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. Based on PR state equation, and a detailed specific heat ratio equation of bubbles, we self-consistently evaluate kinetic equations of the bubbles on the basis of Ergun equation, thermodynamic equation and kinetic equations. It is found that the specific heat ratio of bubbles in such systems strongly depends on the bubble pressures and temperatures, which play an important role on the characteristics of the bubbles. The theoretical studies show that with a increasing of the 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. With a increasing the height, bubble sizes show a variation of first decreasing and then increasing (U type). The bubble velocity is affected by the gas velocity and the bubble size, which gradually declined and eventually stabilized. It shows that gas phases and solid phases in a gas-solid two-phase flow interact with each other and come into being a self-consistent system. The theoretical results have exhibited important guiding value for understanding the properties and effects of bubbles in the gas-solid two-phase flows.