Modeling and calculation of dispersed media flows in a channel with rapid expansion in the presence of nucleation, coagulation and phase transitions

Abstract

Background and Objectives: In practice, there are often processes in which in the initial state the working medium is single-phase, for example, in the form of gas (steam), and during the process under study conditions are created for the appearance of a new phase in the form of droplets (nuclei). The process of nucleation and further condensation growth of clusters in supersaturated vapor is one of the most important processes leading to the development of the dispersed phase. The liquid phase nuclei that appear as a result of nucleation are quite small (nano-sized) and, therefore, subject to Brownian wander, which leads to their mutual collisions and coagulation. The processes of evaporation and condensation in various media are used to obtain nanomaterials (in particular, in the synthesis of carbon nanotubes), as well as to obtain nano- and ultradisperse particles in expanding channels due to nucleation and their condensation and coagulation growth. Materials and Methods: Using a quasi-equilibrium model based on the equations of mechanics of multiphase media, the flow of a dispersed mixture in a channel with sudden expansion in the presence of processes of nucleation, coagulation of nuclei (clusters) and phase transitions (evaporation, condensation) in a two-dimensional formulation was studied. The homogeneous nucleation model is used to describe the nucleation process. It is assumed that the process of coagulation of clusters occurs due to their Brownian motion. To determine the rate of phase transitions, the Hertz – Knudsen – Langmuir formula is used. The problem of the flow of a gas-dispersed mixture in a channel with sudden expansion in a twodimensional formulation is considered. It was assumed that in the narrow part of the channel, under certain conditions, nuclei of the dispersed phase continuously appear, which enterthewidened part ofthe channelwiththe flow. The calculationswere carried out based onthe algorithm of the numerical “large particles” method, which is based on splitting the original equations into physical processes. Results: As a result of the study, the basic properties of the flow of a two-phase mixture in a channel in the presence of nucleation, coagulation and phase transitions have been established. It has been shown that the flow has a vortex structure, and the largest particles are formed precisely in the vortex zone. Calculations have established that the coagulation process has a fairly strong effect on the distribution of cluster sizes inside the channel. The influence of the degree of steam supercooling on the flow of the dispersed mixture in the channel has been studied and it has been found that this parameter significantly affects the density distribution of the dispersed phase. The flow pattern obtained using calculations is consistent with experiment. Conclusion: The basic properties of the behavior of the mixture parameters along the expanding channel at presence of nucleation, coagulation and phase transitions have been established. The results obtained can be useful in various areas of modern technology: when designing various heat-power and heat-exchange installations, for studying the process of outflow of various mixtures from containers, for modeling the processes of formation and growth of nuclei (in particular, nanoclusters) in saturated media, etc.

Keywords

• channel
• dispersed medium
• nucleation
• coagulation
• phase transitions
• clusters
• quasi-equilibrium model
• large particles method