Transition map for vortex rings over an axial rod

Abstract

Vortex rings are one of the most robust and fundamentally important fluid-structure in vorticity dominated flows. The rolling up of a slug of fluid mass, impulsively pushed out of an orifice, is generally stable. Owing to proposition of many applications of such flows, in the present study, an attempt has been made to characterize the nature of formation of vortex rings formed due to orifice in the presence of an axial rod. Experimental investigations are carried out to find the conditions under which the generated vortex ring is initially laminar or turbulent for various parameters. The results are used to draw a transition map pointing out the regions of different flow behavior. Keywords—Vortex Rings, transition map, cylindrical rod evolution. These disturbances grow in amplitude and subsequently lead to the breakdown of the vortex ring. In the light of Glezer's work on transition map for vortex rings, the present study is concerned with understanding the role of different exit geometry, i.e., an annular hole in a plane, in affecting their formation characteristics. We delineate the conditions for the formation of initially laminar or turbulent rings for the exit geometry similar to that of Lucey et al. To this effect, an experimental study of formation of a vortex ring in the presence of an axial rod is carried out in order to assess the effectiveness of operation of such vortex generators. II. Experimental Arrangement The apparatus used for generation of vortex ring in a controlled manner is shown in Fig. (1). A tank of square cross section, measuring 0.5 m by 0.5 m, and 2 m long is divided into two compartments. The plate is placed at a distance of 0.5 m from one end forming the driving section. A flat rectangular piston is attached to one of its ends. The other compartment is used as the test section for observing the formation of vortex rings and its further dynamics. This arrangement facilitates in leaving all electronic equipment outside the testing region in order to prevent undesired air motion produced by them. A thick polystyrene sheet is used as the piston, which is attached to and driven by a loudspeaker (100 W). The piston almost fits the walls of the chamber with the gaps sealed using flexible polythene strips. This allows a smooth and unobstructed motion of the piston against the walls without rubbing on its surface, at the same time, ensuring a leak proof arrangement. The loudspeaker is driven by a forcing signal that is first synthesized and stored in the non-volatile memory of an arbitrary function generator. This moves the connected piston which in turn displaces a slug of air volume through an orifice. A TTL trigger signal from the NI-DAQ (NI USB 6210) card is used to trigger the signal generation which is then amplified by a power amplifier and fed to the speaker.