Consider an ordinary funnel (click here for an illustration) one might use in the kitchen for cooking. If you blow in at the funnel's orifice what would you expect the flow to be at the exit of the large opening of the funnel?

To visualize the result hold a lit candle up against the large outlet of the funnel at its centerline. You will need a mirror (or a colleague) to see the rather astonishing result. Results may vary, so try it a couple of times. Remember, hold the candle right up against the funnel rim.

Displaying the simulation of this behaviour is the object of this Web page.

It turns out that this apparently simple problem has subtle 3d, time dependent behavior. Capturing these results computationally is not simple.

2 Dimensional Simulation

Since the geometry is cylindrically symmetric we start with a 2D, cylindrically symmetric model.

Velocity(z) Plot shows a jet along the centerline axis

Animation (side view; inlet air shown in red)
(0.59 MByte Quicktime animation)

The result of this simulation does not agree with what we see experimentally (telling us that the flow is not 2 dimensional).

2.5 Dimensional Simulation

The next step was to run the model in 3 dimensions, but make use of symmetry to model just the right half of the system. Thus, all motions in 3 dimensions are not allowed. We call this a 2.5 dimensional simulation. The blue plume in the plot and animation is air traveling back toward the nozzle of the funnel.

Mesh

Plot of Two Velocity(z) Isosurfaces

Animation (face on; inlet air shown in red)
(0.80 MByte Quicktime animation)

Animation (isoparametric view; inlet air shown in red)
(0.60 MByte Quicktime animation)

This result agrees well with the what is often seen experimentally. It includes an initial outward puff followed by an inward motion that would reverse the direction of the candle flame.

3 Dimensional Simulaion

After the encouraging results with the 180 degree model, we expand the computational domain to a full 360 degree model. Now all motions are available. Again the blue plume in the plots and animations is air traveling back towards the nozzle of the funnel.

Plot of Two Velocity(z) Isosurfaces (after 1 second)

Plot of Two Velocity(z) Isosurfaces (after 1.68 seconds)

Plot of Two Velocity(z) Isosurfaces (after 2.5 seconds)

Animation (face on; inlet air shown in red)
(2.20 MByte Quicktime animation)

Animation (isoparametric view; inlet air shown in red)
(1.14 MByte Quicktime animation)

Now we see a highly time dependent motion with the jet gyrating and moving in many directions. The direction of flow at the candle flame switches many times toward and and away from the funnel nozzle. This is sometimes seen experimentally.

Comments

The 2-D animation shows the jet (inlet air) in red, and the original air previously in the system in blue. Other colors are a mixture of inlet air and air previously in the system.

Displaying the flow field in 3-D is more difficult than for a 2-D flow, and thus is presented a bit differently. The 3-D animations show two evolving "plumes" to trace the development of the flow field. The red plume is an isosurface with the z-velocity component equal to 1.0 Meter/sec (note: z = 0 at the inlet; z = 0.12 Meters at the funnel outlet). The blue plume is an isosurface with z-velocity equal to -0.1. Therefore the red plume encapsulates air that is traveling away from the inlet and the blue plume encapsulates air that is traveling toward the inlet.

Experimenting with different funnels demonstrates that the phenomena illustrated by the candle flame is not very sensitive to the details of the funnel geometry for a fairly broad range of sizes and shapes. The results can be rather sensative to the details of how the air is blown into the funnel.

Fluid dynamics is often counter-intuitive. That's why we experiment and simulate.