Methodologies for inclusion of fluid stress, added mass, and Basset history forces when modeling particle motion in a high-pressure gas jet

Methodologies for modeling forces controlling the motion of a particle in a high-pressure, time-invariant, one-dimensional turbulent jet, such as occurs in pressurized oxy-coal combustion, are examined in this work. Pressurized jet properties suggest key forces to be considered in addition to the usual drag and body forces are fluid stress force, added mass force, and Basset history force. The Basset history force, an unsteady force that is coupled to particle acceleration, is the most challenging to model. The Basset history kernel of Kim et al. is recommended for use with the specified particle and jet conditions. Equations describing these forces and specific numerical methodologies for their solution are identified and validated. The particle equation of motion is solved numerically using an Adams-Bashforth-Moulton predictor-corrector method with an explicit Adams-Bashforth step followed by one or more implicit Adams-Moulton step(s). The values of the dependent variable and its derivative at previous steps are obtained using a 4th order Runge-Kutta method. Simulated particle motion for four test conditions are shown to align well with experimental results for both a stagnant and non-stagnant fluid. The equations and numerical methods identified and validated here can be used to reliably assess the relative contributions of different particle forces acting on a particle in a dilute phase pressurized turbulent jet in future research.