# Obtaining a formula describing the interaction of fine particles with an expanding gas flow in a fluid layer

## Authors

• Yessenbay Alpeissov S. Seifullin Kazakh Agro Technical University, Kazakhstan
• Ruslan Iskakov S. Seifullin Kazakh Agro Technical University, Kazakhstan
• Sultanbek Issenov S. Seifullin Kazakh Agro Technical University, Kazakhstan
• Аru Ukenova L. N. Gumilyov Eurasian National University, Kazakhstan

## Keywords:

fluidized layer, convective drying, gas flows, fine particles, dryer, gas jet, heat and mass transfer

## Abstract

The interaction of fine particles with an expanding gas flow under fluidization conditions is considered. The objects of study are finely dispersed materials, their single particles, gas flow in a fluidized layer. The study used the laws of dynamics and hydrodynamics, the classical laws of mechanics, as well as mathematical methods for the analytical solution of equations. It is emphasized that when a particle moves upwards in a gas jet, three forces act on it: the resistance force Fc, the gravity force P, and the Archimedes force A. As a result, the motion of a fine particle in an expanding gas flow is described taking into account the law of dynamics. During the study, an analytical equation was obtained to determine the velocity of a particle during its rise and fall in a gas jet. During the study, an analytical equation was obtained to find the height of the particle ascent depending on the gas flow rate for given geometric parameters of the gas flow. The obtained formulas can be used in the process of studying the process of convective drying of finely dispersed materials for various design parameters of the dryer. In practice, as a rule, there are various empirical formulas that describe such interactions of particles for specific parameters, which make it difficult to generalize them. In this work, the correctness of the assumed conditions necessary for the analytical solution of the differential equation of particle motion is proved. As a result, formulas were obtained that make it possible to determine the velocity of a particle in a gas jet and the height of its rise depending on the gas flow rate. On the basis of these formulas, graphic dependences of the gas velocity in the jet on the height Vg=f(Z), as well as the dependences of the height of the particle rise hm on the air flow rate in the jet L at different jet expansion angles α=15°; α=20°; α=30° are plotted. It was found that with an increase in the height Z in an expanding jet, the gas velocity in the jet Vg decreases, with an increase in the air flow rate in the jet L, the height of the particle rise hm increases. These formulas are the basis for further consideration of the movement of particles in a fluidized layer in the process of convective drying of fine materials for its intensification of the drying process

## Supporting Agency

• This research has been funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP09259673).

## Author Biographies

### Yessenbay Alpeissov, S. Seifullin Kazakh Agro Technical University

Doctor of Technical Sciences, Professor

Department of Electrical Equipment Operation

### Ruslan Iskakov, S. Seifullin Kazakh Agro Technical University

PhD, Associate Professor

Department of Agrarian Technique and Technology

### Sultanbek Issenov, S. Seifullin Kazakh Agro Technical University

PhD, Associate Professor

Department of Electrical Equipment Operation

### Аru Ukenova, L. N. Gumilyov Eurasian National University

Master of Agricultural Sciences

Department of Systems Analysis and Management

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2022-04-28

## How to Cite

Alpeissov, Y., Iskakov, R., Issenov, S., & Ukenova А. (2022). Obtaining a formula describing the interaction of fine particles with an expanding gas flow in a fluid layer. Eastern-European Journal of Enterprise Technologies, 2(1 (116), 87–97. https://doi.org/10.15587/1729-4061.2022.255258

## Section

Engineering technological systems