Mathematical modeling of operating process and technological features for designing the vortex type liquid-vapor jet apparatus

Abstract

The article discusses the design features of vortex type liquid-vapor jet devices in the form of an oblique cut-off nozzle of the motive flow while entering the vortex chamber. Mathematical modeling allows proving the influence of the oblique cut to a deflection of the flow from the nozzle axis by a certain angle. This model is based on a continuity equation in the modified Baer’s form for the adiabatic process of discharge from the expanding nozzle with an oblique cut, as well as on the fundamental laws of thermodynamics for operating process. The proposed mathematical model allows determining the analytical dependence between the deflection angle of the flow from the nozzle axis in an oblique cut for an expanding nozzle and the following geometrical and physical parameters: The oblique angle of a nozzle, the taper angle of a nozzle, the initial pressure in front of the nozzle, the medium pressure at the outlet of the nozzle, the maximum nozzle expansion, and physical properties of the flow. The results of mathematical modeling of the flow deflection in an oblique cut of the expanding nozzle are presented analytically and graphically. Finally, it is proposed the methodology for numerical calculations of geometrical and operating parameters for ensuring the proper operating process, as well as it is described the technological features for designing the vortex type liquid-vapor jet apparatus.