Abstract
Flowing soap
films presented them self a viable means to conducting an array
of hydrodynamic experiments. The two dimensionality of films and
self visualization properties of soap film offer a unique
opportunity to study truly two dimensional turbulence. Our aim
is to find an experimental arrangement that can yield uniform
flow
conditions and serve as our experimental apparatus for a detail
study of counter flow shear layer. We wish to ultimately compare
our experimental findings with the latest
numerical and computational discoveries to evaluate current
models. We have evaluated different set-up and alteration to
their geometry to arrive at our final deign which has granted us
favorable results. We documented our work and present them on
this site, along with discussion of related concepts and plans
future work. A brief introduction is given on
shear layer instability span and why soap films are used in experimental fluid dynamics. Then
an
overview of the key contribution to evolution of soap film
experiments is offered. Our laboratory efforts in
developing a robust flowing film with the goal of conducting
counter flowing shear layer
experiment are reviewed. A discussion on the difficulties we
encountered with the different arrangements, and path to our
final design is also given. We have found that soap are
inexpensively implemented, but can be temperamental and very
sensitive to controllable parameters. This can make the
development of an experimental rig frustrating at times, but
when ideal conditions are achieved the results are phenomenal.
Introduction
The physics
of fluid motion and the transition from laminar to turbulence
remanded as one of the unsolved problems in physics, making the
investigation of fluidic phenomenon a hot topic.
In order to further our understanding of the
mechanisms that govern fluid flow and affect engineering
applications, theoretical work has to be applied in conjunction
with experimental and computational studies.
Fluids
are exceptionally difficult to study experimentally because of
the difficulty in observing the inherent motion of fluids. This
issue arises due to the fact that fluids are usually transparent
or of uniform color. Fluids also have the tendency to develop in
three dimensions meaning that typically they must be held in a
container. These complications can be circumvented by seeding
particles in the flow to visualize the development of
streamlines. Ample effort has gone into the study of fluid flow
using of more conventional wind tunnel and water tunnel
experiments, but these cases are difficult to model and
implement. The elimination of one flow direction (degree of
freedom) can simplify the conditions and allow comparison to the
simplified numerical computer model. This gives us a starting
point from which we may expand our understandi g. The
experimental method that we have adopted has unique physical
properties that make running fluidic studies simple, cost
efficient, self containing and easily visualized. To gain some
insight into the general case researchers study simpler cases
which are easier to model. Our method to doing this
experimentally is to use flowing soap films, which are
essentially the walls of soap bubbles which flow thru a channel.
Soap bubbles are very thin film, essentially a two dimensional
surfaces, which when flowing behave as a two dimensional fluid.
The molecular properties of soap films create color variations
on the soap film's surface which represent thickness variation
created by disturbances in the flow. This gives soap film
brilliant flow visualization ability; coupled with their two
dimensionality make soap films a formable tool for the study of
fluids. Soap films provide a novel and inexpensive approach to
investigating 2D fluid instability. Experimental studies can
serve as a supplement to undergraduate course work giving
students a deeper understanding of the physical concepts learned
in class. The level of difficult and the complexity of operation
and design of fluid dynamic experiments can limit the
involvement of
undergraduate student in experimental work .The
simplicity of the use of flowing soap films tunnels make them
appropriate for an undergraduate research projects, and that the
same time soap films are a powerful tool for running fluid
dynamic experiments. The prim goal of our experimental work is
to construct a counter-flowing shear layer experiment through
the use of soap films.
Kelvin- Helmholtz
instability is very important in the context of transition to
turbulence. Kelvin Helmholtz instability arises from shear- layers,
acquiring when two parallels flows at different velocities meet. The
differences in velocity between the layers cause shearing in the
contact layer resulting in a mixing region with high vortices. There
are two kinds of shear layers, co-flowing and counter flowing shear
layer. They create the same instabilities, but they differ in the
manner that they develop. For instance co-flowing shear, which are
two parallel flows traveling in the same directions, develops in
space and are periodic in time. On the other hand counter flowing
shear layer, which are two parallel flow move in opposite direct,
develops in time and are periodic in space. These condition can be
remarkable replicated with soap film tunnel and test can be run on a
truly two dimensional system. Two dimensional models for this
instability can be assessed with experimental data acquired for the
soap film scenario. The fact that counter flowing shear is periodic
in space makes the computation lest cumbersome because a smaller
special domain can be use for the simulation. Shear layer have many
engineering applications including per-combustion mixing, jet noise
reduction, scram jet combustion and trust vectoring. Shear layers
can also be seen in nature, in atmospheric and oceanic flows.
Fig 1) The different experimental
set-up used, Y. Couder Rectangular frame (Top left), Goldburg's
vertically Flowing design (Right), Gharid Horizontal water jet
design (bottom left).
Gharid (fig[1]) later developed a water jet propelled soap
film for flow visualization.
With this design one draws a soap film from a solution
reservoir, and then proceeds to run it along horizontal supports and
onto a sheet of moving water. The flow of the water sheet and the
surface tension difference between the water and the soap film
drives the film forward. This difference in surface tension limits
the maximum speed to about 30cm/s and the film thickness to about 6
micrometers.
In the mid- 90's Goldburg, Kellay and others developed a
gravity propelled soap film tunnel. It consisted of a reservoir of
solution that dispensed solution through nozzle onto two wires. The
wires are then separated to creating a bubble between them. In this
set up there is little control over the flow speeds and the solution
does not spread evenly over the guide wires creation non-uniform
flow conditions. This bubble would flow down under the pull of
gravity. This method produces fast flowing films that can attain
speed up to several hundred cm/s. This method was then improved on
by the use of nozzles to spread the solution evenly across the
wires. The wire would come out of the nozzle then expand to the
width of the test section and then contract into a lower reservoir.
This arrangement is affected more by air drag because it produces
faster flowing films.
Fig 2) The molecular make up of the soap film bilayer geometry.
Soap films have
long fascinated our youth, and provided them countless hour of
enjoyment. This fascination has translated in to a general interest
in govern properties of soap films. Many researchers have study soap
films for physical and geometrical properties. Soap solution or
surfactants, have particular molecular structure which given them
the ability to take the shape of a film. Surfactant molecules have
hydrophilic heads (water seeking) and hydrophobic tails (water
fearing) fig2. When they dissolve in water they tend to settle at
the free surface. This reduces the surface tension of the solution
and allows for the creation of soap bubbles or films. With out the
surfactant the liquid films would be unstable and burst in to
droplets. As a result of its molecular composition, soap films are
made of three layers fig 2; two layers of soap molecules separated
by a layer of solution. This interior layer replenishes the outer
layer when they thin due to evaporation and controls any local
thinning that can lead to rupture.
The distance between these layers is usually very small
and on order of an integer multiple of the wave length of visible
light.
This allows interferences between light reflect off the
top and bottom surface of the soap film fig3. This interaction
between these two light waves cause destructive and/or constructive
interference creating vivid color variations (bright colors
represent wavelengths experiencing constructive interference). This
interference changes depending on the thickness of the film,
creating different interference patterns for different thickness
variations. The thickness of the soap film is a scalar and can be
thought as being concentration of substance in a fluid. Differences
in the films thinness that arise when the bodies that inserted in
the flow cause disturbances in the flow are analogous to the
differences in concentration of fluid under the same condition. This
property of soap films to display thickness variations as color
fingers allow for good qualitative observations.
Fig 3) Light wave interference that create the thickness dependent
color variations.
The approximation
that soap films are 2D is appropriate, however damping effect of the
surrounding air on the development of turbulent vortices can be
considerable at times. This can add to the damping effects on the
films internal viscosity and complicate the determination of the
Reynolds number which is essential for the understanding of the flow
condition.
If the air drag becomes substantial the flow can no longer
be consider be consistent with the Navier-Stokes equations. There
are ways to reduce the influence of air drag on the film, the use of
slow moving and thicker films, rather then thinner and fast moving
ones can reduce this effect. An extremely effective but expensive
method for eliminating the influence of air drag is to enclose the
apparatus in a vacuum chamber. Soap films are also relatively
inexpensive to implement in experiment and easy to analysis.
Although soap
films are prim candidate for the study two-dimensional
incompressible flow, soap films can also demonstrate properties
analogues to compressible fluids. A flow is considered a
compressible flow if the change in Density of the flow with respect to Pressure is non-zero and in general this occurs in Mach numbers approaching or exceeding 0.3 .
Compressible flow is governed by the gas dynamics equations, and
while soap doesn’t travel at should high speed, under some condition
they can still behave in a manor consistent with the gas dynamics
equations. The presences of wave propagation in soap films and their
behavior being consistent with gas dynamic equation can allow soap
films use in conducting compressible fluid dynamics experiment. Soap
films have considerable potential for study two-dimensional fluid
flow and growing implication for there use in Experimental
compressible fluid dynamics.
Our ultimate goal
is to develop an arrangement that combination two flowing films
moving in opposite directions, with a removable barrier separating
them. This barrier is removed once the films are flowing and the
counter flowing shearing that arise between the contacting flows can
observation. In order to accomplish our goal of constructing a
counter flowing shear layer experiment we first had to evaluate the
different approaches to see which can provide the desirable results.
We started with the horizontal water jet-propelled soap film which
was developed by Gharid. We had some luck with this approach but it
had its pitfalls. This approach to flow visualization was plagued by
its short observation periods. The films were unstable due to the
horizontal section of the set up, which is susceptible to
evaporation. The film would also tend to burst from evaporation.
The pulling force of the reservoir was another problem
that needed to be resolved. The water jet pulled the film in the
flow direction and the water tension force from the reservoir pull
the film in the opposite direction. This would cause a stretching in
the film and if these forces did not reach equilibrium they would
ultimately burst the film.
Fig 4) The test on the water jet set-up with different nozzle
geometry.
Fig 5) Test on the effect that solution concentration has on the
bursting of the films
Fig 6) Our counter flowing shear layer design.
Gravity propelled approach provide a more
robust films that is more resilient to sudden bursting. The constant
"down hill" flow that gravity propelled films provide meant that the
film didn't have to fight gravity to flow out of the reservoir as it
does in the water jet set-up. Starting with Goldburg's design at
first, then implementing some alterations to his design we
investigated the optimal geometry that would produce the best
results. Our set-up was a vertical to horizontal arrangement and
this was selected because it was more appropriate use in counter
flowing experiment fig 6. The counter flowing experiment requires
two flowing films, which flow against each other, so two purely
vertical films wouldn't work. There could be no way to get one of
them to flow up against gravity. We use telephone poles made out of
copper rods as the support for the horizontal section and fish wires
as guide line for the film (Refer to fig 6). Like the horizontal
setup, we found some pitfalls to the gravity propelled design. The
expanding section in this design would cause undesirable fringe
patterns in the flow and turbulent flows near the guide wires fig 7.
These patterns were caused by differences in thickness of the film,
which in turn would make the film undesirably too 3D. The flow would
separate from the wires in the expanding section and caused
instabilities in the test section.
Fig 7) Turbulence Along the guide wires
There was also a band
of very thick film in the center of the test section. For very fast
flow rates the film would display shock wave down the center of the
flow, this is an example of soap films behaving in a compressible
manor fig 8. This effect was well documented by
Fig 8) Soap film behaving in a compressible manor
The finger pattern were final removed
when we went to a lower soap concentration, the test we ran on the
water jet set-up showed that lower concentrations reduced the
thickness of the films and lengthen the run times. Although we
weren't having issues with the run times with the gravity propelled
approach, reducing the thickness of the film reduce the effect of
air drag and lessen the turbulence in the test section. This coupled
with bigger nozzles and the alterations to the expansion angle gave
us high level of uniformities in the test sections. Once uniform
thickness was achieved we preceded with demonstrating wake flows and
fluid instabilities. We inserted a cylinder in the flow to observe
the different wakes that are formed at varying Reynolds numbers fig
9 . Then we observing grid turbulence by inserting a com in the flow
fig 10. We observed the characteristic reverse energy cascade that
accurse with the grid turbulence. By placing a wall in the flow we
created Kelvin-Helmholtz instability and observing the down stream
development fig 11. We tried other flow scenario and documented the
results with photographs.
Fig 9) The wake of a cylinder in the flow
Fig 10) Grid Turbulence produced by a com up stream
Fig 10) Kelvin
Helmholtz instability
Our work with the different experimental
arrangements we have obtained optimal flow conditions and wish to
capitalize on this and expanded the experimental program. If we can
produce quantitative date comparison can be made between expected
baseline data to prove the validity of our apparatus and the
comparison to computational studies can be made.
Although we found that the a lower concentration worked
best for the water jet arrangement, the effect of nozzle shape and
soap concentration aren't well known for the gravity propelled film.
More systematical test need to be run to discover how
these variables affect the flow condition. It has also been
suggested that household nondairy creamer helps with the
visualization of thickness. This is something that deserves more
detail investigation. We have discovered that soap films can be used
for compressible fluid dynamic experiments and therefore a study
should be done on what solutions and additives create behavior
resembling compressible fluids.
The empirical relationship between the vortex frequency
and other quantities can be tested to see the validity and
creditability of our soap films experimental rig. The effect of a
down stream object on the reduction of interactions between vortices
and vortex shedding can also be test to improve engineering design.
We are currently perusing the use of PIV (particle imagine
velocomitry) for gathering qualitative data. The PIV systems are use
to measure instantaneous velocity of the fluid. In this method of
measuring the fluids velocity a high energy light source is used to
illuminate the particles which are seeded in the flow. Then digital
images of the flows are captured with the time between exposures
being held constant. Using the fact that the time elapsed between
images is constant, the distance vectors that connects a particular
particles in successive can be used to calculate a velocity vector
for that particle. This vector field is created with the aid of
computer programs. Besides this vector field one can reliably
obtained such as vortices field, thickness measured by diffuse light
scattering, pressure fields, Reynolds stresses and other
important quantities. The quantities can be to show weather a
particular model can adequately predict the flow.
The counter
current shear layer is of the most interest to us
because it takes fewer computations to simulate and because of it's
applications in thrust vectoring and per combustion mixing. This
comparison between experimental and theoretical find can help
further our under standing of the dynamics of fluid motion. The
experimental study of 2D flow mechanisms have greatly importance in
engineering design, oceanic and atmospheric understanding. Soap
films have been nominated as a new tool for 2D fluid dynamics, both
for compressible and uncompressible flows.
Soap films experiments are a great vehicle for the
furthering of theory and understanding in fluid dynamics because of
their compact, low cost and novel designs. There is numerous ways to
implement soap film for the study of 2D fluid flows and they present
a more affordable approach then there more high tech counter parts.
These qualities make soap film experiment very adaptable and an
ideal introductory experiment for a being experimentalist.