Mathematical Modeling Of Downward Gas-solid Flow Based On Energy-minimization Multi-scale (EMMS) Theory

Gas-solid downers,similar to fast fluidized beds,are typical non-linear and nonequilibrium systems,featuring spatio-temporal multi-scale structures.Taking the heterogeneous structure into account,the energy-minimization multi-scale(EMMS)model predictes well the hydrodynamic characteristics of gas-solid two phase flow,and thus is widely used in circulating fluidized beds(CFB).In this paper,we will apply the EMMS theory to the modeling of gas-soild downers to explore their axial flow structures.By resolving a cocurrent downer into a dilute phase,a dense phase,and an interphase in between,multi-scale mass and momentum conservation equations can be built on the basis of 10 hydrodynamic parameters.In the different development sections of the cocurrrrent gas-solid downward flow,cross-sectional stable distribution is constrained by different stability conditions,which however can be unified according to the principle of the compromise in competition between dominant mechanisms.By optimizing the volume average number density of particle clusters with respect to the unified stability condition,the formulated model can be numerically solved without introducing cluster-specific empirical correlations.Both qualitative and quantitative analyses of the calculation results show that the one-dimensional model successfully captures the axial hydrodynamic characteristics in gas-soild cocurrent downers and can be expected to be applicable in a wide range from air fine to coarse particle gas-soild systems.Considering the similarities and differences between counter-and co-current gas-solid downward flow in the particle clustering mechanism,a one-dimensional model for a countercurrent gas-solid downer can be similarly developed by adopting the following steps: firstly multi-scale resolution of the system,then establishment of the constitutive equations,finally analysis of the cross-sectional stability conditions.This model can also be solved by adopting a similar scheme to that used in the solution of the one-dimensional model for the cocurrent gas-solid downer.However,it should be noted that an empirical wall friction significantly affects the model prediction,which thus needs to be carefully determined in order to ensure accuracy of the the calculation results.The one-dimensional models for co-and counter-current gas-solid downward flow are developed on the basis of the anslysis of the multi-scale interactions in gas-solid two-phase flow according to the EMMS theory,thereby can be expected to be much more universal than the existing models without consideration of particle clustering phenomena.This reseach enriches the theory of global computation of complex gas-solid systems,hence helping to the real-time simulation of industrial processes,so as to realize so-called virtual reality in chemical engineering.