Investigation of the Quality of the Mixture at the First Stage of Operation of a Gravitational Apparatus

Abstract

The quality of the mixture obtained after the first stage of batch mixing of loose components in the preparation of a finished mixture with a ratio of 1:10 or more is assessed, according to the proposed method of three stages and the results of stochastic simulation of the process of mixing of loose materials in a gravitational apparatus during operation of drums with screw-wound brush elements installed above the trays and with inclined bumpers. The models of the formation of rarefied torches of two types of particles in two cases were employed: (1) after the interaction with the brush elements of the layers of dosage components coming from the drum–tray gap and (2) after the impact of the incoming torches on the bumper. For the first stage of mixing, dependences of the volume and weight fraction of the key component on the reflection angles are simulated with allowance for the physical mechanical properties of the materials and the design and regime parameters of the apparatus, based on the corresponding nonequilibrium differential distribution functions for the number of particles of each component in the angle of scattering from the brush elements (case 1) and the angle of reflection from the bumpers surface (case 2). Using the proposed recurrence relation for dosage materials, the coefficient of inhomogeneity of the mixture at the first stage of mixing particulate components is calculated with the focus on the most significant factors of a quality mixing: the angular speed of drum rotation ω; the degree of deformation of brush elements Δ (the ratio of their length to the height of the drum–tray gap); and the angle of inclination of bumpers to the horizon ψ₁. Analysis of the theoretical and experimental results showed their satisfactory agreement and made it possible to reveal the most rational ranges of variation of the сhosen process parameters at the first mixing stage: ω = (45.5–47.2) s^–1; Δ = (1.48–1.52); and ψ₁ = (0.87–1.04) rad. These findings can be used in the development of the engineering methodology for calculating new gravity mixers.