۱- Introduction

۲- Mathematical model and calculation conditions

۳- Gas–solid heat transfer characteristics of packed binary-size particles

۴- Gas–solid heat transfer characteristics of packed quintuple-size particles

۵- Comparative study of the heat transfer characteristics of packed multi-size particles with the same mean diameter

۶- Conclusions

References

Abstract

Real industrial particles generally have a wide size distribution. Therefore, the gas–solid heat transfer characteristics of packed multi-size particles should be studied. A mathematical model of gas–solid heat transfer for packed multi-size particles is established. This model includes gas–solid convection heat transfer and intraparticle and interparticle conduction. The cooling processes of packed binary- and quintuple-size particles ranging from 10 mm to 60 mm under different conditions are investigated. The EDEM software is used to obtain the porosities of different cases. Results show that the presence of small particles in the packed multi-size particles reduces porosity and increases specific surface area, thereby benefiting the gas–particle heat transfer process. The temperature of large particles is always higher than that of small particles during particle cooling. Particle–particle conduction helps in the cooling process of large particles, and the maximum heat flux ratio of interparticle conduction to gas–solid convection for large particles reaches 0.196. The volumetric heat transfer coefficient of the packed multi-size particles varies with time. The initial heat transfer coefficient is the average value weighted by mass fractions, and the limit of the final value is that of the large particle under the actual porosity. The proposed dimensionless volumetric heat transfer coefficient can be a general description of gas–solid heat transfer characteristic of various packed multi-size particles. Its time variation can be well described by an exponential correlation, and the variation rate is related to the variance of particle size in each case.

Introduction

Fixed and moving beds with particles are widely used in industrial applications, such as waste heat recovery [1], gas separation [2], and chemical looping combustion [3]. The gas–solid heat transfer that occurs between the flowing gas and packed particles plays a vital role in determining the performance of such devices [4]. Numerous studies have been conducted to investigate the gas– solid heat transfer characteristics of various packed particles in the last decades [5,6], and information regarding packed mono-size spherical particles has been successfully achieved. Ranz and Marshall [7] theoretically studied the heat transfer process of gas flows over a single sphere and derived a relation for predicting the heat transfer intensity of a single sphere in Nusselt form depending on the Prandtl and Reynolds numbers. Wakao et al. [8] improved an expression on the basis of the experimental data of packed sphere beds. Their result had the same form as but different coefficient from the result of Ranz’s study, which excluded the porosity. Kunii and Levenspiel [9] proposed a heat transfer expression in an improved form, including the porosity of the packed beds. Similar studies were conducted by Gnielinski [10] and Achenbach [11], and corresponding correlations were established to extend the range of the Reynolds number, porosities, and Prandtl number. These expressions perform well in predicting the gas–solid convective heat transfer of packed mono-size spherical particles under various conditions. However, the effects of heat conduction inside a sphere should be considered when the particle size is large. Jeffreson [12] proposed a modified effective heat transfer coefficient for gases and spheres by incorporating the effects of intraparticle conduction, which is based on a theoretical solution of the heat conduction process inside a sphere. Furthermore, Kye et al. [13] derived the expression of a gas–solid volumetric heat transfer coefficient on the basis of the representative elementary volume method of porous medium.