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

Haiming Dong,Jingfeng He,Chenlong Duan,Yuemin Zhao

doi:10.3390/app8030360

Abstract

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.

Highlights

Gas solid two-phase flow is a complex flow system composed of gas and solid particles, and represents an important branch of fluid dynamics
The properties of the bubbles in the gas-solid systems have been self-consistently investigated based on fluid mechanics theory, bubble thermodynamic equations, and kinetic equations
We found that the bubble heat ratio of the gas-solid two-phase flow significantly increases with the increase of temperature and pressure in the bubble system

Summary

Introduction

Gas solid two-phase flow is a complex flow system composed of gas and solid particles, and represents an important branch of fluid dynamics. Bubble dynamic behavior is responsible for the most basic characteristics and phenomena in the gas solid two-phase flow system. This is significant for the understanding and study of the properties of gas solid two-phase flow systems [4]. The study of bubbles in gas solid two-phase flow forms an important part of the field of fluidization state [6]. Research into bubble properties in the gas-solid two-phase flow system represent some of the most important and basic studies in the field [8]. The dynamic properties of bubbles in the gas-solid two-phase flow system as shown in Figure 1 are studied using the self-consistent theoretical method. Through establishing and researching the bubble thermodynamic equation, we examine the properties of bubbles in the gas-solid two-phase flow system on the basis of Ergun and bubble dynamics equations

Theoretical Model

PR Equation and the Heat Capacity Ratio of Bubbles

Gas Velocity Equation in the Gas-Solid Two-Phase Flow System

Bubble Size and Velocity Equation

Results and Discussion

Conclusions