Mathematical modeling and calculation of minimum gas energy for dispersing liquid into drops

Column devices of chemical technology with regular nozzle elements are widely used in conducting heat and mass transfer processes and cleaning waste gases. The basis for the operation of these devices is the dispersion of the treated liquid into droplets using the kinetic energy of the ascending gas flow. The paper considers a two-phase flow with a low concentration of droplets, and the plate attachment elements are arranged regularly along the axis of the vertical contact device. The research method is based on mathematical modeling of the process of liquid dispersion by gas using the discovery of academician Balabekov O.S. on the multi-stage interaction of flows and structural elements when gas flows around symmetrically arranged packing elements. The main condition for the beginning of liquid dispersion is the predominance of the kinetic energy of the gas over the potential energy of the liquid jet flowing down. Therefore, the goal is to determine the lower bound of the kinetic energy value, at which a stable operating mode of the device is realized. To find the components of the kinetic energy of a gas, it is proposed to find the components of the gas velocity from the numerical solution of the Navier-Stokes (laminar regime) and Reynolds (turbulent regime) equations. In this case, the entire length of the contact device is considered as a set of initial and stabilized sections. An algorithm for the numerical solution of the Navier-Stokes equations in Helmholtz variables in a two-dimensional formulation has been developed. By implementing this algorithm, distributions of current and vorticity functions for the entire length of the channel are found and they are used to calculate the minimum kinetic energy of a gas sufficient to start the process of liquid dispersion into droplets. Using the values of the gas velocity and the kinetic energy of turbulent pulsations, an inequality is proposed that also uses information about the physico-chemical parameters of the liquid and the dynamic characteristics of the gas. The use of this inequality makes it possible to reduce the number of field experiments to determine the parameters of the operating mode and the size of the operated and newly created mass transfer devices. The found estimate can also be used to optimize the geometric dimensions of contact devices, design and calculation of structures of mass transfer devices for the organization of specific processes.