A Self-Consistent Physical Model of the Bubbles in a Gas-Solid Two-Phase Flow

In this work, we develop a self-consistent physical model of bubbles in a gas solid two-phase flow. Using the Peng-Robonson state equation and a detailed specific heat ratio equation of bubbles, we obtain the kinetic equations of the bubbles on the basis of the Ergun equation, thermodynamic equations, and kinetic equations. It is found that the specific heat ratio of bubbles in such systems strongly depends on bubble pressures and temperatures, which play an important role in the characteristics of the bubbles. The theoretical studies show that with increasing height in the systems, the gas flow rate shows a downward trend. Moreover, the larger particles in the gas solid flows are, the greater the gas velocity is. The bubble sizes increase with the increasing heights of the gas solid systems, and then decrease. The bubble velocity is affected by the gas velocity and the bubble size, which gradually increase and eventually quasi-stabilize. This shows that gas and solid phases in a gas solid two-phase flow interact with each other and a self-consistent system comes into being. The theoretical results have exhibited important value as a guide for understanding the properties and effects of bubbles in gas solid two-phase flows.