Analysis of compressibility effects on multiscale cavitating flow in the nozzle using Eulerian-Lagrangian method

Abstract

A compressible two-way coupling Eulerian-Lagrangian (E-L) method is developed to investigate the compressibility effects on multiscale cavitating flow inside a nozzle. The compressible Navier-Stokes (N-S) equations and compressible Rayleigh-Plesset (R-P) equation are introduced to fully describe compressible effects. Compared with the traditional incompressible E-L method, the compressible E-L method more accurately simulates the characteristics of unsteady cavitating flow, including cavity shedding frequency, mean cavity length and bubble size distribution. Results show that compressibility exacerbates the instability of cloud cavitation, causing macroscopic cavities to break into microbubbles more frequently, further increasing the number of bubbles and expanding their distribution. Further analysis reveals that compressibility effect amplifies mid- and high-frequency bands of pressure fluctuations, especially in the cavity tailing region where only discrete bubbles exist. Additionally, the compressible E-L approach avoids the problem of pseudo-pressure pulsation caused by computational simplification in the incompressible E-L approach. The variation of velocity divergence is driven not only by water-vapor mass transfer but also by density changes in compressible cavitating flow. The temperature distribution indicates that low temperature always exists inside the attached cavity due to evaporation and heat absorption. Strong temperature fluctuation, reaching up to 1.5 K, occurs during the upstream movement of the re-entrant jet and the cavity shedding process. The Mach number distribution illustrates that transient supersonic flow appears only in the wake of the attached sheet cavities and at the shedding cloud interface. These findings provide deeper insights into the multiscale cloud cavitation instability induced by compressibility effects.