The time-dependent method of the computational fluid dynamics is applied to solving the 2-dimensional axisymmetric Navier-Stokes equations, and the flowfields of the 2-dimensional axisymmetric annular supersonic air-ejectors are simulated. Based on the previous work, the balance mechanism of the blind-cavity is considered and the effect of the second-flow on the ejected vacuum is discussed. It's found that the existence of second-flow has an important effect on the flowfield structure of the ejector, and that in comparison with the zero-second-flow condition, a little of the second-flow will reduce the ejector vacuum remarkably.