Thrust Enhancement Through Bubble Injection Into an Expanding-Contracting Nozzle With a Throat

Abstract

This paper addresses the concept of thrust augmentation through bubble injection into an expanding-contracting nozzle with a throat. The presence of a throat in an expanding-contracting nozzle can result in flow transition from the subsonic regime to the supersonic regime (choked conditions) for a bubbly mixture flow, which may result in a substantial increase in jet thrust. This increase would primarily arise from the fact that the injected gas bubbles expand drastically in the supersonic region of the flow. In the current work, an analytical 1D model is developed to capture choked bubbly flow in an expanding-contracting nozzle with a throat. The study provides analytical and numerical support to analytical observations and serves as a design tool for nozzle geometries that can achieve efficient choked bubbly flows through nozzles. Starting from the 1D mixture continuity and momentum equations, along with an equation of state for the bubbly mixture, expressions for mixture velocity and gas volume fraction were derived. Starting with a fixed geometry and an imposed upstream pressure for a choked flow in the nozzle, the derived expressions were iteratively solved to obtain the exit pressures and velocities for different injected gas volume fractions. The variation of thrust enhancement with the injected gas volume fraction was also studied. Additionally, the geometric parameters were varied (area of the exit, area of the throat) to understand the influence of the nozzle geometry on the thrust enhancement and on the flow conditions at the inlet. This parametric study provides a performance map that can be used to design a bubble augmented waterjet propulsor, which can achieve and exploit supersonic flow. It was found that the optimum geometry for choked flows, unlike the optimum geometry under purely subsonic flows, had a dependence on the injected gas volume fraction. Furthermore, for the same injected gas volume fraction the optimum geometry for choked flows resulted in greater thrust enhancement compared to the optimum geometry for purely subsonic flows.