Modeling of biomass gasification in fluidized bed

Behavior of the solid phase in fluidized beds was studied by a 2D CFD-DEM approach to obtain more information on the solid mixing and circulation. Hydrodynamic parameters, including solid diffusivity, and internal and gross circulations were considered in this study. To validate the simulation, time-position data obtained by the Radioactive Particle Tracking (RPT) technique were used. It was shown that the 2D model can satisfactorily predict the axial diffusivity, while the radial diffusivity calculated based on the model is an order of magnitude smaller than the experimental one in 3D. The influence of aspect ratio of the bed, type of distributor, and inlet gas velocity on solids mixing pattern were also studied. The solids flow pattern in the bed changed considerably by increasing the aspect ratio. Different solid circulations were captured by numerical model for the two types of distributors, namely porous and injection types. The results suggested that increasing the superficial gas velocity caused rigorous internal and gross circulations, which in return, improved solids mixing and decreased deviations from well mixed state.

Characterization of solids mixing patterns in bubbling fluidized beds

Direct measurements of many properties of real-world systems are not possible. Information on these properties can only be inferred from the result of measurements of other quantities which may be measured directly. The process comprising direct measurements of certain characteristics of the object followed by inference on its sought-for properties from the directly measured characteristics based on a mathematical relation between unknown properties and measured characteristics is called indirect measurement, whereas inference is referred to as an inverse problem in indirect measurement. In general an inverse problem consists either in determining the characteristics of a system under study, driven by controlled or known exciting signals, or in reconstructing exciting signals acting on a system whose internal characteristics are known. In both cases, it is formulated in terms of a mathematical model relating unknown and measured characteristics and signals. One can distinguish continuous and discrete inverse problems, depending on whether the measured and sought-for quantities are represented by functions or by vectors (tuples), respectively. Very many nontrivial inverse problems in indirect measurements are ill-posed which means that they have no solution or the solution exists but is non-unique or unstable, i.e. very small disturbances in the measurement data result in large disturbances in the result of inference. High error amplification is referred to as ill-conditioning. Ill-posedness and ill-conditioning result from the lack of information on sought-for quantities, carried by the measurement data. Therefore, a priori knowledge about the space of admissible solutions has to be employed for solving such inverse problems. The theory of inverse problems and – in particular – effective numerical methods for solving them are of great importance for measurement science and technology; they are crucial for the development of many measurement, imaging and diagnostic techniques. Indirect measurements may be formulated using various mathematical models of the measurement object followed by a measuring system. A broad class of inverse problems, being of importance for indirect measurements, is formulated in terms of Fredholm integral equations of the first kind. These problems are ill-posed and strongly ill-conditioned after discretization. Therefore, sophisticated inverse procedures, utilizing various kinds of a priori knowledge, are applied for solving them. In this paper, theoretical and numerical aspects of inverse problem in indirect measurements are reviewed. In particular the concept of generalized solution (pseudosolution) and the notion of well-posedness is presented and analysed. The review is focused on inverse problems formulated in terms of Fredholm integral equations of the first kind: a general presentation of such problems, at the level of functional analysis, is followed by an overview of numerical aspects of their discretized versions. A concise presentation of selected groups of numerical methods, called inverse methods, for solving inverse problems is also provided.

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Review article inverse problems formulated in terms of first-kind fredholm integral equations in indirect measurements

Direct measurements of many properties of real-world systems are not possible Information on these properties can only be inferred from the result of measurements of other quantities which may be measured directly The process comprising direct measurements of certain characteristics of the object followed by inference on its sought-for properties from the directly measured characteristics based on a mathematical relation between unknown properties and measured characteristics is called indirect measurement, whereas inference is referred to as an inverse problem in indirect measurement In general an inverse problem consists either in determining the characteristics of a system under study, driven by controlled or known exciting signals, or in reconstructing exciting signals acting on a system whose internal characteristics are known In both cases, it is formulated in terms of a mathematical model relating unknown and measured characteristics and signals One can distinguish continuous and discrete inverse problems, depending on whether the measured and sought-for quantities are represented by functions or by vectors (tuples), respectively Very many nontrivial inverse problems in indirect measurements are ill-posed which means that they have no solution or the solution exists but is non-unique or unstable, ie very small disturbances in the measurement data result in large disturbances in the result of inference High error amplification is referred to as ill-conditioning Ill-posedness and ill-conditioning result from the lack of information on sought-for quantities, carried by the measurement data Therefore, a priori knowledge about the space of admissible solutions has to be employed for solving such inverse problems The theory of inverse problems and – in particular – effective numerical methods for solving them are of great importance for measurement science and technology; they are crucial for the development of many measurement, imaging and diagnostic techniques Indirect measurements may be formulated using various mathematical models of the measurement object followed by a measuring system A broad class of inverse problems, being of importance for indirect measurements, is formulated in terms of Fredholm integral equations of the first kind These problems are ill-posed and strongly ill-conditioned after discretization Therefore, sophisticated inverse procedures, utilizing various kinds of a priori knowledge, are applied for solving them In this paper, theoretical and numerical aspects of inverse problem in indirect measurements are reviewed In particular the concept of generalized solution (pseudosolution) and the notion of well-posedness is presented and analysed The review is focused on inverse problems formulated in terms of Fredholm integral equations of the first kind: a general presentation of such problems, at the level of functional analysis, is followed by an overview of numerical aspects of their discretized versions A concise presentation of selected groups of numerical methods, called inverse methods, for solving inverse problems is also provided

Inverse problems formulated in terms of first-kind Fredholm integral equations in indirect measurements

By means of a numerical study we show particle-size distributions retrieved with the Chin-Shifrin, Phillips-Twomey, and singular value decomposition methods. Synthesized intensity data are generated using Mie theory, corresponding to unimodal normal, gamma, and lognormal distributions of spherical particles, covering the size parameter range from 1 to 250. Our results show the advantages and disadvantages of each method, as well as the range of applicability for the Fraunhofer approximation as compared to rigorous Mie theory.

Reconstruction of particle-size distributions from light-scattering patterns using three inversion methods.

A stochastic inverse technique based on a genetic algorithm (GA) to invert particle-size distribution from angular light-scattering data is developed. This inverse technique is independent of any given a priori information of particle-size distribution. Numerical tests show that this technique can be successfully applied to inverse problems with high stability in the presence of random noise and low susceptibility to the shape of distributions. It has also been shown that the GA-based inverse technique is more efficient in use of computing time than the inverse Monte Carlo method recently developed by Ligon et al. [Appl. Opt.35, 4297 (1996)].

Inversion of particle-size distribution from angular light-scattering data with genetic algorithms

Solids mixing in fluidized beds

Model for solids mixing in a two-dimensional gas-fluidized bed

An inverse technique devised from modification of annealing-evolution algorithm for particle sizing by light scattering

Summary form only given. A novel technique for measuring two-dimensional flow field has been developed. It cans measure the vector field by capturing only one frame of picture of flow field and by using the cross-correlation method. The technique employer rather simple equipment compare with common PIV techniques, which normally needs pulse lasers to capture two frame of pictures. The experimental apparatus (1 mW He-Ne laser and common CCD camera) as shown in this paper is currently suitable to measure a certain range of velocity of flow. The range of measured velocity is from 0.007 to 3 m/s, and measured area 16/spl times/12 mm, which could be expanded while using more power of laser.

Yiqian Xu

Papers

Inversion of particle-size distribution from angular light-scattering data with genetic algorithms

Solids mixing in fluidized beds

Model for solids mixing in a two-dimensional gas-fluidized bed

An inverse technique devised from modification of annealing-evolution algorithm for particle sizing by light scattering

A novel PIV technique using one frame of image