Optimum Configuration of an Expanding-Contracting-Nozzle for Thrust Enhancement by Bubble Injection

Abstract

This paper addresses the concept of thrust augmentation through bubble injection into an expanding-contracting nozzle. Two-phase models for bubbly flow in an expanding-contracting nozzle are developed, in parallel with laboratory experiments and used to ascertain the geometry configuration for the nozzle that would lead to maximum thrust enhancement upon bubble injection. For preliminary optimization of experimental setup’s design, a quasi 1-D approach is used. Averaged flow quantities (such as velocities, pressures, and void fractions) in a cross section are used for the analysis. The mixture continuity and momentum equations are numerically solved simultaneously along with equations for bubble dynamics, bubble motion, and an equation for conservation of the total bubble number. Various geometric parameters such as the exit and inlet areas, the area of the bubble injection section, the presence of a throat and its location, the length of the diffuser section and the length of the contraction section are varied, and their effects on thrust enhancement are studied. Investigation on the effect of the injected void fraction is also carried out. The key objective function of the optimization is the normalized thrust parameter, which is the thrust with bubble injection minus the thrust with liquid only divided by the inlet liquid momentum. An approximate analytical expression for the normalized thrust parameter was also derived starting from the mixture continuity and momentum equations. This analytical expression involved flow variables only at three locations; inlet section, injection section, and outlet section, and the expression is simple enough to produce a quick concept design of the diffuser-nozzle thruster. The numerical and analytical approaches are verified against each other and the limitations of the analytical approach are discussed.