Mathematical modeling of sedimentation processes and surfacing of solids, droplets and bubbles in an isotropic turbulent flow

Abstract

Relevance. The problems of separation, stratification and classification of disperse systems that constitute the base of sedimentation and phase displacement are determined by hydrodynamic structure and direction of the flow, physical interaction of forces of different nature of the systems, diffusion transport and deposition in turbulent flows, physical and chemical properties of the particles themselves and the carrier medium and many other factors. Appears the necessity of development of the model of solid spherical particles deposition from a volume with small values of number Re under the condition of absence of effects of interaction of particles and model of constrained deposition from the concentrated disperse flow. The consideration of expressions for determination of effective viscosity of the dispersed system taking into account the concentration of particles in the flow and models of particle deposition from isotropic turbulent flow taking into account the scale of turbulence and specific energy of dissipation. This, in turn, is associated with the determination of the coefficient of resistance for deformable particles (droplets and bubbles), which is used in the model of deposition velocity and surfacing of droplets and bubbles for different numbers of Weber and Morton. Purpose of work. The purpose of this study is an analytical review of all kinds of sedimentation (deposition), separation and stratification of dispersed systems and model representations of their description in different flow conditions. Methodology. To solve given problem, it is necessary to analyze all the effects associated with particle migration, deposition and separation. An essential role in deposition and migration is determined by the forces of resistance, which depend on the number of Reynolds, shape and size, as well as physical and chemical properties of the particles and the corresponding environment. Results. The study of particle deposition in an isotropic turbulent flow for different scales of turbulence in pipes and channels allowed to express the deposition rate through the main parameters of turbulence – specific energy dissipation, scale of turbulence and viscosity of the medium. The deposition and formation of a dense layer of particles on the inner surface of the pipes has a significant influence on all parameters of substance transfer (mass, heat and pulse) and on hydrodynamic stability of the flow. It has been found that the deposition of polydisperse particles is characterized by the size inconstancy or the function of their size distribution, which is related to the confinement of deposition, collision and interaction of particles among themselves. Conclusions. It is concluded that the nature of deposition of particles from the polydisperse turbulent flow is significantly different from their free deposition from the volume. As the result of dispersed particle deposition on the walls of pipes and canals, the following mechanisms and models are distinguished: free-inertial, which is based on the principle of free inertial ejection of particles to the wall; elevating-migration, which binds the deposition of particles with their elevating migration (Magnus effect); convection-inertial, which binds the deposition rate of particles with inertial effects; efficient-diffusion; turbulent-migration, where turbulent migration of particles to the wall is considered as the driving force of deposition. Particle deposition and formation of a dense layer of particles on the inner surface of the pipes has a significant impact on the hydrodynamic flow and heat-mass transfer. Particle deposition and formation of a dense layer of particles on the inner surface of the pipes has a significant impact on the hydrodynamics of the flow and heat and mass transfer. All proposed models are compared with available experimental data, which confirms their effectiveness and adequacy.