at once, simplified or macroscopic models, which describe the real system only with a small number of temperature, pressure and flow rate values, are no more enough, but microclimate field flow models, based on computational fluid dynamics methods (CFD), provide a powerful and versatile tool to obtain a more reliable prediction of the air movement and temperature distribution within the built environment. The case of St. Marien’s church has been investigated to prove the utility of this kind of analysis. On the basis of experimental data collected during winter 2003-2004, a thermal model of St. Marien church has been produced and tuned. The results provided by this model have been used in this work to perform several simulations on St. Marien church with the commercial CFD software FLUENT, in order to find out a computational model which could be a good compromise between simplicity on geometrical representation, saving on computational resources, accuracy and reliability of the solution. Once the model was set up, it has been validated against some temperature values recorded during the monitoring period. Simulations have highlighted a shortcut of the flow from the inlet to the outlet, giving the reason why energy model of the church tuned on the experimental data are overestimating energy consumption. This would not have been possible with a macroscopic analysis, showing the need for large enclosure to carry on both the analyses together. This promising result pushed to test a more direct way to couple energy models and CFD models to predict energy consumptions in buildings or buildings components involving remarkable ventilation phenomena. It came out a method to estimate ventilated components performance on annual bases in a sensible amount of time. The method was applied to a ventilated roof. In this case the considered vented roof showed to increase energy saving with respect to the typical roof layout in climates with high solar radiation levels during a wide period of the year.
Nel lavoro svolto in questa tesi l'attenzione è rivolta ai fenomeni di ventilazione naturale che avvengono negli edifici. Il primo studio ha riguardato il potenziale della modellazione numerica relativamente alle prestazioni dell'edificio come parte di uno schema di controllo della ventilazione mista in riferimento a un caso test. A tal fine è stato utilizzato un software di simulazione dinamica (TRNSYS) per valutare il fabbisogno annuale di energia accoppiato a un programma di ottimizzazione (GenOpt) in grado di modificare i parametri di interesse in maniera iterativa; i risultati dell’analisi hanno permesso di individuare la combinazione di parametri per cui il consumo energetico è minimo su base annuale. Sono state considerate nell'analisi le condizioni climatiche e gli elementi rappresentativi del tipo di utilizzo dell'edificio come i carichi interni. Dai risultati numerici di questa analisi è stato possibile mostrare come un’analisi dettagliata della ventilazione naturale all’interno di ambienti di piccole dimensioni possa portare a un risparmio di energia senza compromettere il comfort termico. Questo è stato provato per diverse regioni climatiche, tarando i diversi parametri che gestiscono la ventilazione naturale nella stanza adibita a ufficio soggetta a ventilazione mista. Il lavoro ha dimostrato come la ventilazione naturale per essere efficiente debba essere pianificata a priori sia per definire le aperture sia per stabilirne la gestione. D'altro canto, in ambienti interni di grandi dimensioni come atri o chiese, dove avvengono fenomeni molto più complessi nei campi di moto dell'aria, la ventilazione naturale non è così semplice da analizzare. Questo fatto spinge all'adozione di metodi caratterizzati da una maggiore risoluzione al fine di meglio definire le caratteristiche del deflusso, quando si studiando intende studiare il comfort termico e la qualità dell'aria. In particolare, negli ultimi anni, c'è stata una crescente attenzione riguardo allo studio dei campi di moto dell'aria all’interno degli edifici, dovuto al diffuso interesse nel ridurre le perdite di energia e a incrementare l'efficienza dei sistemi di riscaldamento. Un problema tecnico non banale riguarda il riscaldamento delle chiese, dal momento che queste oggi sono sempre più utilizzate sia per funzioni religiose che come centri culturali. Tale questione è tuttora aperta, non avendo ancora trovato una soluzione definitiva. Nel corso dell'ultimo secolo, a seguito dell'installazione dei sistemi di riscaldamento, si è manifestato un aumento di danni delle opere d’arte e delle preziose decorazioni all’interno delle chiese storiche. Inoltre in ambienti di questo tipo, a causa dell’accentuato sviluppo verticale e della presenza di grandi finestrature, si possono verificare importanti fenomeni di convezione naturale o fenomeni di stratificazione in cui l'aria calda tende a ristagnare in regioni lontane dalla zona occupata. Le conseguenze possono essere discomfort termico o spreco di energia. Pertanto non è possibile progettare impianti di riscaldamento secondo metodologie standard, quanto dal momento che gli impianti di riscaldamento devono realizzare il miglior compromesso fra conservazione dei beni culturali, costi di esercizio e di manutenzione, risparmio energetico e comfort. Per gestire queste esigenze spesso contrastanti, i modelli macroscopici o ingegneristici che descrivono il sistema reale con un numero ridotto di valori di temperatura, pressione e portata di massa, non sono molto spesso adeguati, mentre la fluidodinamica numerica è uno strumento potente e versatile per ottenere una previsione più affidabile del moto dell'aria e dei campi termici che avvengono negli edifici. Dopo aver illustrato il problema del riscaldamento delle chiese storiche e i principi della CFD, si è condotta un'analisi dettagliata della chiesa di St.Marien a Wismar per dimostrare l'utilità di questi metodi per questo tipo di applicazioni. Sulla base dei dati sperimentali raccolti durante l'inverno 2003-2004, è stato realizzato e tarato un modello energetico dinamico della chiesa. I risultati forniti hanno permesso di stimare le condizioni al contorno per una serie di simulazioni della chiesa di St.Marien basate sul codice commerciale FLUENT, per identificare un modello numerico che potesse essere un buon compromesso fra semplicità del dominio spaziale di calcolo, risparmio di risorse di calcolo, accuratezza e affidabilità della soluzione. Una volta realizzato, il modello è stato validato con alcuni valori di temperatura registrati durante il periodo di monitoraggio. Le simulazioni hanno evidenziato la presenza un cortocircuito in corrispondenza a un fan-coil installato a pavimento. Questo non sarebbe stato possibile con un'analisi basata su modelli semplificati, indicando la necessità, per i grandi ambienti, di portare avanti insieme sia le analisi macroscopiche che quelle di dettaglio con metodi CFD. Questo risultato ha spinto a provare in modo più stretto di accoppiare modelli energetici e CFD al fine di predire le prestazioni energetiche degli edifici. E’ stato quindi prodotto un metodo per stimare le prestazioni di componenti ventilati dell'involucro edilizio su base annuale. Il metodo è stato testato su un tetto ventilato. Si è quindi potuto verificare il miglior comportamento energetico del tetto ventilato rispetto a una equivalente copertura tradizionale.

The rapid growth in data centres has resulted in their consumption of up to 100 times more energy per square metre than office accommodation. IT equipment and systems, housed in data centres, consume a considerable amount of electricity. Energy consumption of data centres can be severely and unnecessarily high due to inadequate localised cooling and densely packed server rack layouts. To highlight the importance of cooling issues in data centres, operational data centres are studied using computational fluid dynamics (CFD). Field measurements of temperature are performed. Numerical analysis of flow and temperature fields is conducted in order to evaluate the thermal behaviour of the data centre. A number of undesirable hotspots are identified. To rectify the problem, a few practical design and remedial solutions to improve the cooling effectiveness are proposed and examined to allow a reduced air-conditioning power requirement. Rack-level architecture and layouts have also been found to have a significant impact on the performance of server cooling systems. In this regard, semi-populated racks are modelled with various server arrangements and void positioning accommodated in a prototype data centre. In raised-floor data centres, the perforated tile flow rate distribution is fundamentally a fluid mechanics problem. The effects of position of the under-floor blockages and percentage opening of perforated tile are studied using CFD. Detailed thermodynamic analysis of air-cooled raised-floor data centres for exploring their optimised performance is performed in this thesis. Exergy based performance metric (EPM) is proposed to assess the irreversibilities in the data centre airspace. Detailed comparison is undertaken of the performance metrics based on the first and Second Laws of thermodynamics.

In der Reaktorsicherheitsforschung sind auftriebsgetriebene Strömungen von Relevanz für Störfall-szenarien mit Verdünnung der Borkonzentration und für thermische Schockbelastungen des Reak-tordruckbehälters. In der numerischen Simulation der Strömungen werden neben der Berücksichtigung der Auftriebskräfte Quell- und Korrekturterme in die Bilanzgleichungen für die turbulente Energie und die turbulente Dissipation eingeführt. Es wurden erweiterte Modelle entwickelt, in die zusätzliche Gleichungen für die Turbulenzgrößen turbulenter Massenstrom und Dichtevarianz eingehen. Die Modelle wurden in den CFD-Code ANSYS-CFX implementiert. Die Validierung der Modelle erfolgte an einem speziellen Versuchsaufbau (VeMix-Versuchsanlage), mit Einspeisung von Fluid höherer Dichte in eine Vorlage. Als Kriterien für die Validierung wurde der Umschlag zwischen impulsdominiertem Strömungsregime mit vertikalem Jet oder ein vertikales Absinken bei Dominanz von Dichteeffekten herangezogen sowie lokale Konzentrationsmessungen mit Hilfe eines speziell entwickelten Leitfähigkeits-Gittersensors. Eine Verbesserung der Simulation dichtedominierter Vermischungsprozesse mit den erweiterten Turbulenzmodellen konnte allerdings nicht nachgewiesen werden, da die Unterschiede zwischen den Rechnungen mit verschiedenen Turbulenzmodellen zu gering sind. Andererseits konnte jedoch die Simulation der Stratifikation von Fluiden unterschiedlicher Dichte im kalten Strang einer Reaktoranlage deutlich verbessert werden. Anhand der Nachrechnung von Ver-suchen am geometrisch ähnlichen Reaktor-Strömungsmodell ROCOM wurde gezeigt, dass diese Stratifikation von bedeutendem Einfluss auf die Vermischung und somit letztendlich auch auf die Temperatur- bzw. Borkonzentrationsverteilung innerhalb des Reaktordruckbehälters ist. Sie lässt sich nur korrekt simulieren, wenn ausreichend große Abschnitte des kalten Stranges mit modelliert werden. Somit konnte doch eine bessere Vorhersagegenauigkeit der Simulation der Vermischung erreicht werden. In reactor safety research, buoyancy driven flows are of relevance for boron dilution accidents or pressurised thermal shock scenarios. Concerning the numerical simulation of these flows, besides of the consideration of buoyancy forces, source and correction terms are introduced into the balance equations for the turbulent energy and its dissipation rate. Within the project, extended turbulence models have been developed by introducing additional balance equations for the turbulent quantities turbulent mass flow and density variance. The models have been implemented into the computati-onal fluid dynamics code ANSYS-CFX. The validation of the models was performed against tests at a special experimental set-up, the VeMix facility, were fluid of higher density was injected into a vertical test section filled with lighter fluid. As validation criteria the switching-over between a momentum controlled mixing pattern with a horizontal jet and buoyancy driven mixing with vertical sinking down of the heavier fluid was used. Additionally, measurement data gained from an especially developed conductivity wire mesh sensor were used. However, an improvement of the modelling of buoyancy driven mixing by use of the extended models could not be shown, because the differences between calculations with the different models were not relevant. On the other hand, the modelling of the stratification of fluids with different density in the cold leg of a reactor primary circuit could be significantly improved. It has been shown on calculations of experi-ments at the ROCOM mixing test facility, a scaled model of a real reactor plant, that this stratification is relevant as a boundary condition for the mixing process inside the reactor pressure vessel. It can be correctly simulated only if sufficient large parts of the cold legs are included in the modelling. On this way, an improvement of the accuracy of the prediction of mixing processes was achieved.

In der Reaktorsicherheitsforschung sind auftriebsgetriebene Strömungen von Relevanz für Störfall-szenarien mit Verdünnung der Borkonzentration und für thermische Schockbelastungen des Reak-tordruckbehälters. In der numerischen Simulation der Strömungen werden neben der Berücksichtigung der Auftriebskräfte Quell- und Korrekturterme in die Bilanzgleichungen für die turbulente Energie und die turbulente Dissipation eingeführt. Es wurden erweiterte Modelle entwickelt, in die zusätzliche Gleichungen für die Turbulenzgrößen turbulenter Massenstrom und Dichtevarianz eingehen. Die Modelle wurden in den CFD-Code ANSYS-CFX implementiert. Die Validierung der Modelle erfolgte an einem speziellen Versuchsaufbau (VeMix-Versuchsanlage), mit Einspeisung von Fluid höherer Dichte in eine Vorlage. Als Kriterien für die Validierung wurde der Umschlag zwischen impulsdominiertem Strömungsregime mit vertikalem Jet oder ein vertikales Absinken bei Dominanz von Dichteeffekten herangezogen sowie lokale Konzentrationsmessungen mit Hilfe eines speziell entwickelten Leitfähigkeits-Gittersensors. Eine Verbesserung der Simulation dichtedominierter Vermischungsprozesse mit den erweiterten Turbulenzmodellen konnte allerdings nicht nachgewiesen werden, da die Unterschiede zwischen den Rechnungen mit verschiedenen Turbulenzmodellen zu gering sind. Andererseits konnte jedoch die Simulation der Stratifikation von Fluiden unterschiedlicher Dichte im kalten Strang einer Reaktoranlage deutlich verbessert werden. Anhand der Nachrechnung von Ver-suchen am geometrisch ähnlichen Reaktor-Strömungsmodell ROCOM wurde gezeigt, dass diese Stratifikation von bedeutendem Einfluss auf die Vermischung und somit letztendlich auch auf die Temperatur- bzw. Borkonzentrationsverteilung innerhalb des Reaktordruckbehälters ist. Sie lässt sich nur korrekt simulieren, wenn ausreichend große Abschnitte des kalten Stranges mit modelliert werden. Somit konnte doch eine bessere Vorhersagegenauigkeit der Simulation der Vermischung erreicht werden. In reactor safety research, buoyancy driven flows are of relevance for boron dilution accidents or pressurised thermal shock scenarios. Concerning the numerical simulation of these flows, besides of the consideration of buoyancy forces, source and correction terms are introduced into the balance equations for the turbulent energy and its dissipation rate. Within the project, extended turbulence models have been developed by introducing additional balance equations for the turbulent quantities turbulent mass flow and density variance. The models have been implemented into the computati-onal fluid dynamics code ANSYS-CFX. The validation of the models was performed against tests at a special experimental set-up, the VeMix facility, were fluid of higher density was injected into a vertical test section filled with lighter fluid. As validation criteria the switching-over between a momentum controlled mixing pattern with a horizontal jet and buoyancy driven mixing with vertical sinking down of the heavier fluid was used. Additionally, measurement data gained from an especially developed conductivity wire mesh sensor were used. However, an improvement of the modelling of buoyancy driven mixing by use of the extended models could not be shown, because the differences between calculations with the different models were not relevant. On the other hand, the modelling of the stratification of fluids with different density in the cold leg of a reactor primary circuit could be significantly improved. It has been shown on calculations of experi-ments at the ROCOM mixing test facility, a scaled model of a real reactor plant, that this stratification is relevant as a boundary condition for the mixing process inside the reactor pressure vessel. It can be correctly simulated only if sufficient large parts of the cold legs are included in the modelling. On this way, an improvement of the accuracy of the prediction of mixing processes was achieved.

Increasing concern about energy consumption and thesimultaneous need for an acceptable thermal environment makesit necessary to estimate in advance what effect differentthermal factors will have on the occupants. Temperaturemeasurements alone do not account for all climate effects onthe human body and especially not for local effects ofconvection and radiation. People as well as thermal manikinscan detect heat loss changes on local body parts. This factmakes it appropriate to develop measurement methods andcomputer models with the corresponding working principles andlevels of resolution. One purpose of this thesis is to linktogether results from these various investigation techniqueswith the aim of assessing different effects of the thermalclimate on people. The results can be used to facilitatedetailed evaluations of thermal influences both in indoorenvironments in buildings and in different types ofvehicles.

This thesis presents a comprehensive and detaileddescription of the theories and methods behind full-scalemeasurements with thermal manikins. This is done with new,extended definitions of the concept of equivalent temperature,and new theories describing equivalent temperature as avector-valued function. One specific advantage is that thelocally measured or simulated results are presented with newlydeveloped "comfort zone diagrams". These diagrams provide newways of taking into consideration both seat zone qualities aswell as the influence of different clothing types on theclimate assessment with "clothing-independent" comfort zonediagrams.

Today, different types of computer programs such as CAD(Computer Aided Design) and CFD (Computational Fluid Dynamics)are used for product development, simulation and testing of,for instance, HVAC (Heating, Ventilation and Air Conditioning)systems, particularly in the building and vehicle industry.Three different climate evaluation methods are used andcompared in this thesis: human subjective measurements, manikinmeasurements and computer modelling. A detailed description ispresented of how developed simulation methods can be used toevaluate the influence of thermal climate in existing andplanned environments. In different climate situationssubjective human experiences are compared to heat lossmeasurements and simulations with thermal manikins. Thecalculation relationships developed in this research agree wellwith full-scale measurements and subject experiments indifferent thermal environments. The use of temperature and flowfield data from CFD calculations as input produces acceptableresults, especially in relatively homogeneous environments. Inmore heterogeneous environments the deviations are slightlylarger. Possible reasons for this are presented along withsuggestions for continued research, new relationships andcomputer codes.

Key-words:equivalent temperature, subject, thermalmanikin, mannequin, thermal climate assessment, heat loss,office environment, cabin climate, ventilated seat, computermodel, CFD, clothing-independent, comfort zone diagram.

Gas turbines are used to convert thermal energy into mechanical energy. The thermal efficiency of the gas turbine is directly related to the turbine inlet temperature. The combustion and turbine technology has improved to such an extent that the operating temperature in the turbine inlet is higher than the melting temperature of the turbine material. Different techniques are used to cope with this problem. One of the most commonly used methods is internal cooling of the turbine blades. Conventionally air from the compressor is used for this purpose but due to higher heat capacity, steam can be used as coolant. This opens up the possibility to increase the gas temperature. In the case of a combined cycle power plant, its availability provides a good opportunity to be used as a coolant. The trailing edge of the gas turbine blades is an important region as it affects the aerodynamics of the flow. The aerodynamics demands a sharp and thin trailing edge to reduce profile losses. The conventional method is the release of a lot of cooling air though a slot along the airfoil trailing edge. However in the case of internal only cooling designs, the coolant is not allowed to leave the channel except from the root section to avoid mixing of the gas in the main flow path with the coolant and loss of cooling medium. The challenge is to design an inner cooling channel, with the cooling medium entering and leaving the blade at the root section, which reduces the metal temperatures to the required values without an increase of the profile losses and at acceptable cooling flow rate and pressure drop. This thesis presents Computational Fluid Dynamic (CFD) based numerical work concentrated firstly on the flow and heat transfer in two-pass rectangular channels with and without turbulator ribs. The aspect ratio of the inlet pass was reduced to accommodate more channels in the blade profile in chord-wise direction. Additionally, the divider-to-tip wall distance was varied for these channels. Their effect on heat transfer and pressure drop was studied for smooth as well as ribbed channels.  It was followed by a numerical heat transfer study in the trapezoidal channel. Different RANS based turbulence models were used to compare the numerical results with the experimental results. Further, new designs to enhance heat transfer in the channel’s side walls (named as trailing edge wall) were studied. These include the provision of ribs at the trailing edge wall only, inline arrangement of ribs at the bottom as well as at the trailing edge wall and a staggered arrangement of these ribs. The final study was a conjugate heat transfer problem with an aim to propose the best internal cooling channel design to reduce the metal temperature of the trailing edge surface for the given thermal and flow conditions. A number of different options were studied and changes were made to get the best possible channel design. The results show that for a two-pass rectangular channel (both smooth and ribbed), the reduction in inlet channel aspect ratio reduces the pressure drop. For a smooth channel the reduction in the width of the inlet pass does not affect the heat transfer enhancement at the inlet pass and outlet pass regions. In case of ribbed channels, heat transfer decreases at the tip and bend bottom with decrease in the width of the inlet pass. Among different turbulence models used to validate numerical results against experimental results for case of trapezoidal channel, the low-Re k-epsilon model is found to be the most appropriate. Using the turbulence model that yields results that are closest to the experimental data, the staggered arrangement of ribs at the trailing edge wall is found to have maximum thermal performance. The results from the conjugate heat transfer problem suggest using steam as coolant if it is available as it requires less mass flow rate to get similar wall temperature values as compared to air at similar thermal and flow conditions. It is also found that staggered arrangement of ribs is the best option compared to others to enhance heat transfer in trailing edge of the gas turbine blade with the pressure drop in the cooling duct in the acceptable range.
Gasturbiner används för att omvandla värmeenergi till mekanisk energi. Den termiska verkningsgraden för en gasturbin är direkt relaterad till turbinen inloppstemperatur. Förbrännings- och turbintekniken har förbättrats så mycket att gastemperaturen i turbininloppet är högre än smälttemperaturen för turbinmaterialet. Olika tekniker används för att hantera detta problem. En av de vanligaste metoderna är intern kylningen av turbinbladen. Konventionellt luft från kompressorn används för detta ändamål, men på grund av högre värmekapacitet kan ånga användas som kylmedel. Detta öppnar för möjligheten att höja gasens temperatur. Vid ett kombikraftverk, ger dess tillgänglighet ett bra tillfälle att användas som kylmedel.   Den bakre delen av turbinbladen är ett viktigt område eftersom geometrin påverkar strömningen. Aerodynamiken kräver en skarp och tunn bakkant för att minska profilförlusterna. Den konventionella metoden för kylning av denna är att släppa ut en stor mängd kylluft genom en spalt längs bakkanten. Men i fallet med enbart inre kylning får kylmediet inte lämna skovelprofilen i strömningskanalen utan endast genom rotsektionen för att undvika blandning av förbränningsluften i turbinens strömningskanal med kylmediet och förlust av kylmedium.   Utmaningen är att utforma en inre kylkanal, i vilken kylmediet kommer in och lämnar bladet i rotsnittet som är tillräckligt bra för att hålla metalltemperaturen på normala värden utan att öka profilförlusterna och med acceptabla kylluftflöden och tryckfall.   Denna avhandling består av ett Computational Fluid Dynamics (CFD) baserat numeriskt arbetet koncentrerat på strömning och värmeöverföring först i två-pass rektangulära kanaler med och utan turbulensalstrande ribbor. Geometrin för inloppspassagen reducerades för att ge utrymme för fler kylkanaler inom bladets profil i kordans riktning. Dessutom varierades mellanväggens avstånd till toppväggen. Effekten på värmeöverföring och tryckfall studerades för båda kanalerna. Därefter följde en numerisk studie av värmeöverföringen i liknande men trapetsformade kanaler. Olika RANS baserade turbulensmodeller användes för att jämföra numeriska och experimentella resultat. Vidare har nya konstruktioner för att förbättra värmeöverföringen i kanalens sidoväggar och bakkant studeras. Dessa inkluderar turbulensribbor på enbart bakkantsväggen samt ribbor på såväl sidoväggar som på bakkantsväggen i linje med och förskjutna mot varandra. Den slutliga studien var ett sammansatt värmeöverföringsproblem bakkantens yta för ett visst angivet tillstånd i form av värmebelastning, tryck, temperatur och flöden. Ett antal olika alternativ har studerats och modifierats för att bästa möjliga kanalutformningen.   Resultaten visar att för en två-pass rektangulär kanal (både släta och ribbade), minskar tryckfallet när inloppskanalens geometri reducerades. För en slät kanal påverkar inte den minskade bredden på inloppskanalen värmeöverförning i inlopps- och utloppskanalerna. Vid ribbade kanaler minskar värmeöverföring vid toppen och på toppväggen med minskad bredd på inloppskanalen. Av de olika turbulensmodeller som används för att validera numeriska resultat mot experimentella för fallet med trapetsformad kanal visade sig låg-Re k-epsilon modellen den mest lämpliga. Genom att använda den turbulensmodell som är närmast experimentella data visar det att geometrin med förskjutna ribbor på bakkantsväggen har maximal termiska prestanda. Resultaten från det sammansatta värmeöverföringsproblemet framhåller användning av ånga som kylmedium om den finns tillgänglig eftersom den kräver mindre massflöde för att få samma värden på väggtemperaturerna jämfört med luft vid samma termiska tillstånd. Det kunde också visas att förskjutna turbulensribbor är det bästa alternativet jämfört med andra för att öka värmeöverföringen i bakkanten av ett gasturbinblad med acceptabelt tryckfall i kylkanalen.
QC 20111108

Reliable thermal modelling approaches are crucial to transformer thermal design and operation. The highest temperature in the winding, usually referred to as the hot-spot temperature, is of the greatest interest because the insulation paper at the hot-spot undergoes the severest thermal ageing, and determines the life expectancy of the transformer insulation. Therefore, the primary objective of transformer thermal design is to control the hot-spot temperature rise over the ambient temperature within certain limit. For liquid-immersed power transformers, the hot-spot temperature rise over the ambient temperature is controlled by the winding geometry, power loss distribution, liquid flow rate and liquid properties. In order to obtain universally applicable thermal modelling results, dimensional analysis is adopted in this PhD thesis to guide computational fluid dynamics (CFD) simulations for disc-type transformer windings in steady state and their experimental verification. The modelling work is split into two parts on oil forced and directed (OD) cooling modes and oil natural (ON) cooling modes. COMSOL software is used for the CFD simulation work For OD cooling modes, volumetric oil flow proportion in each horizontal cooling duct (Pfi) and pressure drop coefficient over the winding (Cpd) are found mainly controlled by the Reynolds number at the winding pass inlet (Re) and the ratio of horizontal duct height to vertical duct width. The correlations for Pfi and Cpd with the dimensionless controlling parameters are derived from CFD parametric sweeps and verified by experimental tests. The effects of different liquid types on the flow distribution and pressure drop are investigated using the correlations derived. Reverse flows at the bottom part of winding passes are shown by both CFD simulations and experimental measurements. The hot-spot factor, H, is interpreted as a dimensionless temperature at the hot-spot and the effects of operational conditions e.g. ambient temperature and loading level on H are analysed. For ON cooling modes, the flow is driven by buoyancy forces and hot-streak dynamics play a vital role in determining fluid flow and temperature distributions. The dimensionless liquid flow and temperature distributions and H are all found to be controlled by Re, Pr and Gr/Re2. An optimal design and operational regime in terms of obtaining the minimum H, is identified from CFD parametric sweeps, where the effects of buoyancy forces are balanced by the effects of inertial forces. Reverse flows are found at the top part of winding passes, opposite to the OD results. The total liquid flow rates of different liquids for the same winding geometry with the same power loss distribution in an ON cooling mode are determined and with these determined total liquid flow rates, the effects of different liquids on fluid flow and temperature distributions are investigated by CFD simulations. The CFD modelling work on disc-type transformer windings in steady state present in this PhD thesis is based on the dimensional analyses on the fluid flow and heat transfer in the windings. Therefore, the results obtained are universally applicable and of the simplest form as well. In addition, the dimensional analyses have provided insight into how the flow and temperature distribution patterns are controlled by the dimensionless controlling parameters, regardless of the transformer operational conditions and the coolant liquid types used.

Thesis (M.S.)--University of New Orleans, 2004.
Title from electronic submission form. "A thesis ... in partial fulfillment of the requirements for the degree of Master of Science in the Department of Mechanical Engineering."--Thesis t.p. Vita. Includes bibliographical references.

It has been found through experiments at Southwest Research Institute that temperature differences between the gas and wall of the pipe through which the gas is flowing can greatly influence the gas flow in the pipe line and give different velocity magnitudes at the top and bottom half of the pipe. The effect on the flow is observed to worsen at low fluid flow and high temperature differences. This effect has been observed by ultrasonic flow meters which measure the chord average gas velocity at four heights across the pipe. A significant variance in chord averaged velocities is apparent at these conditions. CFD analysis was performed. Low flow velocities of 0.1524 m/sec, 0.3048 m/sec and 0.6096 m/sec and temperature differences of 5.5oK, 13.8oK and 27.7oK were considered. When these conditions were imposed onto the three different geometries, it was seen that the heating caused increased errors in the ultrasonic meter response. For the single elbow and double elbow pipe configurations, the errors were below 0.5% for constant wall temperature conditions but rose to 1% for sinusoid varying wall temperature conditions. The error was seen to increase as the axial velocity became more stratified due to momentum or temperature effects. The case of maximum error was noted for the double elbow geometry with sinusoid wall temperature condition where a swirl type of flow was noted to create localized velocity maxima at the center of the pipe. This part of the pipe was barely touched by the ultrasonic meter acoustic path giving maximum error of 1.4%. A thermal well was placed in the path of the gas flow in the pipe to observe the temperature response on the surface of the thermal well. It was noted that the thermal well surface temperature differed by 1.4% for most cases with gas velocity below 0.6096 m/sec.

In this thesis, a Thermal Model Tool (TMT) is developed for standard Avionic Transport Rack (ATR) chassis and thermal design of a standard ATR chassis is done using developed TMT. This ATR chassis is a Digital Moving Map (DMAP) of a helicopter and the tool is used to determine the cooling channel details of DMAP. TMT decreases design process steps and eliminates the complexity of the design. Experimental studies are conducted on one of the existing chassis produced in Aselsan Inc. for different operating conditions. There are two different operating conditions for the chassis as 25 º
C and 55 º
C, which are given, in military standard MIL-STD-810F. Critical temperature values are measured, which are used in analytical calculations, and results are represented. At the first step, outputs of the experimental studies are used in analytical calculation in order to develop TMT. Secondly, heat dissipation rate of two different chassis are v calculated easily by using the TMT, and without making effort for CFD analysis, the necessary number of plate fins of the chassis are assessed considering given geometrical constraints and heat loads. Finally, cooling channels are generated using the results of TMT. In the next step the chassis, which are designed using the results of TMT, are analyzed numerically by using Icepak Computational Fluid Dynamics (CFD) tool and results of TMT are verified. The cooling capacities of the decided plate fins, which are obtained by TMT, are checked whether or not the required heat dissipation rates are ensured. Consequently, TMT is tested under for two different operating conditions on two different chassis. Analytical and numerical studies for both conditions are compared and discussed in detail. Comparisons show that, developed TMT results are meaningful and close to numerical results, therefore TMT can be used in forthcoming ATR chassis designs.

Nonwoven-fabrics have been in use since 1930s. Their advantages over other web fonnation methods like knitting and weaving have attracted many industries such as aerospace, automotive, sports, geotextiles, composites, battery separators etc. to explore and increase their usage. During nonwoven manufacturing, most of the laid loose webs have an insufficient strength as fonned, and require an additional bonding procedure in order to provide the produced nonwoven with its intended properties. To achieve the desired properties of the nonwoven web, the bonding process is therefore, the most important part during production. The thennal bonding through air is one of the modem techniques which is incrementally improved to increase the yield of manufactured nonwoven properties. The system has a disadvantage which is, that the production capacity and energy efficiency is very low. The entitled research aims an industrial optimisation of the thermal bonding through air by entailing a strategic approach and encompassing the whole process chain of the thennal bonding process. The comprehensive and flexible optimisation opportunities provided by the CFD has been used to aid in the control and optimisation of the thermal bonding process and machinery. To optimise the process and product quality, the complex system composing of several components and various physical phenomena occurring during processing is simulated using a hierarchical methodology. More specifically a hierarchical decomposition procedure to recast the original multi scale problem as a sequence of three scale decoupled macro-, meso-, and micro scale subproblems is exploited. The methodology is applied in conjunction with the validation of experiments on through-air bonding product lines. 2D and 3D computational fluid dynamics (CFD) models based on the continuum modelling approach and the theory of porous media coupled with the theory of mixtures are developed to treat the flow behavior, heat transfer, phase change and air moisture transport within the whole through-air bonding system. The model is concluded to be an economic computational tool hence providing rapid process optimisation and valuable infonnation early in the process, which can replace costly experiments and ensure product consistency under variable process and climate conditions. 2D and 3D hybrid modelling considering parametric discrete and continuum parts is also perfonned using conjugate heat transfer analyses. The approach precisely permits the optimisation of the machine component design and the associated optimisation of consistent process and product properties.

Solar energy is one of a very few low-carbon energy technologies with the enormous potential to grow to a large scale. Currently, solar power is generated via the photovoltaic (PV) and concentrating solar power (CSP) technologies. The ability of CSPs to scale up renewable energy at the utility level, as well as to store energy for electrical power generation even under circumstances when the sun is not available (after sunset or on a cloudy day), makes this technology an attractive option for sustainable clean energy. The levelised electricity cost (LEC) of CSP with thermal storage was about 0.16-0.196 Euro/kWh in 2013 (Kost et al., 2013). However, lowering LEC and harvesting more solar energy from CSPs in future motivate researchers to work harder towards the optimisation of such plants. The situation tempts people and governments to invest more in this ultimate clean source of energy while shifting the energy consumption statistics of their societies from fossil fuels to solar energy. Usually, researchers just concentrate on the optimisation of technical aspects of CSP plants (thermal and/or optical optimisation). However, the technical optimisation of a plant while disregarding economic goals cannot produce a fruitful design and in some cases may lead to an increase in the expenses of the plant, which could result in an increase in the generated electrical power price. The study focused on a comprehensive optimisation of one of the main CSP technology types, the linear Fresnel collector (LFC). In the study, the entire LFC solar domain was considered in an optimisation process to maximise the harvested solar heat flux throughout an imaginary summer day (optical goal), and to minimise cavity receiver heat losses (thermal goal) as well as minimising the manufacturing cost of the plant (economic goal). To illustrate the optimisation process, an LFC was considered with 12 design parameters influencing three objectives, and a unique combination of the parameters was found, which optimised the performance. In this regard, different engineering tools and approaches were introduced in the study, e.g., for the calculation of thermal goals, Computational Fluid Dynamics (CFD) and view area approaches were suggested, and for tackling optical goals, CFD and Monte-Carlo based ray-tracing approaches were introduced. The applicability of the introduced methods for the optimisation process was discussed through case study simulations. The study showed that for the intensive optimisation process of an LFC plant, using the Monte Carlo-based ray-tracing as high fidelity approach for the optical optimisation objective, and view area as a low fidelity approach for the thermal optimisation objective, made more sense due to the saving in computational cost without sacrificing accuracy, in comparison with other combinations of the suggested approaches. The study approaches can be developed for the optimisation of other CSP technologies after some modification and manipulation. The techniques provide alternative options for future researchers to choose the best approach in tackling the optimisation of a CSP plant regarding the nature of optimisation, computational cost and accuracy of the process.
Thesis (PhD)--University of Pretoria, 2017.
Mechanical and Aeronautical Engineering
PhD
Unrestricted

Geothermal energy piles (GEPs), buried into the soil, are typically integrated with the circulating pipe inside the piles, where the most common heat transfer fluid (HTF) is water. However, water cannot operate under a sub-zero-degree cold environment without using the antifreeze additive. Carbon dioxide (CO2), which is newly introduced as HTF to save energy by its density difference of flow and circulation, has a more extensive operation range and can operate below zero degrees Celsius as the fluid phase. In this study, GEPs are modelled using a finite element method (FEM) to present the fundamental thermal performance of GEPs under 10-hour daily operation time, and to evaluate the thermal performance of CO2 and H2O in the energy pile system. It is further highlighted the thermo-hydraulic influence acting in the vicinity of GEPs caused by groundwater seepage in fully saturated soil. The concept of the Ragone plot is introduced to evaluate the system, where HTF Péclet number and groundwater Péclet number are considered as the respective main variables. Our numerical results indicated the potential of CO2 as the HTF in similar energy systems. To meet the same energy demand or acquire the same system power efficiency, CO2 GEP could respectively reach up to 4 times the power efficiency and 10 times the energy density than that of water. Moreover, the study on GEPs was extended to coupled hydrothermal analyses. An effective thermal design considering thermohydraulic interaction has the potential to increase the overall thermal performance of GEPs, especially when the groundwater Péclet number is around 1. This research contributes to energy extraction analyses of GEPs by demonstrating thermal performance on the Ragone plot. With the same cutoff efficiency, the GEP with the relatively high groundwater Péclet number could reach more than 10 times the energy density than that with deficient groundwater flow.

In light of rising global temperatures and energy needs, nuclear power is uniquely positioned to offer carbon-free and reliable electricity. In many markets, nuclear power faces strong headwinds due to competition with other fuel sources and prohibitively high capital costs. Small Modular Reactors (SMRs), such as the proposed Advanced Fast Reactor (AFR) 100, have gained popularity in recent years as they promise economies of scale, reduced capital costs, and flexibility of deployment. Fast sodium reactors commonly feature an upper plenum with a large inventory of sodium. When temperatures change due to transients, stratification can occur. It is important to understand the stratification behavior of these large volumes because stratification can counteract natural circulation and fatigue materials. This work features steady-state and transient simulations of thermal stratification and natural circulation of liquid sodium in a simple rectangular slice using a commercial CFD code (ANSYS FLUENT). Different inlet velocities and their effect on stratification are investigated by changing the inlet geometry. Stratification was observed in the two cases with the lowest inlet velocities. An approach for tracking the stratification interface was developed that focuses on temperature gradients rather than differences. Other authors have developed correlations to predict stratification in three dimensional enclosures. However, these correlations predict stratified conditions for all simulations even the ones that did not stratify. The previous models are modified to reflect the two-dimensional nature of the flow in the enclosure. The results align more closely with the simulations and correctly predict stratification in the investigated cases.
Master of Science

Heat exchangers and steam headers are at the heart of any boiler and are susceptible to a range of failures including tube leaks, ligament cracking, creep and fatigue. These common forms of header failure mechanisms can be exacerbated by local thermal stresses due to temperature and flow maldistribution at full and partial boiler load operations. The purpose of this project is to develop process models of the outlet stubbox header of a final superheater (FSH) heat exchanger in a 620MW coal-fired drum type boiler. The process models were used to assess the impact of steam flow and temperature distribution on the thermal stresses in the header material. The process models were developed using Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA). Thermocouples were installed at key locations on the stubbox headers to monitor metal temperatures and the measured metal temperatures served as boundary values and for validation of the CFD results. The thermocouple data was analysed for three different steady state boiler loads, namely full load, 80% load and 60% load. It showed that the temperature distribution across these headers was not uniform, with a maximum temperature difference across the outlet stubbox of 40℃ at full load and 43℃ at partial loads. Other relevant power plant data, such as steam pressure, was provided from the power plant's Distributed Control System (DCS) and was used as boundary conditions for the CFD models. The exact mass flow distribution across the inlet stubs of the outlet stubbox header was unknown and was estimated using a CFD model of the inlet stubbox header and steam mass flow values from power plant's DCS system. A CFD model was created for each of the three boiler loads at steady state conditions. The CFD results provided the metal temperature profile, internal steam temperature distribution and pressure distribution across the header. The CFD solid temperatures were validated using the thermocouple readings and found to be in agreement. The CFD results were exported to the FEA models, where specific displacement constraints for thermal expansion were utilised. The FEA models were used to assess the extent of thermal stresses due to thermal expansion only, as well as stresses due to thermal expansion combined with internal pressure. High local stresses were found at the borehole crotch corners of the rear outlet branch and inlet stubs. However, these are below 0.2% proof strength at elevated temperatures. The high local stresses thus did not result in local plastic deformation but contribute to exacerbate steady state failure mechanisms such as creep.

Solid oxide fuel cell (SOFC) is a device that converts the chemical energy of the fuel into the electricity by the chemical reactions at high temperatures (600-1000oC). Heat is also produced besides the electricity as a result of the electrochemical reactions. Heat produced in the electrochemical reactions causes the thermal stresses, which is one of the most important problems of the SOFC systems. Another important problem of SOFCs is the low fuel utilization ratio. In this study, the effect of the flow arrangement on the temperature distribution, which causes the thermal stresses, and the method to increase the fuel utilization, is investigated. An SOFC single cell experimental setup is developed for Cross-Flow arrangement design. This setup and experimental conditions are modeled with Fluent®
. The experimental results are used in order to validate and verify the model. The model results are found to capture with the experimental results closely. The validated model is used as a reference to develop the models for different flow arrangements and to investigate the effect of the flow arrangement on the temperature distribution. A method to increase the SOFC fuel utilization ratio is suggested. Models for different flow arrangements are developed and the simulation results are compared to determine the most advantageous arrangement.

In order to make gas chromatography (GC) more widely accessible, considerable effort has been made in developing miniaturized GC systems. Thermal gradient gas chromatograpy (TGGC), one of the heating methods used in GC, has recieved attention over the years due to it's ability to enhance analyte focusing. The present work seeks to develop high performance miniaturized GC systems by combining miniaturized GC technology with thermal gradient control methods, creating miniaturized thermal gradient gas chromatography (µTGGC) systems. To aid in this development a thermal control system was developed and shown to successfully control various µTGGC systems. DAQ functionality was also included which allowed for the recording of temperature and power data for use in modeling applications. Thermal models of the various µTGGC systems were developed and validated against the recorded experiemental data. Thermal models were also used to aid in decisions required for the development of new µTGGC system designs. The results from the thermal models were then used to calibrate and validate a stochastic GC transport model. This transport model was then used to evaluate the effect of thermal gradient shape on GC separation performance.

The ability to control the trajectory and understanding the atmospheric effects on the flight performance of a scientific high altitude balloon has long been an aspiring ambition. This thesis work analyses the thermal and optical environments at float using the simulation software, ANSYS FLUENT. The objectives for this thesis were to evaluate how the solar angle, sunshine factor and the ground emissivity altered the altitude for the balloon during floating condition in Steady-state simulations. A transient simulation was conducted to evaluate the diurnal cycle effects on the altitude of the balloon. The understanding of how the parameters influence the altitude will make it possible to autonomously route the balloon to desired altitudes where you have a favorable wind direction. Performing steady-state simulations showcased the significance of certain parameters. Different solar angles greatly influenced the temperature gradient on the balloon and hence a larger lifting force acted on the balloon when the sun was at its highest point. Varying the cloudiness mostly affected the maximum temperature distribution and did not affect the minimum temperature distribution. The steady-state simulations also indicated a limited but noticeable dependence on the ground emissivity. From the transient simulations it was further enhanced how great of influence the solar angle have, which was illustrated by running diurnal cycles. It was also apparent that there are great differences depending on the seasons. For future applications, it would be of interest to investigate the effects caused by wind velocities in the steady-state case. A comparative analytic solution should be performed in order to validate the simulation results.