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© 2018 Elsevier Ltd This paper mainly discusses a pattern of vibration rejection by using a feedforward controller. Conventional filtered-x normalized least mean squares (Fx-NLMS) algorithm converges slow especially when signals are not independent on each other. Therefore, a novel orthogonalized fractional order filtered-x normalized least mean squares (Orth-FONLMS) algorithm is proposed to obtain the precise parameters of the feedforward controller. The proposed algorithm is an improved Fx-NLMS algorithm by using fractional calculus and orthogonal transform. To implement the algorithm, fractional order gradient method and adaptive lattice filter are introduced, respectively. Numerical simulation proves that the proposed algorithm outperforms over the Fx-NLMS and fractional order filtered-x normalized least mean squares (Fx-FONLMS) algorithm in terms of convergence rate and accuracy.

The primary work of this paper is to investigate some potential properties of Grünwald–Letnikov discrete fractional calculus. By employing a concise and convenient description, this paper not only establishes excellent relationships between fractional difference/sum and the integer order case but also generalizes the Z-transform and convolution operation.

One important phenomenon in coal beneficiation fluidized bed (CBFB) is the accumulation of fine coal particles in beneficiation due to poor screening efficiency and attrition of coal samples. The effect of fine coal accumulation is numerically studied in this work using a TFM–DEM hybrid model. The gas phase and medium solid phase are modeled by a two-fluid model (TFM), while the fine coal particles are modeled by the discrete element method (DEM). Particles with a diameter of 0.9 mm are used as the fine coal sample in the simulation. The gas–solid flow pattern and particle dynamics are investigated with different concentrations of fine coal particles accumulated in the bed. For model validation purpose, the mean bed density distributions are compared with the experimental reports from He et al. (2013). The results show that a critical particle concentration exists in the fine coal accumulation process in CBFB. When the fine coal particles are less than 11 wt% in the bed, the flow pattern of medium phase is little affected and the coal particles are well mixed in the bed. However, when the particle concentration exceeds this threshold, the uniformity of bed density distribution is destroyed and particle stratification occurs along the bed height according to their density difference. Flow dynamics of the dense bed and main forces acting on the fine coal particles are analyzed to explain the underlying mechanism. With a large number of particles accumulated in the bed, the mixing effect of medium flow is suppressed. Motion of the fine coal particles is less dependent on the bed disturbance, instead, the particle gravity plays a decisive role in the particle distribution and results in the particle segregation in the fine coal accumulation process.

A TFM–DEM hybrid model is introduced for modeling of the complex gas–solid flows in a pilot scale Coal Beneficiation Fluidized Bed (CBFB). The gas and the dense solid phases are modeled using an Eulerian-Eulerian or two fluid model (TFM), while the beneficiated coal particles are modeled as a dilute phase by the discrete element method (DEM). In this work, the influence of some key operation parameters on particle segregation behavior is studied, including fluidized air velocity, bed depth, and coal feed ratio and bed medium properties. Their effects are evaluated using a single coal sample of diameter 4.3 mm. Particles are divided into five different density fractions to represent the wide density range of raw coal samples. The simulation results demonstrate that by increasing the fluidizing air velocity from 1.2 u mf to 1.8 u mf of the dense medium solids, the segregation degree of beneficiated coal particles is significantly reduced, but the segregation time is only slightly decreased. Increasing the particle feed mass or decreasing the bed depth has a similar influence on CBFB operation. Both help to improve particle segregation, but a shallower bed is demonstrated to be more effective for coal beneficiation. A decrease in the medium density can reduce the bed cut density as well as the beneficiation limit for lighter samples, while a decrease in the medium size will increase the back-mixing effects, resulting in reduced beneficiation quality. Hydrodynamic forces acting on the beneficiated particles are also quantified from the simulation results. By analyzing the magnitude and direction of each force acting on discrete particles, the mechanisms influencing particle segregation under different operation conditions are explained at the particle scale.

Particle segregation behavior in a coal beneficiation fluidized bed (CBFB) is numerically studied using a TFM–DEM hybrid model, in which the gas and the dense solid phases are modeled using a Eulerian–Eulerian or two fluid model (TFM), while the beneficiated coal particles are modeled as a dilute phase by the discrete element method (DEM). For validation purpose, the numerical model was setup using geometric and operating conditions similar to a laboratory experimental model with the bed thickness set to one particle diameter to save computational cost. For a fixed gas injection velocity, the influence of particle size and density of the beneficiated samples was studied. It was found that the particles would segregate along the bed height due to the density differences with the degree of segregation being strongly influenced by particle size. Obvious segregation occurs for the coarse samples (6.7 mm and 4.3 mm) and little segregation occurs for the particles smaller than 3 mm. The flow patterns and segregation kinetics were qualitatively comparable with those observed in physical experiments conducted under similar conditions. On this basis, the underlying mechanisms governing particle segregation have been explained in terms of the hydrodynamic forces acting on individual particles. It was demonstrated that the segregation of coarse particles was mainly controlled by the balance between gravity and the local pressure force, while fine particles were more strongly affected by the direct drag forces from the gas phase and the continuum solid phase, thus making them difficult to separate.

The segregation behaviors of fine coal particles in a coal beneficiation fluidized bed (CBFB) were investigated in this work. The size range of 1–8 mm was taken into account and three separate size fractions were studied comparatively in the experiments, e.g. 1–2 mm, 3–5.5 mm and 5.5–8 mm. Both a clean coal sample and a gangue sample were used as the processed material to study the segregation behaviors of both light particles and heavy particles. The dense bed was divided as seven layers from bottom to top and the particle distribution in each layer for each sample was fully demonstrated. The influences of the particle density, particle size and the fluidized air velocity were revealed, the segregation patterns under different conditions were compared and the segregation mechanism was carefully analyzed. The results showed that the flotation and sedimentation of the particles in CBFB were still largely influenced by the particle density for the fine size range particles, and density stratification occurred even within each size fraction sample. The weight fraction in each layer showed a quadratic increase along the bed height for the coal particles. For gangue particles, a large fraction deposited in the bottom while the mass proportions in the middle layers also showed an increased tendency. With a decrease of the particle size, both the particle segregation and the density stratification phenomena deteriorated seriously. It was proved that particle feed size should be above 3 mm as the separation effect was quite inefficient for finer particles. By increasing the fluidized air velocity, the bed density slightly decreased but the bed turbulence was largely strengthened by the increasing bubble boiling effect. The flotation and sedimentation of the particles in 5.5–8 mm were obviously affected while no clear influence occurred to the rest of the two size fractions. Moreover, the results in this work provide a group of data that are quite suitable for CBFB numerical modeling studies.

Modeling the dynamic behavior of gas -solid flow in a pilot scale coal beneficiation fluidized bed (CBFB) model was performed in this work, a transient two-dimensional simulation was done based on the Eulerian model together with the kinetic theory of granular flows. Three steps were conducted to testify the choices of sub-models in CBFB modeling, including gas -solid exchange drag models, gas phase turbulence models, granular temperature models and wall boundary condition models for solid phase. Instantaneous and time-averaged results of particle volume fraction, bubble number and size, particle velocity distributions and vortices, as well as bed density distributions were obtained. The impacts of the sub-models on the flow characteristics in the dense CBFB were illustrated in detail and suitable models with better predictions of CBFB flow pattern were then demonstrated. The Syamlal -O'Brien drag model predicted better results in bed characteristics. The dispersed k-e turbulence model should be used to describe the gas turbulence in the dense CBFB flow regime. The partial slip wall condition for particles had a slight influence in the small model. The partial differential equation granular temperature model could predict the inter-phase surfaces more clearly and the flow pattern more accurately.

The horizontal diffusion of coarse particles in dense fluidized beds is commonly used for particle mixing and discharging in CFB boilers. However, numerical modeling of such flows is hard at present because of the flow complexity and a lack of reliable methods. In this work, a TFM-DEM hybrid model is used to study the diffusion behavior of coal particle in a dense fluidized bed. The gas phase and the solid medium phase are modeled by the TFM, while the coal particles are modeled by the DEM. The TFM can give a reliable description of the dense medium flow while the DEM can readily designate the size and density distributions of the coarse particles. The diffusion pattern of the particles with different size and density is mainly studied. Influence factors such as the fluidized air velocity and the coal particle number are also investigated. To explain the mechanisms of particle diffusion in the dense bed, main forces exerted on the coal particles are analyzed in the Lagrangian framework.