The stability of viscous liquid jets in a swirling gas

Based on the linear analysis of stability, a dispersion equation is deduced which delineates the evolution of a general 3-dimensional disturbance on the free surface of an incompressible viscous liquid jet injected into a gas with swirl. Here, the dimensionless parameterJ _e is again introduced, in the meantime, another dimensionless parameterE called as circulation is also introduced to represent the relative swirling intensity. With respect to the spatial growing disturbance mode, the numerical results obtained from solving the dispersion equation reveal the following facts. First, at the same value ofE, in pace with the changing ofJ _e , the variation of disturbance and the critical disturbance mode still keep the same characters. Second, the present results are the same as that of S.P. Lin whenJ _e >1; but in the range ofJ _e <1, it's no more the case, the swirl decreases the axisymmetric disturbance, yet increases the asymmetric disturbance, furthermore the swirl may make the character of the most unstable disturbance mode changed (axisymmetric or asymmetric); the above action of the swirl becomes much stronger whenJ _e ≪1. The project supported by the National Natural Science Foundation of China