A Numerical Investigation of Impinging Jets

Steady, incompressible flow solutions are found numerically for a radially expanding liquid sheet in order to confirm analytical results for inviscid flow and to investigate viscous and nonlinear effects. An hp-finite element method is used to perform the numerical simulations. Comparisons are made to theoretical predictions of the radius where the sheet becomes unstable. To determine the critical radius, the inlet Weber number is slowly reduced until the critical radius is within the simulated domain. This causes the sheet to change from a symmetric shape to an asymmetric stable shape. Simulations are run for sheets with liquid Reynolds numbers of 25, 50, 100, and 200, liquid-to-gas density ratios of 32, 160, and 800, and liquid-togas viscosity ratios of 12.5, 25, and 50. These parameters have little effect on the critical sheet radius; It always remains near the point at which the Weber number based on the sheet thickness is one, confirming the theoretical work of G.I. Taylor. We also perform unsteady simulations with forced sinuous pulses at the sheet inlet. We observe that the pulses cause two different speed waves to travel downstream for Weber numbers greater than one. We also witness wave deceleration for Weber numbers less than one, confirming the predictions of inviscid linear stability analysis.