Three-dimensional structure of confined swirling jets at moderately large Reynolds numbers

Abstract

We have performed a series of three-dimensional (3D) numerical simulations of the incompressible flow discharging from a rotating pipe into a coaxial static cylindrical container through a sudden expansion. We have considered several values of the Reynolds number based on the pipe flow rate ReQ between 50 and 300, and an expansion diameter ratio of 8, and have analyzed the emerging 3D flow structures in the swirling jet exiting from the rotating pipe as the swirl parameter S is increased. The results are compared to axisymmetric numerical simulations of the same problem. Three-dimensional, nonlinear instabilities are found in the swirling jet when ReQ≳98 above a critical value of S, which depends on ReQ, that obviously do not appear in the axisymmetric simulations. These nonlinear instabilities are initially triggered by the linear instabilities inside the rotating pipe, which are already present in the pipe from a much lower value of S, and are transformed in the jet. As S increases further, there exists another critical value above which the swirling jet undergoes vortex breakdown, producing a flow in the jet which is basically axisymmetric. This critical value of the swirl parameter for breakdown is significantly larger than that found in the axisymmetric simulations. Thus, one of the main results of the present work is that 3D instabilities delay the formation of vortex breakdown in the jet, in relation to the same axisymmetric flow, but once the vortex breakdown phenomenon occurs, the 3D instabilities coming from the rotating pipe appear to be suppressed in the jet, and the swirling flow becomes basically axisymmetric again. Finally, the axisymmetric simulations show that the jet becomes unstable to axisymmetric perturbations, when ReQ≳188, above another critical value of S. However, these axisymmetric instabilities do not appear in the 3D simulations because the flow becomes unstable to asymmetric perturbations at much lower values of S.