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Courtesy of David Schmidt, University of Massachusetts
Water droplets in the shower are shown colored by velocity magnitude.
Filled contours of pressure are indicated on the shower curtain.
Assistant professor David Schmidt from the University of Massachusetts
has been puzzled by the annoying tendency of shower curtains to billow
in during a shower and stick to the leg or arm of the person attempting
to bathe. An expert in modeling sprays and jet breakup, Schmidt decided
to use some of his custom spray models in FLUENT to analyze this conundrum.
Professor Schmidt was a founder of Convergent Thinking LLC, a software
firm that models sprays, particularly in turbulent or combusting environments.
Convergent Thinking is a Fluent partner, and the spray models are available
for use with FLUENT software. Of particular interest is the Taylor analogy
breakup, or TAB model, which is used to describe the breakup of a jet
into successively smaller drops. Based on an analogy between an oscillating
droplet and a forced mass-spring system, the model has been shown to accurately
predict experimentally observed jet and drop breakup mechanics.
Longstanding theories have attributed the shower curtain behavior to
a combination of two phenomena: the chimney (or buoyancy) effect, and
the Bernoulli effect. Because of buoyancy, the heated air inside the shower
rises, and cooler air from outside the shower is entrained below the curtain
to fill the void left by the rising air. Since the shower curtain has
been found to billow even during cold showers, this effect is believed
to account only partially for the curtain behavior (or not at all). According
to Bernoulli's equation, the static pressure in a fluid decreases
as the fluid velocity increases. Comparing the driven air flow inside
the shower (as a result of momentum transfer from the shower spray) with
the stagnant air outside, the pressure is lower inside the curtain than
outside it. This pressure differential would account for the curtain movement,
independent of the temperature of the water.
Velocity vectors show the movement of air in the shower. In addition to
the drag-induced motion in the vicinity of the shower, there is a large
recirculation pattern above it.
Using the TAB model, Schmidt created a 3D model of his mother-in-law's
shower, where the curtain was well known to exhibit the offending behavior.
The coupled flow of water droplets and air in an isothermal environment
revealed some surprising results. In particular, the inside air, driven
by the shower spray, was found to form a vortex with its axis normal to
the plane of the curtain. The low pressure at the center of the vortex,
reminiscent of the low pressure at the center of a hurricane, was found
to be lower than that caused by the Bernoulli effect alone. While it is
cert ainly a combination of the vortex, Bernoulli effect, and buoyancy
that lead to t he curtain behavior in a hot shower, Schmidt's results
suggest that the vortex motion is the dominant factor that drives this
phenomenon.
The shower curtain deflection shown here (not to scale) was computed using
a force balance.
"Until now, it has been one person's word against another's,"
Schmidt said. "I thought that it would be fun to use FLUENT to say
more definitively what the effect was. The air moves in a stable circle
just like a dust devil indoors. Unlike a dust devil, however, the shower
vortex doesn't die out because it is continuously driven by the shower.
Anyone can test my model. The best way to see it is to turn on the shower
– cold water will do fine. Use a light, thin shower curtain and a
strong showerhead. Stand outside the shower, stick your head in, and blow
in smoke. You will see how the vortex is driven by the water droplets."
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