Mathematical Modeling And Structure Optimizing Of Liquid-Solid Fluidized Bed Separator

The main devices for fine coal beneficiation used in industry include spirals,dens medium cyclone with small diameter,WOC(Water only Cyclone)and LSFBS(LiquidSolid Fluidized Bed Separator),etc.Because of a low fluidization rate under a high solid partilces volume,size effect in LSFBS is suppressed in some extent,which gives rise to a high separation efficiency and wide separation density.Objectives of this thesis is to understand particles settling and fluidizing characteristics in LSFBS,explore effective approach to simplify particles interaction behavior in dense autogenous liquid-solid fluidized bed;a new hindered settling velocity model and two LSFBS mathematical models were developed(one LSFBS mathematical model was based on particles movement equation,another was a new CFD model).By using the new CFD model,LSFBS's structure was optimized preliminarily;according to particles dynamics analysis,the reason of suppression effect of inclined plates on size effect during gravity separation was obtained,which was rised from slip-shear(Saffman)force exerted on particles moving between two inclined plates.A novel LSFBS was proposed,which had a extended column and inclined plates as internals.In the end,the separation properties of the new LSFBS was studied.Flowing findings have been achieved:(1)Influence of autogenous medium size on separation efficiency was obtained.Ep value and separation density increase with the autogenous medium particles size and for the same autogenous medium,separation efficiency gets deteriorated while the fluidization rate increases;taking the liquid-solid fluidized bed as a pseudo fluid,interaction between particles was incarnated by the pseudo-fluid effective density ?eff and apparent viscosity ?app;by using the pseudo-fluid method,a new hindered settling velocity model was deduced on the base of Concha-Almendra free settling velocity model.The predicted hindered settling velocities by using the model in the present study is more accurate compared with others.Particles of different density and diameter was fluidized in the water medium and the fluidization process was simulated through Euler-Euler approach.Hui-Gidaspow model was determined as the most proper fluid-solid exchange coefficient model.A hyperbola model was proposed in the present study,which was more accurate than Rual model.(2)Magnitude comparison between the forces applied by the fluid that exert on particles in the Liquid-Solid Fluidized Bed Separator(LSFBS)was carried out.Particles kinetic equation was simplified according to the comparison results as well as the characteristics of particles segregation process and flow field of LSFBS.The influence of Magnus force,Saffman force as well as Basset force could be neglected on particles hindered settling and separation results in LSFBS.Quasi-fluid method was also used to simplify the influence of other particles nearby on the particle movement,where the apparent viscosity of the dense autogenous solid-liquid fluidized bed was calculated by using the Swanson semi-empirical model.A simplified movement equation for particles in dense autogenous liquid-solid fluidized bed was obtained;based on the simplified movement equation,a new LSFBS model was developed in which the equation was solved by using the fourth order Runge-Kutta algorithm.The hindered settling velocity as well as the separation results of different particles in LSFBS can be predicted accurately compared with the experimental values by using the LSFBS model.(3)Methods for numerical simulation of particles separation process in LSFBS were obtained.A new CFD model was proposed,namely Eulerian-Eulerian-Lagrangian/RNG k-? approach;the quasi-fluid concept was also used and the effective density and apparent viscosity of the dense autogenous solid-liquid fluidized bed were also calculated through the same method as once used in the LSFBS model based on particles movement equations.The predicted separation results could well match the experimental value and was more accurate than the model based on particles movement equations.By using the CFD model,the influence on the separation performance of the pulsating upward currents cycles and waveforms were explored.According to the simulation results,separation performances of steady upward currents were better than those of pulsating upward currents.For pulsating upward currents,the optimal cycle was 1.25 s while the best waveform was rectangular.The influence of the size distribution characteristics(SDC)on gravity separation was studied quantitatively by using the CFD model.The RosinRammler model was used to describe the SDC of the feed,with the parameter Dx and n describing the fineness and particles size variation of the feed respectively.Single-factor tests were then developed and simulated using the CFD model to investigate the influence of the two aspects of SDC on the separation performance of LSFBS based on density.The simulated separation results indicate that the finer the feed is,the greater the separation density(?50)and Ep value are;the smaller the particles size variation is,the smaller the ?50 and Ep value are.A two-factor,five-level central composite design was performed.Results of ANOVA analysis indicated that in the internal of Dx =(0.51,0.79)and n =(1.96,9.04),the influence of feed fineness on ?50 is larger than that of particles size variation while the influence of feed fineness on Ep is smaller than that of particles size variation;the interactive effect between these two factors has a significant influence on Ep but having limited influence on ?50 value.(4)The structure of LSFBS was optimized by using the CFD model.Particles dynamics analysis moving in the inclined channels were carried out,demonstrated that the slip-shear force(Saffman force)was the reason that size effect was surpressed.A new LSFBS with inclined planes and extended-column was designed.The laboratory separation system was set up for the new LSFBS and comparison experiment had been carried out between the new LSFBS and traditional LSFBS.Under the same separation density in the internal of 1.35-1.6 g/cm3,probable error of new LSFBS was lower than that of traditional LSFBS obviously with an average of about 0.027 g/cm3.An index,deashing efficiency ?A,for determining the separation efficiency was put forward.A larger ?A indicated a higher separation efficiency.By being compared with the related partition curves,it was found that the shaper the partition curve was,the large the ?A was.The single factor test was conducted for the number of inclined planes in the new LSFBS.The deashing efficiency increased as the space between inclined planes decreased and the functional relationship between deashing efficiency and the space was obtained by using regression method.A correlation for calculating the Saffman force with space between inclined planes,k,and upward current velocity,u F,was put forward,which was useful for optimizing the operating or structural parameters.The orthogonal experiment(two factors,space between inclined planes and upward current rate;and three levels)was designed and performed.The optimal operating and structural parameters were obtained,which were space between inclined planes 4.83 mm and upward current rate 3.11 m3/h,respectively.According to the ANOVA analysis,the influence of the upward current velocity was the smallest on the deashing efficiency while that of interactive effect between the two factors was highly significant;the space between inclined planes had the maximal influence on the deashing efficiency.