Calculation of coagulation of particles of the condensate in a laval nozzle

Abstract

The article presents a method for calculating the process of the coagulation of particles, resulting from different degrees of velocity lag in a nozzle, and the results of calculations carried out by the methods of Euler and Lagrange. Both methods ensure a good degree of accuracy in a numerical calculation of the change in the degree of dispersion of particles in a nozzle. The process of the collision and coalescence of the drops of a condensate, resulting from different velocity lags of particles of different sizes, with the nonequilibrium flow of a two-phase stream in nozzles, is discussed in [1–5], There are two possible approaches to a description of the change in the degree of dispersion of a system of particles, i.e., the Euler and Lagrange methods [6]. The Euler method postulates a jumpwise growth of the particles, with the collision and coalescence of two drops. In this case, for particles of a definite fraction with a mass m_i (i=1, ⋯, n), determinations are made of the decrease in the number of these particles in a unit of volume n(m_i) due to entrainment of the particles resulting from their coalescence with drops of other fractions, and of the increase of n(m_i) due to the formation of particles m_i, with the coalescence of particles of the fractions m and (m_i−m), where m=m_i. This type of model was used in [2–5] for calculating the coagulation process of particles in a nozzle. In a more complete statement, nonequilibrium flow in a nozzle, taking account of collisions, coalescence, and of the exchange of energies and momentum between particles, is discussed in [3]. The Lagrange method for fixed i-particles considers a continuous increase in the mass m_i as the result of coalescence with smaller j-drops (j=1, ⋯, i−1) and a decrease in the number of particles in unit volume n_i, resulting from their absorption by larger particles (j=i+1,⋯, n). This approach is discussed in [1]. The present article gives below a method for calculating the coagulation process of particles in a nozzle using the Lagrange method, and analyzes the results of electronic-computer calculations, carried out using both of the above-discussed methods.