| Powder or particle mixing is an important unit operation in the process of pharmaceutical and chemical production.Power consumption is one of the key parameters in the design of stirred tank reactors.Establishing a model to predict torque is an important method for the study of power consumption during the powder mixing process.Discrete Element Method(DEM)is a numerical method which can analyze the motion of a single particle and particle group and the forces acting on them.The force model is used to simulate the collision process between particles and calculate the motion information of the particles.This method has been widely used in the particle mixing process.Two different kinds of materials were mixed in a flat bottom stirred tank with diameter of 210 mm.One is glass beads powders with an average diameter of 114 μm,and the other is spherical particles with an average diameter of 5 mm.The torque sensor was used to measure the torques of different impellers.The power consumption for different impellers during the powder mixing was experimentally measured and then a dimensionless model and a semi-empirical model were established.Power consumption of particle mixing with an average diameter of 5 mm was simulated by DEM numerical simulation software.The numerical simulations were carried out for different rotational speeds and different fill levels.The experimental results showed that the torque increases with increasing fill level,the length,the number and the width of blade.With the same number of blades,different stirring impeller torque values ranking from small to large is as follows:45° blade impeller up pumping<Pfaudler<straight blade impeller<45° blade impeller down pumping.According to quantitative analysis,for the glass beads powders with an average diameter of 114μm,the relation between relative fill level and the torque is MT= k2(H/T)1.5,where,different impellers corresponding to different k2 values.For the glass beads powders with an average diameter of 5 mm,the relation with relative fill level,the torque and the rotational speed is MT=k3(H/T)1.3(N)0.1,also,different impellers corresponding to different k3 values.With the dimensional analysis,the relationship between the Power Number Np and the ratio of the diameter of the impeller to the fill level(D/H),the ratio of the width of the impeller to the fill level(w/H),the dimensionless item of speed g/(HN)and number of blades(n)is Np=4.206(D/H)-3.131(w/H)0.550(g/(HN2))1.034n0.2 with R2 of 0.990,and the relative deviation between the calculating value and the experimental value was within 15%.The semi-empirical model to relate the torque(MT)with impeller diameter D,impeller width w,fill level H,rotational speed N and friction coefficient μ among powders is as follows,with relative deviation between the predicting values and the experimental values within 20%,MT=0.504D2ρg[(H-C)2-(H-w-C)2]+0.168D3ρg(2H-w-2)-0.488N2D4ρwThe DEM simulation results show that the predicted torque values of each impeller are in good agreement with the torque values measured in the experiments.The particles motion pattern and the range of circulating flow are affected by the blade width and the blade inclination.Given the same impeller shape,circulation flow area is mainly affected by the number of blades. |
