532.529.5The unsteady azisymmetric jet produced by discharge of a mixture of a pressurized gas and dispersed particles from a circular duct into the atmosphere is studied within the framework of two-velocity, two-temperature gas dynamics. An attempt is undertaken to allow for the effective pressure due to random particle motion. The collision mechanism is found to be essential to radial expansion of the flow. Ezperimental data that support the results obtained are reported.Introduction. Development of new technologies for fire extinguishing, neutralization of toxic vapors and fluids, and protective shielding is based on pulsed ejection and spraying of disperse working media. In this connection, it is desired to establish the regularities of the two-dimensional, axisymmetric, two-phase jet formed upon discharge of a pressurized gas with dispersed particles from a circular duct of finite dimensions into the atmosphere.The present paper continues our studies [1], in which ducted flows were treated within the model of a collision-free, two-phase, gas-disperse medium. A feature of gas-dispersion flow in the out-of-duct region is that the collision mechanism plays an important part in random particle motion. This is manifested primarily in radial expansion of the two-phase jet and is supported by the experimental data reported below and results of comparative calculations using t.he collision-free model and considering the effective pressure of the disperse phase.1. Formulation of the Problem. We consider a two-phase disperse mixture of particles and a carrier phase (gas). To simplify the mathematical description of the mixture, we adopt the following assumptions [2]: the particle sizes are larger than the molecular-kinetic dimensions and smaller than the distances at which the parameters of the mixture change appreciably; the mixture is monodisperse: there are no fragmentation, aggregation or formation of new particles taking place; the gas is calorically perfect, the viscosity and thermal conductivity are manifested only in interphase interaction processes; the energy of the small-scale motion of the carrier gas is low.From a statistical viewpoint, any disperse phase can be treated as a real gas. Conservation equations for a pseudogas of particles can be derived by the classical Enskog method applied to the Boltzmann equation [3], which corresponds to the Navier-Stokes approximation for a disperse phase. Buevich [3] points to the possibility of simplifying this system of equations of motion by ignoring quasiviscous stresses and pulsation energy flux (an analog of thermal conductivity in a gas). Then, the isotropic pressure of the pseudogas of particles should be taken into account in the equation of conservation of momentum, and the specific energy of particle pulsation motion and the work done by pressure forces to compress or expand the pseudogas should be taken into account in the equation of conservation of the total energy of the mixture.
Developing new technologies of fire extinguishing based on the processes of pulsed supply of a fireextinguishing powder under the action of a pressurized gas requires a comprehensive investigation of the mechanism of such phenomena and predictions of the performances of corresponding devices.A method of supply uses unsteady discharge from a duct of a two-phase medium [1-9] (a mixture of a pressurized gas and close-packed particles that fill the duct uniformly at the initial time). Lyubarskii and Ivanov [1] report results of studies of one-dimensional, two-phase flow in an immovable duct using an equilibrium (one-velocity approximation) flow model. Lyubarskii et al.[2] studied the effect of duct recoil on the parameters of one-dimensional, equilibrium, unsteady flow of a two-phase medium from the duct. The dynamics of discharge of a gas-disperse mLxture into a gas was studied numerically by Kazakov et al. [3] and Kutushev and Rudakov [4] for disperse-phase volume concentrations a2 ~< 0.16 and a2 ~-0.7, respectively, within the framework of a one-dimensional model of a nonequilibrium, collision-free, two-phase medium as applied to the experimental conditions of [5,6]. Vorozhtsov et al. [7] and Fedorov [8] analyzed the equations describing the process of sudden ejection of coal and gas taking account of desorption. Ivanov et al. [9] studied the unsteady discharge of a two-phase medium from an immovable cylindrical duct of finite dimensions into the atmosphere in a two-dimensional axisymmetric formulation within the framework of the mechanics of heterogeneous media; they obtained an exact solution of the corresponding model problem (one-dimensional, one-velocity approximation) for a two-phase medium with arbitrary concentration of the disperse phase.In the present study, we pose two main problems: to establish the regularities of the initial stage of discharge of a two-phase disperse medium from a bounded duct capable of longitudinal motion and to examine the validity of the one-velocity flow model for the problem considered.Formulation of the Problem. Within the framework of conventional assumptions, the equations of two-dimensional plane motion of a gas-disperse medium taking into account inertial effects in flow around particles [10]
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