Theoretical model of swirling thick film flow inside converging nozzles of various geometries

Pressure-swirl jets are of paramount importance in such applications as liquid rockets, gas turbines, and internal combustion engines. Although the external spray has been extensively studied, the internal nozzle flow, which determines the external spray characteristics outside the nozzle, is relatively underexplored. Experimental studies of the internal nozzle flow are available, whereas theoretical approaches are less common, especially for strong swirl flows in which the boundary layer effect at the nozzle walls is significant. Herein, we explore a strongly swirling film flow, where viscous effects become dominant in the entire film and the boundary-layer approximation fails. The parabolized Navier-Stokes equations are solved by using the integral von Karman-Pohlhausen method, and the viscous liquid film flow over the entire nozzle wall is predicted including the central free surface configuration, the film characteristics such as its thickness, velocity components, and the spray cone angle, at the nozzle exit. The theoretical predictions are compared to the experimental data, and the dependence of the spray-cone angle on mass flow rate is experimentally validated. The theoretical parametric studies include the effect of the internal nozzle geometry, initial film thickness, the mass flow rate, and the effect of the swirling strength.