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Mass flow measurement of solids in a gravity drop conveyor using capacitance transducersXie, Cheng-Gang January 1988 (has links)
No description available.
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Simulação sub-malha com modelo de dois fluidos do escoamento gás-sólido em risers de leitos fluidizados circulantes / Sub-grid simulation with two-fluid model to gas-solid flow in circulating fluidized bed risersRotava, Elói 24 November 2008 (has links)
Modelagem de dois fluidos é largamente aplicada para simular escoamentos gássólido em risers de leitos fluidizados circulantes. As atuais simulações são de grandes clusters (SGC), executadas em domínios reais com malhas numéricas grosseiras, ou simulações sub-malha, executadas em malhas numéricas refinadas em domínios reduzidos. O propósito das simulações sub-malha é principalmente produzir dados de meso-escala a serem aplicados em simulações de grandes clusters. A atual literatura apresenta apenas umas poucas simulações sub -malha de escoamentos gás-sólido em risers aplicando modelagem de dois fluidos, todas para condições típicas de reatores de leito fluidizado circulante de craqueamento catalítico. Neste trabalho realizou-se uma simulação sub-malha para esta condição, e também para uma outra condição típica de reatores de leito circulante para combustão/gaseificação. Correlações teóricas derivadas da teoria cinética dos escoamentos granulares (TCEG) foram aplicadas para determinar a pressão e as viscosidades da fase sólida. Considerou-se um domínio de pequenas dimensões sob condições de contorno periódicas, aplicando-se malhas numéricas refinadas. Os resultados das simulações foram comparados entre si, com outros resultados de simulação de literatura, e com dados experimentais. Então, a correção das simulações foi abordada em vista dos dados empíricos disponíveis. / Two-fluid modeling is widely applied to simulate gas-solid flows in risers of circulating fluidized beds. Current simulations are either large cluster simulations (LCS), performed in real domains under coarse numerical meshes, or sub-grid simulations, performed in reduced domains under refined numerical meshes. The purpose of subgrid simulation is mostly to provide meso-scale data to be applied in large cluster simulations. The up to date literature presents only a few sub -grid simulations of gassolid flows in risers applying two-fluid modeling, all of them for conditions typical of catalytic cracking circulating fluidized bed reactors. In the present work a sub-grid simulation was performed for this condition, as well as for a condition typical of circulating fluidized bed coal combustion/gasification reactors. Theoretical correlations derived from the kinetic theory of granular flows (KTGF) were applied to determine pressure and viscosities of the solid phase. A small size domain was considered under periodic boundary conditions, and a refined numerical mesh was applied. The results of the simulations were compared to each other, to other literature results of simulation, and to experimental data. Then, the accuracy of the simulations was addressed in view of the available empirical data.
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NUMERICAL ANALYSIS OF TURBULENT GAS-SOLID FLOWS IN A VERTICAL PIPE USING THE EULERIAN TWO-FLUID MODEL2013 January 1900 (has links)
Turbulent gas-solid flows are readily encountered in many industrial and environmental processes. The development of a generic modeling technique for gas-solid turbulent flows remains a significant challenge in the field of mechanical engineering. Eulerian models are typically used to model large systems of particles. In this dissertation, a numerical analysis was carried out to assess a current state-of-the-art Eulerian two-fluid model for fully-developed turbulent gas-solid upward flow in a vertical pipe. The two-fluid formulation of Bolio et al. (1995) was adopted for the current study and the drag force was considered as the dominant interfacial force between the solids and fluid phase. In the first part of the thesis, a two-equation low Reynolds number k-ε model was used to predict the fluctuating velocities of the gas-phase which uses an eddy viscosity model. The stresses developed in the solids-phase were modeled using kinetic theory and the concept of granular temperature was used for the prediction of the solids velocity fluctuation.
The fluctuating drag, i.e., turbulence modulation term in the transport equation of the turbulence kinetic energy and granular temperature was used to capture the effect of the presence of the dispersed solid particles on the gas-phase turbulence. The current study documents the performance of two popular turbulence modulation models of Crowe (2000) and Rao et al. (2011). Both models were capable of predicting the mean velocities of both the phases which were generally in good agreement with the experimental data. However, the phenomena that small particles cause turbulence suppression and large particles cause turbulence enhancement was better captured by the model of Rao et al. (2011); conversely, the model of Crowe (2000) produced turbulence enhancement in all cases. Rao et al. (2011) used a modified wake model originally proposed by Lun (2000) which is activated when the particle Reynolds number reaches 150. This enables the overall model to produce turbulence suppression and augmentation that follows the experimental trend.
The granular temperature predictions of both models show good agreement with the limited experimental data of Jones (2001). The model of Rao et al. (2011) was also able to capture the effect of gas-phase turbulence on the solids velocity fluctuation for three-way coupled systems. However, the prediction of the solids volume fraction which depends on the value of the granular temperature shows noticeable deviations with the experimental data of Sheen et al. (1993) in the near-wall region. Both turbulence modulation models predict a flat profile for the solids volume fraction whereas the measurements of Sheen et al. (1993) show a significant decrease near the wall and even a particle-free region for flows with large particles.
The two-fluid model typically uses a low Reynolds number k-ε model to capture the near-wall behavior of a turbulent gas-solid flow. An alternative near-wall turbulence model, i.e., the two-layer model of Durbin et al. (2001) was also implemented and its performance was assessed. The two-layer model is especially attractive because of its ability to include the effect of surface roughness. The current study compares the predictions of the two-layer model for both clear gas and gas-solid flows to the results of a conventional low Reynolds number model. The effects of surface roughness on the turbulence kinetic energy and granular temperature were also documented for gas-particle flows in both smooth and rough pipes.
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A novel solar-driven system for two-step conversion of CO2 with ceria-based catalystsWei, Bo January 2014 (has links)
Global warming is an unequivocal fact proved by the persistent rise of the average temperature of the earth. IPCC reported that scientists were more than 90 % certain that most of the global warming was caused by increasing concentrations of greenhouse gases (GHG) produced by human activities. One alternative to combat the GHG is to explore technologies for utilizing CO2 already generated by current energy systems and develop methods to convert CO2 into useful combustible gases. Two-step conversion of CO2 with catalysts is one of the most promising methods. Ceria (CeO2) is chosen as the main catalyst for this conversion in the thesis. It releases O2 when it is reduced in a heating process, and then absorbs O2 from CO2 to produce CO when it is re-oxidized in a cooling process. To make the conversion economic, solar power is employed to drive the conversion system. In this thesis, a flexible system with fluidized bed reactors (FBRs) is introduced. The thermogravimetric analysis (TGA) was carried out to examine the performance of ceria during its reduction and oxidation. Subsequently, the exergy analysis was used to evaluate the system’s capability on exporting work. The theoretical fuel to chemical efficiency varied from 4.85 % to 43.2 % for CO2 conversions. To investigate the operation mechanism of the system, a mathematical model was built up for the dynamic simulation of the system. Variables such as temperatures and efficiencies were calculated and recorded for different cases. The optimum working condition was found out to be at 1300 ⁰C for the commercial type of ceria. Finally, an experimental system was set up. The hydrodynamics and heat transfer in the fluidized bed reactor were studied. A CFD model was built up and validated with the experimental trials around 120 ⁰C. The model was then used as a reliable tool for the optimization of the reactor. The entire work in the thesis follows the procedure of developing an engineering system. It forms a solid basis for further improvements of the system to recycle CO2. / <p>QC 20141006</p>
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Estudo experimental da distribuição de pressão estatica no escoamento gas-solido em um leito recirculante / Experimental study of the static pressure distribution in the gas-solid flow in a recirculating bed.Betioli, Mario Luis Penteado 13 June 2007 (has links)
Orientadores: Marco Aurelio Cremasco, Alexandre de Paula Peres / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-08-08T18:40:27Z (GMT). No. of bitstreams: 1
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Previous issue date: 2007 / Resumo: Este trabalho tem por objetivo apresentar a distribuição axial de pressão estática ao longo de um leito fíuidízado circulante (CFB) para diversos valores de velocidade de gás e fluxo mássico de sólidos; para tanto, avaliou-se a influência da concentração de sólidos presente em um escoamento gás-sólido ao longo de todo o CFB, o que possibilitou estudar, em um mesmo sistema, a fluidodinâmica dos reatores downer e riser, de uma seção que os une - uma curva em "U" - assim corno de um sistema de recirculação de sólidos. Os CFBs são utilizados em diversas indústrias, particularmente naquelas que envolvem processos de craqueamento catalítico em leito fluidizado (FCC). O FCC é um processo de refino de petróleo utilizado para aumentar a produção de gasolina e GLP (gás liquefeito de petróleo) de uma refinaria, por meio da conversão de frações pesadas, provenientes da destilação do petróleo (gasóleo e resíduos), em trações mais leves. Os experimentos foram conduzidos em uma planta piloto instalada no Laboratório de Processos em Meios Porosos (LPMP) da DTF/FEQ/UMCAMP, denominada Unidade Multipropósito de Craqueamento Catalítico. Realizaram-se ensaios utilizando vazões de ar iguais a 7,5m3/h, 10m3/h, 15 m3/h, 20 m3/h, 25 m3/h, 30 m3/h alimentadas: i) na entrada do downer; ii) na entrada da curva em "U"; iii) numa combinação da entrada do downer e da entrada da curva era "U". Os fluxos mássicos de sólidos utilizados para cada vazão de ar foram iguais a 0,000kg/m2s, 0,032kg/m2s, 0,076kg/m2s, 0,120kg/m2s, 0,164kg/m2s e 0,208kg/m2s alimentados na entrada do downer. Decorrente deste estudo experimental, além do perfil axial de pressão, foi avaliado um modelo simplificado para a descrição da fluidodinâmica em questão, cujos resultados obtidos para diferença de pressão foram comparados com aqueles obtidos de forma experimental, estes por meio de deflexão / Abstract: The aim of this work is to present the axial distribution of static pressure throughout a circulating fluidized bed (CFB) for diverse values of gas velocity and solids circulation rate; for this, it was evaluated the influence of the present solids concentration in a gas-solid flow throughout the entirety CFB, which made it possible to study, in the same system, the fluid-dynamics of the downer and riser reactors, of a section joining them --- a "IT bend - as well as of a solid recirculation system. The CFBs have been used in several industries, particularly m those involving processes of fluid catalytic cracking (FCC). The FCC is a refining process of petroleum used to increase the gasoline production and LPG {liquefied petroleum gas) of a refinery, by the conversion of weighed fractions, proceeding from petroleum distillation (gasoil and residues), in lighter fractions. The experiments have been led in a pilot plant installed in the Laboratory of Processes in Porous Media (LPMP) of the DTF/FEQ/UNICAMP, called Multipurpose Unit of Catalytic Cracking. Assays have been performed using air flow rates equal to 7,5m³/h, 10m³/h, 15 m³/h, 20 m³/h, 25 m³/h, 30 m³/h fed: i) in the entrance of the downer; ii) in the entrance of the "U" bend; iii) in a combination of the entrance of the downer and the entrance of the "U" bend. The solids circulation rates used for each air flow rate were equal to 0,000kg/m²s, 0,032 kg/m²s, 0.076 kg/m²s, 0,120 kg/m²s, 0,I64 kg/m²s and 0.2O8 kg/m²s fed in the entrance of the downer. Due to this experimental study, besides the pressure axial profile, a simplified pattern for the fluid-dynamics description in question was evaluated, whose results obtained for pressure difference were compared with those obtained through experiments, the latter being by the means of pressure gauge deflection / Mestrado / Engenharia de Processos / Mestre em Engenharia Química
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Simulação sub-malha com modelo de dois fluidos do escoamento gás-sólido em risers de leitos fluidizados circulantes / Sub-grid simulation with two-fluid model to gas-solid flow in circulating fluidized bed risersElói Rotava 24 November 2008 (has links)
Modelagem de dois fluidos é largamente aplicada para simular escoamentos gássólido em risers de leitos fluidizados circulantes. As atuais simulações são de grandes clusters (SGC), executadas em domínios reais com malhas numéricas grosseiras, ou simulações sub-malha, executadas em malhas numéricas refinadas em domínios reduzidos. O propósito das simulações sub-malha é principalmente produzir dados de meso-escala a serem aplicados em simulações de grandes clusters. A atual literatura apresenta apenas umas poucas simulações sub -malha de escoamentos gás-sólido em risers aplicando modelagem de dois fluidos, todas para condições típicas de reatores de leito fluidizado circulante de craqueamento catalítico. Neste trabalho realizou-se uma simulação sub-malha para esta condição, e também para uma outra condição típica de reatores de leito circulante para combustão/gaseificação. Correlações teóricas derivadas da teoria cinética dos escoamentos granulares (TCEG) foram aplicadas para determinar a pressão e as viscosidades da fase sólida. Considerou-se um domínio de pequenas dimensões sob condições de contorno periódicas, aplicando-se malhas numéricas refinadas. Os resultados das simulações foram comparados entre si, com outros resultados de simulação de literatura, e com dados experimentais. Então, a correção das simulações foi abordada em vista dos dados empíricos disponíveis. / Two-fluid modeling is widely applied to simulate gas-solid flows in risers of circulating fluidized beds. Current simulations are either large cluster simulations (LCS), performed in real domains under coarse numerical meshes, or sub-grid simulations, performed in reduced domains under refined numerical meshes. The purpose of subgrid simulation is mostly to provide meso-scale data to be applied in large cluster simulations. The up to date literature presents only a few sub -grid simulations of gassolid flows in risers applying two-fluid modeling, all of them for conditions typical of catalytic cracking circulating fluidized bed reactors. In the present work a sub-grid simulation was performed for this condition, as well as for a condition typical of circulating fluidized bed coal combustion/gasification reactors. Theoretical correlations derived from the kinetic theory of granular flows (KTGF) were applied to determine pressure and viscosities of the solid phase. A small size domain was considered under periodic boundary conditions, and a refined numerical mesh was applied. The results of the simulations were compared to each other, to other literature results of simulation, and to experimental data. Then, the accuracy of the simulations was addressed in view of the available empirical data.
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Development of Diagnostic Tools for Use in a Gas Turbine Engine Undergoing Solid Particulate IngestionOlshefski, Kristopher Thomas 30 May 2023 (has links)
Aircraft propulsion systems can be exposed to a variety of solid particulates while operating in either arid or other hazardous environments. For conventional takeoff and landing aircraft, debris can be ingested directly into the gas turbine powerplant which is exposed to the ambient environment. For helicopters and other vertical takeoff and landing (VTOL) aircraft, rotor down wash presents a particular threat during takeoff and landing operations as significant amounts of groundlevel particles can be entrained in the surrounding air and subsequently ingested into the engine. Prolonged exposure to particle ingestion events leads to premature engine wear and, in extreme cases, rapid engine failure. Expanding our current understanding of these events is the first step to enabling engine manufacturers to mitigate these damage mechanisms through novel engine designs.
The work described in this dissertation is aimed at increasing the scientific understanding of these ingestion events through the development of two distinct diagnostic instruments. First, an anisokinetic particle sampling probe is designed to be used for in-situ particle sampling inside of a gas turbine engine compressor. Offtake of particles during engine operation in dusty conditions will provide researchers with an improved understanding of particle breakage tendency and component erosion susceptibility. Both experimental and numerical investigations of the probe present a comprehensive realization of probe performance characteristics. Secondly, a novel particle visualization technique is developed to provide users with particle distribution and particle mass flow estimates at the inlet of a gas turbine engine. This technique yields both time-resolved and time-averaged quantities, allowing users to have a comprehensive account of particles entering the engine. / Doctor of Philosophy / Foreign debris ingested into aircraft engines can cause serious damage and degrade their performance. The source of these ingested particles may be from atmospherically suspended ash due to volcanic eruption, high altitude ice crystals, or ground-level sand and dust. Both conventional takeoff and landing aircraft and vertical takeoff and landing (VTOL) aircraft are at risk. In extreme cases, exposure to a particle-laden atmosphere has resulted in catastrophic engine failure and loss of life. For this reason, researchers are intensely focused on mitigating the effects of these harmful particulates.
The work described in this dissertation establishes two novel diagnostic capabilities. These are aimed at providing the research community with an increased understanding of how particles enter an aircraft powerplant as well as describe the behavior of these particles as they traverse the initial stages of an engine. The first instrument described is a particle sampling probe which is meant to be inserted into the compressor section of a gas turbine engine. This probe will offtake particles as they enter the engine after they have had an opportunity to interact with the rotating components of the compressor. In doing so, researchers gain an improved understanding of particle breakage tendency and component erosion susceptibility. The second instrument provides a snapshot of particle distribution at the inlet of the engine as well as estimates of total particle mass flow. This capability allows researchers to have a precise understanding of the quantity of ingested material as well as a qualitative understanding of how the inflow distribution of particles looks. Each of the developed tools represent a first step to enabling engine manufacturers to mitigate these damage mechanisms through novel engine designs.
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Simulação numérica de escoamentos gás-sólido em leito fluidizado borbulhante utilizando a teoria cinética dos escoamentos granulares /Mineto, Andreza Tangerino. January 2009 (has links)
Orientador: Hélio Aparecido Navarro / Banca: Paulo Cesar Razuk / Banca: Luben Cabezas Gomez / Resumo: No presente trabalho desenvolve-se um estudo de modelagem matemática e simulação numérica do escoamento gás-sólido em um leito fuidizado borbulhante. É apresentado o modelo hidrodinâmico, A, para escoamentos bifásicos gás-solido considerando a Teoria Cinética dos Escoamentos Granulares. É usado o modelo Euleriano de duas fases separadas considerando a modelagem do tensor das tensões da fase sólida através do atrito entre as partículas e da teoria cinética dos escoamentos granulares. O código fonte MFIX (Multiphase Flow with Interphase eXchanges) desenvolvido no NETL (National Energy Technology Laboratory) é utilizado para as simulações numéricas. Os resultados de simulação são obtidos resolvendo a temperatura granular algebricamente ou através de uma equação diferencial parcial. Obtêm-se resultados mais realísticos no uso da EDP com condição de contorno de deslizamento parcial na parede. Uma variação no diâmetro das partículas (partículas do grupo B e do grupo A/B) é investigada, concluindo-se que deve ser acrescentado ao código MFIX outros parâmetros físico para simulações com partículas do grupo A/B. / Abstract: In the present work is described a mathematical model and numerical simulation of gas-solid flow in the bubbling fluidized bed. It is presented the hydrodynamic model, A, for gas-solid flow considering the Kinetic Theory of Granular Flows. It is used the two fluids Eulerian model where the solid phase stress tensor is modeled considering the friction between the particles and the kinetic theory of granular flows. The code MFIX (Multiphase Flow with Interphase eXchanges) developed in NETL (National Energy Tecnology Laboratory) is used for numerical simulations. The results are obtained with the compute of the granular temperature using a partial differential equation or an algebraic expression. It was obtained more realistic results when is used a PDE with boundary conditions of the partial slip. A variation in the diameter of the particles (particles in Group B and Group A/B) it is analyzed. It is also concluded that should be added to the code MFIX other physical parameters for simulations with particles of group A/B. / Mestre
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MASS FLOW SENSOR DEVELOPMENT FOR AN AIR SEEDING CART2011 October 1900 (has links)
The air seeding cart is an important piece of farming equipment used in the seeding process. Three factors which are necessary to monitor during the seeding process are the seeding rate (material mass flow rate), air flow rate, and blockages. In current practice, there are systems that monitor and report air flow and blockages but not the actual seeding rate. Presently, the seeding rate is based on the metering calibration before the seeding process starts, which requires a lot of time and energy from the operator. If that goes wrong, it not only takes longer, but also costs more money and increases the already significant stress and fatigue which farmers and operators have during the seeding period. Therefore, the development of reliable, and easily calibrated, on-line sensors for flow monitoring would be beneficial. Further, such sensors would facilitate closed-loop control of the flow rate itself.
In order to develop a laboratory prototype for mass flow measurement, a model for mass flow estimation was established. This was accomplished by using pressure transducers to determine the pressure drop across an elevation in the primary air cart run (between the air seeding cart and the air hoe drill). An air seeding test station was designed and developed for the study.
Three different types of seeds and a granular fertilizer were chosen and tested. These tested materials were canola, wheat, chickpea and urea fertilizer (46-0-0). The general form of the model was developed using data from the canola tests. The input parameters for this mass flow estimation model were pressure drop and air flow information. The average percent error of the material mass flow rate’s full range was under 10%, except for the highest rate which tested up to 20%. Overall, more than 75% of the estimations had percent errors being less than 5%. The form of the model was also applicable to other individual tested materials with the percent error of their full ranges up to 20%. However, their average of their median error was around 5% of their full ranges.
The general model was also applied to the combined data from all tested materials. The results were not as accurate as when the model was applied to the individual tested material. The median of the percent error (of material mass flow rate full range) varied from as low as 1% to as high as 30%, depending on the tested materials. Nevertheless, it demonstrated that there were consistencies between the behaviour of the four tested materials.
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Determinação experimental das distribuições radial e axial de concentração de solidos em uma seção riser utilizando sonda de fibras opticas / Experimental determination of radial and axial solids concentration distributions in a riser section using an optical-fiber probeCastilho, Guilherme José de, 1983- 15 June 2007 (has links)
Orientador: Marco Aurelio Cremasco / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-08-09T06:13:25Z (GMT). No. of bitstreams: 1
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Previous issue date: 2007 / Resumo: Regimes gás-sólido têm inúmeras aplicações industriais, sendo empregados, por exemplo, em sistemas de transporte pneumático das partículas e em leito fluidizado. Nas últimas duas décadas notou-se a aplicação crescente do leito fluidizado circulante, principalmente para facilidades de geração de energia, como caldeira e reações catalíticas. No processo de craqueamento catalítico fluidizado (FCC), dentre os vários equipamentos que compõem uma unidade conversora, é no riser onde praticamente ocorrem todas as reações de craqueamento. Medidas de grandezas como concentração de sólidos são fundamentais para a compreensão da fluidodinâmica nestes reatores e é pré-requisito para o projeto técnico bem sucedido de sistemas de transporte pneumático. Dentre as várias técnicas utilizadas para medidas de grandezas básicas em sistemas particulados, a sonda de fibra óptica é relativamente simples, de alta precisão e utilizada em várias situações que envolvem o sistema fluido-partícula. Nesta Dissertação, a oncentração volumétrica dos sólidos é medida por meio de uma sonda de fibra óptica. A concentração volumétrica dos sólidos é tomada radialmente e em diversas posições axiais ao longo do riser sob diferentes condições de operação, na Unidade Multipropósito do Laboratório de Processos em Meios Porosos da Faculdade de Engenharia Química da Universidade Estadual de Campinas. Resultados mostram que a concentração volumétrica de sólidos é maior na parede em comparação ao centro do riser, para todas posições axiais, exceto para o ponto mais alto do reator, onde há a influência da região de saída do escoamento. Sobre a distribuição axial de de concentração, verificou-se que o escoamento é mais concentrado na parte inferior do equipamento e tende a ficar menos concentrado ao longo do reator. Através dos espectros de sinais obtidos pela sonda, pôde-se analisar as flutuações através da distribuição de probabilidade dos sinais e da distribuição do desvio padrão do sinal médio. Distribuições de
probabilidade permitem identificar a presença de clusters em determinados pontos radiais, revelando que para as condições de mais concentradas, as flutuações são as maiores. As distribuições de desvio padrão apresentam picos, onde sugere maior interação entre as partículas / Abstract: Gas-solid systems have innumerable industrial applications, being used, for example, in the pneumatic conveying of particles and in fluidized bed. In the last two decades it was noticed increasing application of the circulating fluidized bed, mainly for easinesses of energy generation, as boilers and catalytic reactions. In the process of fluidized catalytic cracking (FCC), amongst some equipment that composes a converting unit, it is in riser where the cracking reactions practically occur at all. Measures as solid concentration are basic for the understanding of the fluidodynamic in these reactors and are prerequisite for the successful design of pneumatic transport systems. Amongst the several techniques used for measures in particulates systems, the optical-fiber probe is relatively simple, of high precision and used in some situations that involve fluid-particle system. In this Dissertation, the volumetric concentration of solids is measured by means of an optical-fiber probe. The volumetric concentration of solids is taken radially and in diverse axial positions throughout riser under different operation conditions, in the Multipurpose Unit of the Laboratory of Processes in Porous Means of the College of Chemical Engineering of the State University of Campinas. Results show that the volumetric solid concentration is bigger in the wall in comparison to the center of the riser, for all axial positions, except forthe highest point of the reactor, where it has the influence of the exit region of the flow. On the axial distribution of concentration, it was verified that the flow is more concentrated in the inferior part of the equipment. Through the electrical signs specters gotten by the probe, it could be analyzed the fluctuations through the distribution of probability of the signals and the distribution of the standard deviation of the average signal. The distribution of probability allows identifying the presence of clusters in determined radial points, disclosing that for the most concentrated conditions, the fluctuations are the greater. The distributions of the standard deviation present peaks, where it suggests greater interaction between particles / Mestrado / Engenharia de Processos / Mestre em Engenharia Química
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