Evaluation of the physical forces exerted on a spherical bubble inside the nozzle in a cavitating flow with an Eulerian/Lagrangian approach

Abstract

An Eulerian/Lagrangian approach is used to calculate the physical forces acting on a spherical bubble. Reynolds average Navier–Stokes (RANS) equations for the Eulerian approach are solved with a finite volume scheme. The SIMPLE algorithm is utilized for pressure and velocity linkage. To model convective fluxes, an upwind scheme is used. The Reynolds stress transport model (RSTM) is used to calculate the turbulent parameters. In the Lagrangian approach, a modified form of the Reyleigh–Plesset (RP) and Maxey equations are solved with MATLAB programming software for evaluation of bubble motion and bubble dynamics. The carrying fluid in this study is diesel fuel. Continuous filter white noise (CFWN) is solved parallel to the Maxey and RP equations to calculate fluctuating terms of velocity in x and y directions. Six forces exerted on the bubble during its motion are investigated inside the cavitating flow regime. The cavitating regime can be extremely effective on bubble force and increase bubble forces up to several thousand times. Added mass force in the y direction has the highest value among all forces exerted on the bubble during its motion inside the nozzle.