Linear and nonlinear dynamics of swirl injectors
Abstract
The dynamics of a classical swirl injector has been studied using a linear analytic model and a nonlinear computational model using the boundary element method (BEM). A methodology was developed to compare the responses of both these models. The existing linear inviscid analytical model has been amended to account for additional wave interactions arising from two rows of channels within the vortex chamber. As expected, such an injector has better overall stability characteristics. A perturbing chamber pressure boundary condition was incorporated along with a more accurate integration of mass flow at the exit plane in the BEM code. The amplitude and phase response for various operating frequencies are studied. A linear stability analysis of an infinitely long annular swirling liquid sheet with an outer wall and inner gas core was performed to study the growth of small disturbances on the liquid surface. It was validated by introducing simplifying constraints and comparing it with the classic Kelvin-Helmotlz solution for wind over water. Trade studies show that surface tension is a stabilizing force when Rossby number is greater than unity. The effects of swirl, velocity ratio and density ratio are also examined. However, results indicate that this type of wave growth plays no part in the dynamics of a realistic swirl injector under consideration whose operating conditions are beyond the range wherein such a phenomenon would occur. The linear and nonlinear dynamics of swirl injectors are characterized for various frequencies. Although the injector does not show any nonlinear behavior there is a deviation from the linear model results after a certain frequency. A thorough analysis indicates that this phenomenon is dependent on the axial momentum of the liquid. It is theorized that this is associated with the flow turning from the inlet channels into the vortex chamber. Also the effect of oscillating chamber pressure boundary condition on the dynamics of the classic swirl injector is small and an analysis that assumes a pulsed mass flow gives nearly identical results.
Degree
Ph.D.
Advisors
Heister, Purdue University.
Subject Area
Aerospace engineering
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