Two dimensional varicose oscillations of a plane free jet exhausting from a channel

This study concerns the plane jet exhausting from a channel in a semi-infinite space filled bounded upstream by a wall and free downstream. The flow is incompressible, viscous and two-dimensional. Varicose oscillations are superimposed on the entrance flow yielding a perturbed parabolic velocity profile at exhaust of the channel. A major hypothesis is that the problem admits axial symmetry and remains two dimensional. The Reynolds number is taken between 100 and 900. The Vortex-in Cell method is used for this simulation. It consists of following the Lagrangian paths of point 2D-vortices advected by the local velocity and diffused by random walk displacements. The stream function is updated at each time step and the velocity field is deduced. The transient state in the jet starting from rest is examined first. It is shown that the axis velocity increases in the channel and reaches the limit value of the parabolic profile for a sufficient length. It is shown that for Reynolds number lower then 500 a quasi steady states is observed. For Reynolds number greater than 500 an oscillating flow regime is observed. The jet is taken as the basic flow for studying the effect of perturbations. A sinusoidal oscillation of the uniform flow is superimposed at the entrance of the channel with a fixed amplitude and at the natural frequency observed during the transient. The flow rate variation propagates through the channel and interacts with the jet. (author)