A study of stability of difference scheme of Markov counting chain method for fluidization modeling

Abstract

Devices with a fluidized bed of granular material are applied in many energy power technology processes. The fluidized bed is a heterogeneous system, so mathematical models assuming its spatial discretization are necessary for its proper description. Markov chain theory is one of the most effective tools for the mathematical description of the fluidized bed structure. Many research papers are devoted to the issues of the theory application when developing mathematical models of various technological processes in the fluidized bed. At the same time, much less attention is paid to the issue of stability analysis of the proposed algorithms. Thus, it is a highly topical issue to analyze the computational stability of models of fluidized bed based on the mathematical principles of the Markov chain theory. The Markov chain approach is used as a mathematical basis for modeling of the flow patterns in a fluidized bed. The parametric identification of the model is performed using the dependencies known from the scientific papers, and the transition matrices are aligned with the physical parameters of the mass flows, which makes the proposed model nonlinear. The mixed criterion of the stability algorithm is formulated. It shows the influence of the spatiotemporal parameters of the problem sampling on the stability of computational procedures. The stability of the difference scheme to calculate formation of a fluidized bed of a monodisperse granular material is studied. The influence of the time sampling frequency on the stability of the resulting solution is considered. The effect of various parameters of the model on the loss of computational stability is estimated. It is proved that the time and spatial sampling frequencies should be chosen as a result of a mixed stability criterion. The study proves that the methodology of the Markov chain theory is an acceptable tool to describe the structure of such particle systems as a fluidized bed. It is established that macro-diffusion parameter of particle motion is the most influential in the process of computational stability loss. Thus, on the one hand, it is relevant to conduct further comparative studies of existing models of macrodiffusion, and on the other hand, it is possible to use models based on the theory of Markov chains considering the proposed stability criterion.