Analytical free streamline solutions for geometrical cavitation inside sharp-edged and profiled nozzles

An analytical solution for cavitation inside a contracting nozzle is obtained applying free streamline theory. The present mathematical model is derived for two different geometries, representing sharp-edged and profiled nozzle shapes. The nondimensional cavity profile, width, and length are obtained as a function of the nozzle contraction ratio and the cavitation number. In addition, ideal flow assumptions and control volume theory are applied to predict the mass flow choking characteristics of the nozzle as a function of the pressure drop. This calculation is used to successfully validate the performance of the proposed model against experimental results and computational fluid dynamics calculations, exhibiting close agreement in both cases. Pressure recovery after cavity breakup is also calculated, and cavity condensation is modeled by means of a homogeneous relaxation model coupled to the pressure profile along the free streamline, allowing to graphically represent the cavity morphology. The analytical solution being introduced is therefore aimed at providing a valuable theoretical tool for the design process of injection and atomization systems, allowing to perform a quick check on cavitation occurrence.