Vortex Ring / Wall Interactions

Have you ever seen someone blow smoke rings? Have they ever aimed those rings at a flat wall? Smoke rings are probably the most commonly seen form of vortex ring, although if you allow a drop of cream to fall into a glass of water while watching it from the side or top, you'll see a vortex ring form there, too.

We have a somewhat more complex vortex ring generator, but it has the advantage of producing exactly the same vortex ring each time the solenoid valve is opened.

The dimensions in the diagram above all in (cm) except where noted. When the valve is opened, a 6 cm slug of fluid is ejected from the vortex ring tube. The slug is short enough so that it is not influenced by the valve or bends upstream - all of the fluid originates entirely within the terminal straight portion of the tube. The vortex ring finishes forming after the valve closes, then it convects downward at approximately 5 cm/s. A solid, flat wall is placed normal to the axis of the vortex ring tube, and when the ring encounters the wall, a very interesting interaction takes place.

These pictures are the result of using two different colors of laser dye in the flow facility: a green dye (disodium fluorescein) was put in the vortex ring generator, and a very thin line of a red/orange dye (rhodamine-B) was injected along the wall before the experiment started. In this way we can track fluid which originated in the tube (green), fluid which started out near the wall (red), and fluid from elsewhere in the facility (black) throughout the course of the experiment.

As the ring approaches the wall (a), it starts to flatten out and expand radially. At the point of closest approach (b), the unsteady boundary layer separates, and fluid is entrained into a developing secondary vortex. The original, or primary, vortex ring interacts very strongly with this secondary vortex ring (c), while producing a tertiary ring as well (d). In our experiments when a stable vortex ring interacts with a wall that is 3 diameters or less away from the tip of the vortex ring tube, the secondary and tertiary vortex rings rebound so strongly that they actually travel up and out, toward the top of our tank (e).

We used the vortex ring / wall interaction as our testbed during the developmental phase of Molecular Tagging Velocimetry (MTV) , a new non-intrusive experimental technique for measuring velocities in fluid flows. The tank into which the vortex rings were shot contains 120 liters of fluid, which allowed for a great deal of inexpensive experimentation, especially when compared to using our 10,000 liter water tunnel for technique development!

The ideal velocity field associated with a vortex ring is quite simple along the center line of the experiment: The radial velocity component, labelled ``v'' in the adjacent plot, should remain zero all of the time, while the downward velocity component, labelled ``u'' in the figure, should smoothly rise to a maximum and then fall. One way we verified that MTV measurements have low uncertainties is by considering the u- and v-velocity components at many different points on the center line of many different experiments; one representative pair of these time traces is shown in the figure above. As you can see, the v-velocity component remains within 0.125 cm/s of zero, while the u-velocity component smoothly rises to a maximum then falls back to zero as it ought.

Numerous experiments and simulations have confirmed the fact that we can consistently estimate the displacement of molecularly tagged regions to within +/- 0.1 pixel. We generally configure our experiments to give a 15 pixel maximum displacement, so a typical MTV experiment has a dynamic range of 150:1, and 30 or 60 velocity fields are acquired per second.

The velocity field shown in the adjacent figure corresponds to the flow field at t=1.57 sec (part (a) in the color figure above). The rotational behavior of the core is well captured, in addition to the stagnation flow at the wall along the axis of symmetry. These are raw data; all of the vectors are shown, no ``bad vectors'' have been removed, and the results have not been smoothed in any way.

If you would like to see animations of MTV velocity data taken during the intake stroke of an I.C. engine, click here for velocity vectors + vorticity contours , and click here for a close-up of just the velocity field near the valve. These results are courtesy of Dr. Bernd Stier . (NOTE that you won't see animated data if you are using an older web browser like Mosaic 2.7b4.)

We have published some articles on the topic of vortex ring/wall interactions which you might find of interest:

C. P. Gendrich, M. M. Koochesfahani, and D. G. Nocera (1997) Molecular Tagging Velocimetry and Other Novel Applications of a New Phosphorescent Supramolecule. Experiments in Fluids, 23(5): 361-72.

C. P. Gendrich, D. G. Bohl, and M. M. Koochesfahani (1997) Whole-Field Measurements of Unsteady Separation in a Vortex Ring / Wall Interaction. Presented at the 28th AIAA Fluid Dynamics Conference, Snowmass, CO, June 29 - July 2, 1997, AIAA Paper 97-1780.

M. M. Koochesfahani, R. K. Cohn, C. P. Gendrich, and D. G. Nocera (1996) Molecular Tagging Diagnostics for the Study of Kinematics and Mixing in Liquid-Phase Flows. Plenary presentation at the Eighth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, July 8-11, 1996: pp. 1.2.1 - 1.2.12.

C. P. Gendrich, M. M. Koochesfahani, and D. G. Nocera (1994) Analysis of Molecular Tagging Velocimetry Images for Obtaining Simultaneous Multi-Point Velocity Vectors. Bull. Am. Phys. Soc., 39(9): 1980. Presented at the APS /DFD 47th Annual Meeting, Atlanta, GA, November 20-22, 1994.

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