Dissertations / Theses on the topic 'Natural (free) convection'

Pressurized water reactor nuclear plants, currently under construction, have been designed with passive containment cooling systems. Turbulent, natural-convective condensation, with high non-condensable mass fraction, on the walls of the containment vessel is a primary heat transfer mechanism in these new plant designs. A number of studies have been completed over the past two decades to justify use of the heat and mass transfer analogy for this scenario. A majority of these studies are founded upon natural-convective heat transfer correlations and apply a diffusion layer model to couple heat and mass transfer. Reasonable success in predicting experimental trends for vertical surfaces has been achieved when correction factors are applied. The corrections are attributed to mass transfer suction, film waviness or mist formation, even though little experimental evidence exists to justify these claims. This work examines the influence of film waves and mass transfer suction on the turbulent, natural-convective condensing flow with non-condensable gas present. Testing was conducted using 0.457 m x 2.13 m and a 0.914 m x 2.13 m condensing surfaces suspended in a large pressure vessel. The test surfaces could be rotated from vertical to horizontal to examine the inclination angle effect. The test facility implements relatively high accuracy calorimetric and condensate mass flow measurements to validate the measured heat and mass transfer rates. Test results show that application of the Bayley (1955) and Al-Arabi and Sakr (1988) heat transfer correlations using the heat and mass transfer analogy is appropriate for conditions in which the liquid film remains laminar. For transitional and wavy film flows, a clear augmentation in heat transfer was observed due to disruption of the gas layer by film waves. This result has implications for the scalability of existing correlations. A new correlation is proposed and results compared to several other datasets.

A parallel numerical method has been implemented for solving the Navier Stokes equations on Cartesian and non-orthogonal meshes. To ensure the accuracy of the code first, second and third order differencing schemes, with and without flux-limiters, have been implemented and tested. The most computationally expensive task in the code is the solution of linear equations, and a number of linear solvers have been tested to determine the most efficient. Krylov space, incomplete factorisation, and other iterative and direct solvers from the literature have been implemented, and have been compared with a novel black-box multigrid linear solver that has been developed both as a solver and as a preconditioner for the Krylov space methods. To further reduce execution time the code was parallelised, after a series of experiments comparing the suitability of different parallelisation techniques and computer architectures for the Navier Stokes solver. The code has been applied to the solution of two classes of problem. Two natural convection flows were studied, with an initial study of two dimensional Rayleigh Benard convection being followed by a study of a transient three dimensional flow, in both cases the results being compared with experiment. The second class of problems modelled were free surface flows. A two dimensional free surface driven cavity, and a two dimensional flume flow were modelled, the latter being compared with analytic theory. Finally a three dimensional ship flow was modelled, with the flow about a Wigley hull being simulated for a range of Reynolds and Froude numbers.

Thesis (Ph. D.)--University of Sydney, 2000.
Title from title screen (viewed Apr. 23, 2008). Submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the Dept. of Mechanical Engineering, Faculty of Engineering. Includes bibliography. Also available in print form.

High Rayleigh number(Ra) turbulent free convection has many unresolved issues related to the phenomenology behind the flux scaling, the presence of a mean wind and its effects, exponential probability distribution functions, the Prandtl number dependence and the nature of near wall structures. Few studies have been conducted in the high Prandtl number regime and the understanding of near wall coherent structures is inadequate for $Ra > 10^9$. The present thesis deals with the results of investigations conducted on high Rayleigh number turbulent free convection in the high Schmidt number(Sc) regime, focusing on the role of near wall coherent structures. We use a new method of driving the convection using concentration difference of NaCl across a horizontal membrane between two tanks to achieve high Ra utilising the low molecular diffusivity of NaCl. The near wall structures are visualised by planar laser induced fluorescence. Flux is estimated from transient measurement of concentration in the top tank by a conductivity probe. Experiments are conducted in tanks of $15\times15\times 23$cm (aspect ratio,AR = 0.65) and $10\times10\times 23$cm (AR = 0.435). Two membranes of 0.45$\mu$ and 35$\mu$ mean pore size were used. For the fine membrane (and for the coarse membrane at low driving potentials), the transport across the partition becomes diffusion dominated, while the transport above and below the partition becomes similar to unsteady non penetrative turbulent free convection above flat horizontal surfaces (Figure~\ref{fig:schem}(A)). In this type of convection, the flux scaled as $q\sim \Delta C_w ^{4/3}$,where $\Delta C_w$ is the near wall concentration difference, similar to that in Rayleigh - B\'nard convection . Hence, we are able to study turbulent free convection over horizontal surfaces in the Rayleigh Number range of $\sim 10^- 10 ^$ at Schmidt number of 602, focusing on the nature and role of near wall coherent structures. To our knowledge, this is the first study showing clear images of near wall structures in high Rayleigh Number - high Schmidt number turbulent free convection. We observe a weak flow across the membrane in the case of the coarser membrane at higher driving potentials (Figure \ref(B)). The effect of this through flow on the flux and the near wall structures is also investigated. In both the types of convection the near wall structure shows patterns formed by sheet plumes, the common properties of these patterns are also investigated. The major outcomes in the above three areas of the thesis can be summarised as follows \subsection* \label \subsubsection* \label The non-dimensional flux was similar to that reported by Goldstein\cite at Sc of 2750. Visualisations show that the near wall coherent structures are line plumes. Depending on the Rayleigh number and the Aspect ratio, different types of large scale flow cells which are driven by plume columns are observed. Multiple large scale flow cells are observed for AR = 0.65 and a single large scale flow for AR= 0.435. The large scale flow create a near wall mean shear, which is seen to vary across the cross section. The orientation of the large scale flow is seen to change at a time scale much larger than the time scale of one large scale circulation The near wall structures show interaction of the large scale flow with the line plumes. The plumes are initiated as points and then gets elongated along the mean shear direction in areas of larger mean shear. In areas of low mean shear, the plumes are initiated as points but gets elongated in directions decided by the flow induced by the adjacent plumes. The effect of near wall mean shear is to align the plumes and reduce their lateral movement and merging. The time scale for the merger of the near wall line plumes is an order smaller than the time scale of the one large scale circulation. With increase in Rayleigh number, plumes become more closely and regularly spaced. We propose that the near wall boundary layers in high Rayleigh number turbulent free convection are laminar natural convection boundary layers. The above proposition is verified by a near wall model, similar to the one proposed by \cite{tjfm}, based on the similarity solutions of laminar natural convection boundary layer equations as Pr$\rightarrow\infty$. The model prediction of the non dimensional mean plume spacing $Ra_\lambda^~=~\lambda /Z_w~=~91.7$ - where $Ra_\lambda$ is the Rayleigh number based on the plume spacing $\lambda$, and $Z_w$ is a near wall length scale for turbulent free convection - matches the experimental measurements. Therefore, higher driving potentials, resulting in higher flux, give rise to lower mean plume spacing so that $\lambda \Delta C_w^$ or $\lambda q^$ is a constant for a given fluid. We also show that the laminar boundary layer assumption is consistent with the flux scaling obtained from integral relations. Integral equations for the Nusselt number(Nu) from the scalar variance equations for unsteady non penetrative convection are derived. Estimating the boundary layer dissipation using laminar natural convection boundary layers and using the mean plume spacing relation, we obtain $Nu\sim Ra^$ when the boundary layer scalar dissipation is only considered. The contribution of bulk dissipation is found to be a small perturbation on the dominant 1/3 scaling, the effect of which is to reduce the effective scaling exponent. In the appendix to the thesis, continuing the above line of reasoning, we conduct an exploratory re-analysis (for $Pr\sim 1$) of the Grossman and Lohse's\cite scaling theory for turbulent Rayleigh - B\'enard convection. We replace the Blasius boundary layer assumption of the theory with a pair of externally forced laminar natural convection boundary layers per plume. Integral equations of the externally forced laminar natural convection boundary layer show that the mixed convection boundary layer thickness is decided by a $5^{th}$ order algebraic equation, which asymptotes to the laminar natural convection boundary layer for zero mean wind and to Blasius boundary layer at large mean winds. \subsubsection*{Effect of wall normal flow on flux and near wall structures} \label{sec:effect-wall-normal} For experiments with the coarser($35\mu$) membrane, we observe three regimes viz. the strong through flow regime (Figure~\ref{fig:schem}(b)), the diffusion regime (Figure \ref{fig:schem}(a)), and a transition regime between the above two regimes that we term as the weak through flow regime. At higher driving potentials, only half the area above the coarser membrane is covered by plumes, with the other half having plumes below the membrane. A wall normal through flow driven by impingement of the large scale flow is inferred to be the cause of this (Figure \ref{fig:schem}(b)). In this strong through flow regime, only a single large scale flow circulation cell oriented along the diagonal or parallel to the walls is detected. The plume structure is more dendritic than the no through flow case. The flux scales as $\Delta C_w^n$, with $7/3\leq n\leq 3$ and is about four times that observed with the fine membrane. The phenomenology of a flow across the membrane driven by the impingement of the large scale flow of strength $W_*$, the Deardorff velocity scale, explains the cubic scaling. We find the surprising result that the non-dimensional flux is smaller than that in the no through flow case for similar parameters. The mean plume spacings in the strong through flow regime are larger and show a different Rayleigh number dependence vis-a-vis the no through flow case. Using integral analysis, an expression for the boundary layer thickness is derived for high Schmidt number laminar natural convection boundary layer with a normal velocity at the wall. (Also, solutions to the integral equations are obtained for the $Sc\sim 1$ case, which are given as an Appendix.) Assuming the gravitational stability condition to hold true, we show that the plume spacing in the high Schmidt number strong through flow regime is proportional to $\sqrt{Z_w\,Z{_{v_i}}}$, where $Z{_{v_i}}$ is a length scale from the through flow velocity. This inference is fairly supported by the plume spacing measurements At lower driving potentials corresponding to the transition regime, the whole membrane surface is seen to be covered by plumes and the flux scaled as $\Delta C_w^{4/3}$. The non-dimensional flux is about the same as in turbulent free convection over flat surfaces if $\frac{1}{2}\Delta C $ is assumed to occur on one side of the membrane. This is expected to occur in the area averaged sense with different parts of the membrane having predominance of diffusion or through flow dominant transport. At very low driving potentials corresponding to the diffusion regime, the diffusion corrected non dimensional flux match the turbulent free convection values, implying a similar phenomena as in the fine membrane. \subsubsection*{Universal probability distribution of near wall structures} \label{sec:univ-prob-distr} We discover that the probability distribution function of the plume spacings show a standard log normal distribution, invariant of the presence or the absence of wall normal through flow and at all the Rayleigh numbers and aspect ratios investigated. These plume structures showed the same underlying multifractal spectrum of singularities in all these cases. As the multifractal curve indirectly represents the processes by which these structures are formed, we conclude that the plume structures are created by a common generating mechanism involving nucleation at points, growth along lines and then merging, influenced by the external mean shear. Inferring from the thermodynamic analogy of multifractal analysis, we hypothesise that the near wall plume structure in turbulent free convection might be formed so that the entropy of the structure is maximised within the given constraints.

The steady-state natural convection heat transfer from vertical rectangular fins extending perpendicularly from vertical rectangular base was investigated experimentally. The effects of geometric parameters and base-to-ambient temperature difference on the heat transfer performance of fin arrays were observed and the optimum fin separation values were determined. Two similar experimental set-ups were employed during experiments in order to take measurements from 30 different fin configurations having fin lengths of 250 mm and 340 mm. Fin thickness was maintained fixed at 3 mm. Fin height and fin spacing were varied from 5 mm to 25 mm and 5.75 mm to 85.5 mm, respectively. 5 heat inputs ranging from 25 W to 125 W were supplied for all fin configurations, and hence, the base and the ambient temperatures were measured in order to evaluate the heat transfer rate from fin arrays. The results of experiments have shown that the convection heat transfer rate from fin arrays depends on all geometric parameters and base-to-ambient temperature difference. The effect of these parameters on optimum fin spacing was also examined, and it was realized that for a given base-to-ambient temperature difference, an optimum fin spacing value which maximizes the convective heat transfer rate from the fin array is available for every fin height. The results indicated that the optimum fin spacings are between 8.8 mm and 14.7 mm, for the fin arrays employed in this work. Using the experimental results of present study and experimental results in available literature [2,3,9,10,11,12,14], a correlation for optimum fin spacing at a given fin length and base-to-ambient temperature difference was obtained as a result of scale analysis.

Experimental observations indicate the presence of attached, gravity induced, horizontal buoyant currents above large area fires. Their driving mechanism is indirect and resembles the one observed above heated horizontal plates. Classic plume modelling is satisfactory for providing information for the flow far from the source. In dealing with large areas and directing attention to the flow close to the source, the classic plume theory should fail because the radial pressure gradient that is responsible for the driving of the flow is squeezed in the long and thin classic plume assumption. For this we propose a new plume structure for the description of the buoyant flow above a circular region of large radius L as “The flow field must be divided into three regions. A region where the flow is predominantly horizontal and attached to the surface, a transition region from horizontal to vertical where separation of the attached current takes place, and a region where vertical flow is established and classic plume theory can be applied”. A model for the description of the gross properties of the horizontal currents is developed under the term “horizontal plume”. The modified Richardson number for the horizontal plume a, being analogous to the radius of the large area, is studied asymptotically in the limit a → ∞ and second order uniformly valid semi-analytical solutions are obtained. The hot plate experiment was set up in order to test the model and facilitate its improvement. A chapter is dedicated to the data analysis coming from thermocouple readings and visualisation of the flow using particle image velocimetry.In the remainder of this thesis two classic problems of laminar natural convection are revisited. That of the first order laminar boundary layer above an isothermal circular plate of radius a and the first order laminar boundary layer above the semi- infinite plate inclined to horizontal. In both cases allowances to variable property effects were made through the introduction of a nondimensional parameter λT, with its value set to zero implying the assumption of the Boussinesq approximation. For the circular plate, fourth order series solutions were obtained valid at the edge of the plate where the effects of λT and Prandtl number Pr are studied. Furthermore a finite difference scheme for the numerical solution of the nonsimilar partial integro- differential equation was developed using the Keller Box method and compared with results obtained from the commercial finite element software COMSOL Multiphysics 3.5a. For the semi-infinite plate, fourth order series approximations valid at the edge of the plate were obtained, while an extensive analysis for the effect of λT, Pr and inclination parameter σ was performed on the flow. Positions of the separation points when the inclination is negative (σ < 0) as a function of Pr and λT were recovered.

Orientador: Vicente Luiz Scalon
Banca: Helio Aparecido Navarro
Banca: Sergio Rodrigues Fontes
Resumo: A fluidodinâmica computacinal (CFD) tem sido utilizada, estudadda e implementada ao longa das duas últimas décadas na solução dos mais diversos problemas de engenharia. O princípio básico desta ciência é a aplicação de métodos numéricos em problemas que envolvam mecânica dos fluidos. Nesse contexto, este trabalho utiliza essa técnica para analisar o comportamento de um fluido incompreensível, que se encontra numa cavidade cilíndrica fechada onde as faces inferior e superior são adiabáticas e as superfícies laterais se encontram em diferentes temperaturas. Os perfis de velocidade e temperatura resultantes - ocasionados pela convecção natural - serão avaliados em todo o domínio do problema. Existe uma série de técnicas para a solução de problemas envolvendo escoamentos, sendo as mais comuns as que se utilizam do "Esquema de Passo Fracionado" proposto por Chorin no final da década de 60. Dentre as diversas soluções que se utilizam desta técnica, este trabalho optou pelo uso do método das características e do algoritmo CBS de solução proposto por Zienkiewicz e Codina (1995). Para a implementação do algoritmo de solução do problema proposto foi realizada uma discretização geral através do método dos elementos finitos usando-se de uma malha formada por elementos bilineares. A solução foi obtida a partir de um ambiente matemático adequado, a GNU-Octave (2008). Os resultados foram analisados para diferentes razões de curvatura, números de Rayleigh e métodos de solução, sendo plotados para as suas diversas variáveis buscando descrever o comportamento do fenônemo
Abstract: The Computational Fluid Dynamics (CFD) has been used, studied and performed through the last two decades to solve the series of problems in Engineering. The most basic aim of this science is the appliance of numerical methods in cases that envolve fluid mechanics. In this context, this work uses this technic to analyze the behaviour of an incompressible fluid, which is found in a closed cylindrical cavity, a place where the inferior and superior surfaces are adiabatic and the lateral surfaces are shown in different temperatures. The resultant profiles of speed and temperature - induced by the free convection - are going to be appraised in all the dominion of the problem. There is a set of technics to solve the problems which involve the drainage, but the most usual are those which use the techic "Fractional Step Method" offered by Chorin in the final of 60s. Among the several solutions that are solved through this technic, this research used the characteristics method and of the CBS algorthm, offered by Zienkiewicz e Codina (1995). For the implementation of the algorithm, it was realized a general discretization through the finite elements method, making use of a loop formed by bilinear elements. The resolution was obtained from an adequated mathematical ambient, the GNU-Octave (2008). The results were analysed for different curvature ratios, Rayleigh numbers and methods of solution, being plotted for its different variables searching to describe the behavior of the phenomenon
Mestre

Orientador: Vicente Luiz Scalon
Banca: Ivan De Domenico Valarelli
Banca: Carlos Alberto Carrasco Altemani
Resumo: Com a crise energética recente, houve uma nova conscientização da necessidade de utilização mais racional da energia. Desta feita, uma série de pesquisas com fontes alternativas de energia, que vinham sendo preteridos em função da impressão que a crise energética do início da década de 1970 havia passado, tem ganho nova força. Dentre todas as alternativas para aproveitamento de energia solar, uma das mais utilizadas são os chamados "sistemas domésticos de aquecimento de água". Este tipo de sistema, entretanto, ainda é complexo, constituído de uma série de dutos e conexões entre coletor e tanque armazenador, que contribuem para o elevado custo destes dispositivos. Uma alternativa para otimizar o custo final é o uso dos sistemas solar integrados coletor-tanque (ICS). Neste trabalho, foi avaliado o processo de movimentação natural do fluido em uma das geometrias mais comuns de sistemas deste tipo: a trapezoidal. Foi aplicada a condição de fluxo de calor constante na face inclinada para avaliação... (Resumo completo, clicar acesso eletrônico abaixo)
Abstract: The recent energy crisis has developed a new conscience for necessity of rational energy use. Several works treating about renewable energy was stopped in past based in a false idea that the 1970's energy crisis was finished. Nowadays, these works have been retaken with the large use of solar energy in the Solar Domestic Hot Water Systems. However, this device is quite complex and has several components like pipes and fittings coupling solar collectors and storage tanks. This characteristic makes it an expensive system and bring difficulties for his large use. An alternative to turn it cheaper is the construction of a device with solar collector and storage tank integrated in one single component (ICS). In this work was done an evaluation of free convection process in a common geometry of this device: the trapezoidal shape. For this analysis, a constant heat flux condition was applied to the inclined face for evaluation of free convection process. Numerical results... (Complete abstract click electronic access below)
Mestre

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
A fluidodinâmica computacinal (CFD) tem sido utilizada, estudadda e implementada ao longa das duas últimas décadas na solução dos mais diversos problemas de engenharia. O princípio básico desta ciência é a aplicação de métodos numéricos em problemas que envolvam mecânica dos fluidos. Nesse contexto, este trabalho utiliza essa técnica para analisar o comportamento de um fluido incompreensível, que se encontra numa cavidade cilíndrica fechada onde as faces inferior e superior são adiabáticas e as superfícies laterais se encontram em diferentes temperaturas. Os perfis de velocidade e temperatura resultantes - ocasionados pela convecção natural - serão avaliados em todo o domínio do problema. Existe uma série de técnicas para a solução de problemas envolvendo escoamentos, sendo as mais comuns as que se utilizam do Esquema de Passo Fracionado proposto por Chorin no final da década de 60. Dentre as diversas soluções que se utilizam desta técnica, este trabalho optou pelo uso do método das características e do algoritmo CBS de solução proposto por Zienkiewicz e Codina (1995). Para a implementação do algoritmo de solução do problema proposto foi realizada uma discretização geral através do método dos elementos finitos usando-se de uma malha formada por elementos bilineares. A solução foi obtida a partir de um ambiente matemático adequado, a GNU-Octave (2008). Os resultados foram analisados para diferentes razões de curvatura, números de Rayleigh e métodos de solução, sendo plotados para as suas diversas variáveis buscando descrever o comportamento do fenônemo
The Computational Fluid Dynamics (CFD) has been used, studied and performed through the last two decades to solve the series of problems in Engineering. The most basic aim of this science is the appliance of numerical methods in cases that envolve fluid mechanics. In this context, this work uses this technic to analyze the behaviour of an incompressible fluid, which is found in a closed cylindrical cavity, a place where the inferior and superior surfaces are adiabatic and the lateral surfaces are shown in different temperatures. The resultant profiles of speed and temperature - induced by the free convection - are going to be appraised in all the dominion of the problem. There is a set of technics to solve the problems which involve the drainage, but the most usual are those which use the techic Fractional Step Method offered by Chorin in the final of 60s. Among the several solutions that are solved through this technic, this research used the characteristics method and of the CBS algorthm, offered by Zienkiewicz e Codina (1995). For the implementation of the algorithm, it was realized a general discretization through the finite elements method, making use of a loop formed by bilinear elements. The resolution was obtained from an adequated mathematical ambient, the GNU-Octave (2008). The results were analysed for different curvature ratios, Rayleigh numbers and methods of solution, being plotted for its different variables searching to describe the behavior of the phenomenon

Circuitos de convecção natural ou sistemas de circulação natural são empregados em diversas áreas da engenharia. Reatores nucleares refrigerados a água utilizam circuitos de circulação natural como método passivo de seguranca. Em situações críticas, sem qualquer controle externo, o sistema permanece em segurança por suas próprias características de funcionamento (intrinsecamente seguro). O trabalho proposto consiste em estudar numericamente o circuito de circulação natural de água, localizado no Instituto de Pesquisas Energéticas e Nucleares / Comissão Nacional de Energia Nuclear em São Paulo, por meio do uso de modelos matemáticos, objetivando determinar o padrão do escoamento em condições sem mudança de fase líquido-vapor. A comparação dos resultados de temperatura obtidos por cada um dos modelos de turbulência aos pontos instrumentados no circuito experimental, na condição transitória, revelou desvios significativos nas respostas do modelo de zero equação. Desvios intermediário foram observados nos modelos de transporte da viscosidade turbulenta (EVTE), k - ω, SST e SSG e resultados melhores foram vericados nos modelos k - ε e DES (com significativa superioridade do primeiro modelo).
Natural circulation loops apply to many engineering applications such as: water heating solar energy system (thermo-siphons), thermal management of electrical components (voltage converter), geothermal energy, nuclear reactors, etc. In pressurized water nuclear reactors, known as PWR\'s, the natural circulation loops are employed to ensure passive safety. In critical situations, the heat transfer will occur only by natural convection, without any external control or mechanical devices. This feature is desired and has been considered in modern nuclear reactor projects. This work consists of a numerical study of the natural circulation loop, located at the Instituto de Pesquisas Energeticas e Nucleares / Comissão Nacional de Energia Nuclear in São Paulo, Brazil, in order to establish the ow pattern in single phase conditions. The comparison of numerical results to experiments in transient condition revealed significant deviations for the Zero Equation turbulence model. Intermediate deviations for the Eddy Viscosity Turbulence Equation (EVTE), k - ω, SST e SSG models. And the best results are obtained by the k - ε e DES models (with better results for the k - ε model).

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Com a crise energética recente, houve uma nova conscientização da necessidade de utilização mais racional da energia. Desta feita, uma série de pesquisas com fontes alternativas de energia, que vinham sendo preteridos em função da impressão que a crise energética do início da década de 1970 havia passado, tem ganho nova força. Dentre todas as alternativas para aproveitamento de energia solar, uma das mais utilizadas são os chamados sistemas domésticos de aquecimento de água. Este tipo de sistema, entretanto, ainda é complexo, constituído de uma série de dutos e conexões entre coletor e tanque armazenador, que contribuem para o elevado custo destes dispositivos. Uma alternativa para otimizar o custo final é o uso dos sistemas solar integrados coletor-tanque (ICS). Neste trabalho, foi avaliado o processo de movimentação natural do fluido em uma das geometrias mais comuns de sistemas deste tipo: a trapezoidal. Foi aplicada a condição de fluxo de calor constante na face inclinada para avaliação...
The recent energy crisis has developed a new conscience for necessity of rational energy use. Several works treating about renewable energy was stopped in past based in a false idea that the 1970's energy crisis was finished. Nowadays, these works have been retaken with the large use of solar energy in the Solar Domestic Hot Water Systems. However, this device is quite complex and has several components like pipes and fittings coupling solar collectors and storage tanks. This characteristic makes it an expensive system and bring difficulties for his large use. An alternative to turn it cheaper is the construction of a device with solar collector and storage tank integrated in one single component (ICS). In this work was done an evaluation of free convection process in a common geometry of this device: the trapezoidal shape. For this analysis, a constant heat flux condition was applied to the inclined face for evaluation of free convection process. Numerical results... (Complete abstract click electronic access below)

Orientador: Luiz Fernando Milanez
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica
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Resumo: A transferência de calor em cilindros horizontais isolados é de grande importância na indústria tanto no caso em que se pretende minimizar a dissipação térmica (quando dutos isolados são usados no transporte de fluidos), como quando se pretende maximizá-la (no caso de cabos de eletricidade revestidos, por exemplo). Em ambas as situações, convecção natural e radiação térmica estão presentes, podendo ser consideradas como os principais mecanismos envolvidos de dissipação térmica. Normalmente o isolamento térmico é circular e concêntrico ao cilindro. No entanto, o coeficiente convectivo e a temperatura da superfície não são constantes ao redor do cilindro, levando a crer que a adoção de isolantes concêntricos pode não ser o melhor método de se distribuir o isolante. Assim, se um isolamento excêntrico for adotado, a temperatura superficial deve apresentar variação ainda maior, alterando o escoamento ao redor do cilindro e, portanto, as perdas térmicas. No presente trabalho é apresentada uma análise numérica da dissipação térmica em cilindros horizontais isotérmicos isolados excentricamente expostos a convecção natural (Pr= 0,715) e a radiação. A condução na camada de isolante foi resolvida analiticamente (através do uso do sistema de coordenadas bicilíndricas) e integrada numericamente. A partir da temperatura obtida para a superfície externa do isolante, o software PHOENICS foi utilizado para resolver o problema de convecção natural, fornecendo um novo perfil para o coeficiente convectivo. Para cada caso, algumas iterações foram necessárias para se alcançar a convergência. Os parâmetros analisados são a emissividade da superfície externa, a razão entre os raios externo e interno do isolante, a razão entre as condutividades térmicas do isolante e do ar, o número de Rayleigh (definido de forma a ser independente dos outros parâmetros) e a excentricidade do isolante. A dissipação e a temperatura superficial local são mostradas graficamente, assim como os campos de temperatura e velocidade do escoamento. Uma equação é sugerida para a determinação da influência da excentricidade sobre o calor total dissipado em função da razão entre as resistências térmicas de convecção natural-radiação e a resistência térmica de condução, para determinada razão de raios e excentricidade
Abstract: Heat transfer in horizontal insulated cylinders is of importance in industry as when one wants to reduce the heat dissipation (when insulated ducts are used to transport fluids), as when one wants to enhance it (in the case of covered electric cables, for example). In both cases, free convection and thermal radiation are present and can be considered as the main mechanisms of heat dissipation. Generally, the insulating layer is round and is arranged concentrically in the cylinder. However, the heat transfer coefficient and the surface temperature are not constant around the cylinder, raising the point that the use of concentric insulation may not be the best way to arrange the insulating layer. Thus, if an eccentric layer is used, the surface temperature should have a larger variation, changing the flow around the cylinder and, therefore, the heat dissipation. A numerical analysis of the heat dissipation in horizontal isothermal eccentrically insulated cylinders exposed to free convection (Pr= 0,715) and radiation is presented. The conduction through the insulating layer was solved analytically (using the bicylindrical coordinate system) and integrated numerically. From the solution for the surface temperature, the PHOENICS software was used to solve the problem of free convection, giving a new profile for the heat transfer coefficient. For each case, some iterations were necessary to reach convergence. The parameters analyzed were the emissivity of the external surface, the ratio between the outer and the inner radius of the insulating layer, the ratio between the insulation and the air thermal conductivities, the Rayleigh number (defined in such a way to be independent of the other parameters) and the eccentricity of the insulation. The heat dissipation and the surface temperature are shown graphically, as well as the temperature and velocity flow fields. An equation is suggested to define the importance of the eccentricity over the total heat as a function of the ratio between the free convection-radiation thermal resistance and the conduction thermal resistance, for a given ratio of radius and eccentricity
Mestrado
Termica e Fluidos
Mestre em Engenharia Mecânica

Simulation numérique de l'écoulement laminaire bidimensionnel créé par un fil chaud placé sous une surface libre. Le code de calcul inclut les convections naturelle et de Marangoni, les transferts de chaleur à l’interface ainsi que la viscosité interfaciale. Analyse linéaire de stabilité dans le cas d'une couche liquide horizontale d'extension infinie, limitée par une paroi rigide et une surface libre. Modélisation

Дисертаційна робота присвячена дослідженню теплогідравлічних процесів навколо циліндричних поверхонь теплообміну в залежності від зміни режимних параметрів процесу та конструктивних характеристик оточення. В роботі представлено результати візуалізації динамічного поля та поля температури теплоносія, що дозволило значно поглибити знання про механізми тепло- та масопереносу та більш обґрунтовано описати результати дослідження. Отримані результати дослідження дозволили, в діапазоні зміни режимних та конструктивних характеристик, описати вплив цих факторів на коефіцієнти тепловіддачі та характеристики омивання циліндрів, і вивести залежності для розрахунку коефіцієнтів тепловіддачі з врахуванням виявленого впливу.
In the investigation are developed heat and mass transfer theory around horizontal cylinders which depends on heat flux and several constructive characteristics: presents or absence of vertical walls, other horizontal cylinders placed close to each other. Results of dynamic and temperature field visualization are also presented. These results made our knowledge significantly deeper in a part of heat and mass transfer mechanism during natural convection around cylinder systems. Cylinder, placed inside a vertical channel, has variable heat transfer coefficient, which depend on channel geometrical characteristic. If a cylinder will be placed inside the channel with optimal characteristic, its heat transfer coefficient will be increased around 20%. These optimal width is 2,2-2,3 cylinder diameter. Heat transfer coefficient of cylinder bundl is deeply depends on its constructive characteristic. Based on obtained results, formulas and calculation algoritm of heat transfer coefficient was developed, take into consideration several variables.
Диссертационная работа посвящена исследованию теплогидравлических процессов вокруг цилиндрических поверхностей теплообмена в зависимости от изменения режимных параметров процесса и конструктивных характеристик окружения: наличия адиабатных стенок канала, соседних цилиндров в горизонтальном и/или вертикальном направлениях. В работе представлены результаты визуализации динамического поля и поля температуры теплоносителя, которые позволили значительно углубить знания о механизмах тепло- и массопереноса, более точно и обосновано описать изучаемые процессы и результаты исследования. Кроме этого, проведення работа по визуализации исследуемых процессов разрешила проявить коренные изменения в динамическом поле вокруг горизонтального цилиндра (в частности, при его размещении в вертикальном канале), развитию теплового следа над цилиндром в большом объеме, в и над системой цилиндров. Полученные результаты исследования позволили, в изученном диапазоне изменения режимных и конструктивных характеристик, описать влияние этих факторов на коэффициенты теплоотдачи и характеристики движения теплоносителя вокруг системы цилиндров, вывести зависимости для расчета коэффициентов теплоотдачи с учетом такого влияния. В частности показано, что при размещении горизонтального цилиндра в вертикальном щелевидном канале возможно значительное изменение условий течения теплоносителя, что, в свою очередь, может приводить как к повышению, так и понижению интенсивности теплоотдачи на поверхности такого цилиндра. Впервые предложена диаграмма теплогидравлических режимов, которая позволяет уже на этапе конструирования теплообменной поверхности и её окружения ответить на вопрос об оптимальности выбранной конструкции. Кроме инженерных методик расчета интенсивности теплоотдачи от цилиндров в различных условиях, в работе представленные рекомендации по проектированию цилиндрических теплообменных поверхностей, которые рассчитаны на работу в условиях свободной конвекции и учитывают вскрытые изменения динамического и температурного полей при изменении конструктивного окружения цилиндров. В частности, среди таких рекомендацый не обходимо выделить следующие: интенсивность теплоотдачи значительно снижается при формировании пучка цилиндров с малими вертикальным и горизонтальным шагом установки элементов системы; при этом, большее значение имеет вертикальный шаг установки цилиндров; интенсивность теплоотдачи от цилиндров пучка равная такой для одиночного горизонтального цилиндра в большом объеме достигается при относительном вертикальном шаге их установки равном 5,0; впервые предложена и обоснована методика разделения системы цилиндров на отдельные группы при расчете локального и среднего коэффициента теплоотдачи, что позволяет учитывать особенности теплогидравлических процессов внутри системы; показано, что интенсивность теплоотдачи от глубинных цилиндров в системе до 11 элементов, устанавливается равной, примерно, среднему значению между интенсивностями теплоотдачи второго и третього цилиндров; интенсивность теплоотдачи вдоль течения теплоносителя сильно зависит от геометрических характеристик системы и может как уменшаться (при малых вертикальних шагах установи цилиндров), так и увеличиваться (при наибольших из исследованных).

In dieser Arbeit werden neuartige Flachrohre für die Verwendung als Rückwandverflüssiger in der Haushaltskältetechnik mit numerischen und dynamischen Simulationen sowie Experimenten untersucht. Dabei kommen unterschiedliche überströmte Längen sowie der Einfluss horizontaler Abstände auf den Wärmeübergang durch freie Konvektion zur Betrachtung. Realisiert wird die numerische Strömungssimulation mit der Software Fluent 3.6.26, wobei das RNG-k-epsilon- als Turbulenzmodell und diskrete Ordinaten zur zusätzlichen Modellierung des Strahlungswärmeübergangs verwendet werden. Zur Verifizierung werden experimentelle Untersuchungen mit natürlicher Konvektion durchgeführt. Ebenso kommt ein kompakter Verflüssiger bei erzwungener Konvektion zur experimentellen Analyse. Mit einem neuen Verflüssigermodell wird außerdem ein Haushaltskühlschrank in Modelica 2.2.1 dynamisch simuliert. Diese Arbeit zeigt, dass die Verwendung eines Flachrohrverflüssigers großes Potenzial einer konkurrenzfähigen Alternative zu konventionellen Verflüssigern besitzt
In this work novel flat tubes used as rear panel condensers in the household refrigeration technology are examined with numerical and dynamic simulations as well as experiments. Therefore different overflowed lengths and the influence of horizontal spacing on the heat transfer by free convection are taken into consideration. The CFD calculations are realized with the software Fluent 3.6.26, where the RNG-k-epsilon turbulence model and discrete ordinates for an additional modelling of radiation heat transfer are applied. For the verification, experimental studies with natural convection are carried out. Likewise, a compact condenser is experimentally analysed in forced convection. With a new model for the liquefier a domestic refrigerator is also dynamically simulated in Modelica 2.2.1. This work shows that the use of a flat tube condenser has a great potential of a competitive alternative to conventional liquefiers

This study solves the problem of unsteady free convection from an inclined heated tube both numerically and analytically. The tube is taken to have an elliptic cross-section having a constant heat flux applied to its surface. The surrounding fluid is viscous and incompressible and infinite in extent. The Boussinesq approximation is used to describe the buoyancy force driving the flow. The underlying assumptions made in this work are that the flow remains laminar and two-dimensional for all time. This enables the Navier-Stokes and energy equations to be formulated in terms of the streamfunction, and vorticity. We assume that initially an impulsive heat flux is applied to the surface and that both the tube and surrounding fluid have the same initial temperature. The problem is solved subject to the no-slip and constant heat flux conditions on the surface together with quiescent far-field and initial conditions. An approximate analytical-numerical solution was derived for small times, t and large Grashof numbers, Gr. This was done by expanding the flow variables in a double series in terms of two small parameters and reduces to solving a set of differential equations. The first few terms were solved exactly while the higher-order terms were determined numerically. Flow characteristics presented include average surface temperature plots as well as surface vorticity and surface temperature distributions. The results demonstrate that the approximate analytical-numerical solution is in good agreement with the fully numerical solution for small t and large Gr.

The problem of laminar and turbulent conjugate mixed convection flow and heat transfer in shallow enclosures with a series of block-like heat generating components is studied numerically for a Reynolds number range of zero (pure natural convection) to typically 106, Grashof number range of zero (pure forced convection) to 1015 and various block-to-fluid thermal conductivity ratios, with air as the working medium. The shallow enclosure has modules consisting of heat generating elements, air admission and exhaust slots. Two problems are considered. In the first problem, the enclosure has free boundaries between the modules and in the second problem, there are partitioning walls between the different modules. The flow and temperature distributions are taken to be two-dimensional. Regions with the same velocity and temperature distributions can be identified assuming repeated placement of the blocks and fluid entry and exit openings at regular distances, neglecting end wall effects. One half of such rectangular region is chosen as the computational domain taking into account the symmetry about the vertical centreline. On the basis of the assumption that mixed convection flow is a superposition of forced convection flow with finite pressure drop and a natural convection flow with negligible pressure drop, the individual flow components are delineated. The Reynolds number is based on forced convection velocity, which can be determined in practice from the fan characteristics. This is believed to be more meaningful unlike the frequently used total velocity based Reynolds number, which does not vanish even in pure natural convection and which makes the fan selection difficult. Present analysis uses three models of turbulence, namely, standard k-ε (referred to as Model-1), low Reynolds number k-ε (referred to as Model-2) and an SGS kinetic energy based one equation model (referred to as Model-3). Results are obtained for aiding and opposing mixed convection, considering also the pure natural and pure forced convection limiting cases. The results show that higher Reynolds numbers tend to create a recirculation region of increasing strength at the core region and that the ranges of Reynolds number beyond which the effect of buoyancy becomes insignificant are identified. For instance, in laminar aiding mixed convection, the buoyancy effects become insignificant beyond a Reynolds number of 500. Results are presented for a number of quantities of interest such as the flow and temperature distributions, local and average Nusselt numbers and the maximum dimensionless temperature in the block. Correlations are constructed from the computed results for the maximum dimensionless temperature, pressure drop across the enclosure and the Nusselt numbers.