In the continuum approach to problems of geologic mechanics, the ground surrounding a deformation zone is replaced mathematically by an idealized material that deforms in accordance with principles of continuum mechanics. Studies published to date have been rather few in number and have often followed a methodclogy characterized by restrictive material property and boundary condition assumptions. In order to avoid these difficulties, emphasis in this paper is given to modern numerical methods. Discrete-element formulations of matrix structural analysis are shown to be particularly useful, inasmuch as they are adaptable to solutions of systems characterized by nonlinear anisotropic materials, heterogeneously distributed, containing internal discontinuities, and of arbitrary topographic or internal boundary configuration.
Large centrifugal forces of rotational flow are used in hollow cone nozzles to form a thin liquid film in the outlet, which disintegrates into relatively small droplets. The flow in the nozzle can be calculated by means of simple physically meaningful balances, based on the cyclone theory. The influence of wall friction is taken into account via a wall friction coefficient which depends on the Reynolds number of the nozzle flow. The break-up mechanism of the liquid film was investigated under the consideration of nozzle outlet velocity and film thickness as well as gas and liquid properties. With increasing velocity and film thickness, a transition from aerodynamic wave break-up to turbulent atomization was observed to take place. Equations presented in this paper allow the calculation of mass flow rate, pressure drop and drop size distribution of hollow cone nozzles with any given geometry.
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