Numerical Description of Acoustic Vibrations of a Vapor–Gas–Droplet Mixture in a Closed Channel Based on a One-Velocity, One-Temperature Model

Abstract

The paper describes a mathematical model and the results of numerical calculations of resonance acoustic vibrations of a vapor-gas-droplet mixture in a closed volume under the action of periodic acoustic waves generated by a harmonically vibrating piston. The numerical method of solving the equations of the model is based on MacCormack′s scheme. The model of equilibrium phase transitions used in the numerical scheme has allowed a chart of regimes of the vapor-gas-droplet mixture vibrations to be constructed depending on the initial vapor content. In accordance with the piston vibration amplitude, the limit of the critical vapor content below which vapor condensation is impossible has been found.Introduction. In mechanical and power engineering there exist a number of processes accompanied by an acoustic effect exerted on a vapor-gas-droplet medium. Such a situation develops in the course of motion of a vapor-gas-droplet mixture in pipes and channels of cooling systems and in acoustical resonators of adjustable exhaust systems. If the frequency spectrum of an external agency, to which aeroelastic vibrations of a structure or recurrent phases of ejections of combustion products can be related, contains resonance frequencies of an acoustic system, then there appear vibrations that depend on the mixture composition. The composition, in turn, depends on phase transitions and on the temperature and pressure attained in acoustical resonators, namely, in tubes, channels, and in the bounded volumes of baffl e chambers.Numerous experimental and numerical investigations show that with resonance vibrations of a gas in tubes considerable pressure and temperature drops are achieved at the rarefaction and compression fronts of nonlinear and shock waves [1]. If a gas mixture, along with an inert gas, contains vapor and liquid droplets, then in the process of vibrations phase transitions may occur that alter the temperature, pressure, and the speed of sound in a medium and, consequently, also the parameters of the dynamic process. Experimental and theoretical investigations of the indicated processes [2-4] carried out in recent years confi rm their complex character due to the mutual imposition of the indicated effects. Investigation of the mechanisms of these processes is an urgent problem in the mechanics of multiphase systems [5].The purpose of this work was to construct a mathematical model that would allow us to describe the dynamics of a vapor-gas-droplet mixture in an acoustical resonator depending on the initial mixture composition and the characteristics of external excitation.Mathematical Model. The method of describing the dynamics of a vapor-gas-droplet mixture with account for the acoustic effect is based on numerical solution of a system of mass conservation equations of the mixture and its components and of the momentum and energy conservation equations of the mixture with regard for the mass, momentum, and energy exchange between a liquid and its vapor in the process of phase transitions [5][6][7]. Let the mixture...