Mathematical Model of the Deaeration of Finely Dispersed Solid Media in a Spherical Matrix of a Roller-Type Apparatus

Anna Kapranova,Natalya Badaeva,Irina Sheronina,Mikhail Tarshis

doi:10.3389/fenrg.2021.769940

Anna Kapranova, Natalya Badaeva + Show 2 more

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https://doi.org/10.3389/fenrg.2021.769940

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Abstract

The additional operation of deaeration (compaction) of powders affects the quality of many products of chemical industries, the conditions for their delivery. Otherwise, energy consumption increases significantly. The aim of this work is the modeling of the deaeration of solid finely dispersed media in a gap with perforated hemispherical shapes on the surfaces of the shaft and conveyor belt within the framework of the mechanics of heterogeneous systems. A plane-deformation model is described, neglecting the forces of interphase interaction and taking into account the compressibility of a solid-particle-gas mixture without elastoplastic deformations. The model assumes consideration of the movement of (1) the components of the solid skeleton together with the carrying phase as a whole; (2) gas in an isothermal state through the pores of a finely dispersed material. This work is devoted to the study of part (a), i.e., behavior of the solid particle-gas system as a whole. The efficiency of the seal-deaerator is estimated using the obtained analytical dependencies for the main strength and speed indicators. The change in the degree of compaction of a spherical granule made of kaolin with given strength characteristics is investigated. It is shown that for the initial time interval up to 3.7⨯10−2 s, the growth of the porosity value relative to the horizontal coordinate along the conveyor belt is exponential and increases by a factor of 1.1. After eight such time intervals, the porosity values stabilize along the indicated coordinate with an increase of more than 1.4 times from the initial value.

Highlights

Preliminary deaeration of powder components (Akiyama et al, 1986; Kapranova and Zaitzev, 2011; Francis, 2016), including soot and kaolin, affects the strength characteristics of the finished product, for example, car tires, and other polymer products
For the initial time interval ( t0 ≤ t < t1 3.7 × 10−2 s), the growth of α(21) (Figure 2A) relative to the horizontal coordinate along the conveyor belt is exponential and increases by 1.1 times. After eight such time intervals, the porosity values stabilize along the indicated coordinate with an increase of more than
It is noted that the porosity of the finished granule-sphere at the final stage of deaeration in the described gap of the conveyor shaft with a spherical matrix almost uniformly reaches its limiting value

Summary

Introduction

Preliminary deaeration (compaction) of powder components (Akiyama et al, 1986; Kapranova and Zaitzev, 2011; Francis, 2016), including soot and kaolin, affects the strength characteristics of the finished product, for example, car tires, and other polymer products. The design of roller devices for the deaeration of dispersed media is associated with the formation of theoretical foundations (Kapranova et al, 2000; Kapranova, 2010; Kapranova et al, 2015) for the engineering calculation of the parameters of these devices (Kapranova et al, 2001; Kapranova et al, 2006a; Kapranova et al, 2006b) This is relevant in the manufacture of granules (Zaitsev et al, 2010) from bitumen (Santos et al, 2014; Fingas and Fieldhouse, 2009) and mineral powder (Renner et al, 2007). The importance of understanding the mechanism of the behavior of compacted materials is obvious for any type of modeling methods: analytical (Kapranova and Zaitzev, 2011; Kapranova et al, 2015; Udalov et al, 2019) or numerical (Khoei, 2005; Pizette et al, 2010; Bayle et al, 2016; Seong et al, 2020)

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