Recently, a colleague and I took a design of experiments class at work. The following is the report of the project we did for the class.
Introduction
A fire whirl (also known as a
fire devil or fire tornado) occurs when a whirlwind (also known as a dust
devil) develops in the presence of a fire.
In such instances, the fire acquires a vertical vorticity and forms a
whirl, or tornado-like vertically oriented column of fire. (1) Fire whirls can be created in a laboratory
setting using a turntable, a cylindrical screen, and a burner. The cylindrical screen on the spinning turn
table creates a vortex, and the burner provides the fire. Compare pictures of a natural and laboratory
fire whirl, below.
Figure 1: Natural Fire Whirl (1)
Figure 2:
Laboratory fire whirl
Objective
The objective of this experiment
was to determine the factors that most influence fire whirl height. The following two level factors were
investigated: screen diameter (small/7” and large/10”); screen height (short/18”
and tall/36”); screen material (aluminum and fiberglass); turn table speed
(slow and fast); and burner lighter fluid brand (Kent’s/Western Family and
Lowe’s/Kingsford). These factors were
investigated using a 5 factor / 1 block / 16 run Box, Hunter & Hunter
designed experiment. The test runs are
summarized in Table
1,
below.
Table 1: Test runs for DOE
Set Up
The set up of this experiment consisted
of assembling and constructing various items.
Three of the five factors were related to the cylindrical screens. Each factor had two levels. Thus, eight cylindrical screens of various
diameters, heights, and materials were constructed and are shown in Figure
3,
below. Another factor was burner lighter
fluid brand. Two brands were
investigated, so two burners were used. Each
burner consisted of lighter fluid soaked rolled corrugated cardboard positioned
in a tin can. One of the burners, two
brands of lighter fluid, and burner snuffer are shown in Figure
4,
below. The complete test fixture,
consisting of a wooden turntable with brackets securing a cylindrical screen and
burner is show in Figure
5,
below. Flame height measurement was facilitated
via a measuring tape positioned adjacent to the turntable, as show in Figure
6,
below.
Figure 3: Fiberglass (left) and aluminum
(right) cylindrical screens
of two heights and two diameters used in
DOE
Figure 4: Burner, two lighter fluids, and
snuffer
Figure 5: Turntable with cylindrical
screen and burner installed
Figure 6: Measuring tape installed next to
cylindrical screen
Procedure
The test procedure was as
follows:
1.
Install the specified cylindrical screen on the
turntable brackets
2.
Charge the burner with the specified lighter
fluid*
3.
Install the burner in the turntable brackets
4.
Light the burner
5.
Spin the turntable at either fast or slow rates**
6.
Measure the peak flame height three times by
visual inspection***
7.
Stop the turn table and snuff the burner
*It is noted that the burners
were not recharged or charged equally for every test run. The burners were initially charged with their
respective lighter fluids, and then recharged only occasionally, between
runs. The burners were never exhausted,
and the volume of fluid not controlled.
**The turntable was spun at
either a fast or slow rate, as determined qualitatively by the operator. One operator performed all the tests to
reduce variation.
***Flame height varied during
burn time, even after the turntable spin rate seemed to achieve a steady state. Peak flame height was record by visual
inspection three times during the course of a test run. Each measurement of a given test run was
separated by a few seconds.
The fully assembled test fixed
with lit burner on the stationary turntable is shown in Figure
7,
below. The same assembly with lit
burner, but on the spinning turntable is shown in Figure
8,
below. Note the difference in flame
shape and height.
Figure 7: Stationary turntable with
burning and cylindrical screen
Figure 8: Spinning turntable with burning
and cylindrical screen
Results
The results of the experiment are
shown in Table
2, below. Columns 6 through 8, labeled “Run1,” “Run2,”
and “Run3,”correspond to the three height measurements (in inches) taken for a
given test case. The median of the three
“runs” is shown in column 9.
Statistical Analysis
A statistical analysis of the
data was performed to determine the significance of the various factors. Since each test case was only run once
(subgroup size of one), A Priori Pooling is used to separate signals from
noise. Using this method, some of the
contrasts are combined in order to obtain a Mean Square Error (Within) term. (2) The signs of each confounding group are shown
in Table
3,
below. Because the subgroup size equals
one, no interactions were used.
Table 3: Correlation matrix
The estimated contrast effects
are shown in Table 4,
below. As can be seen, all of the p
values are much larger than 0.05, suggesting none of the effects are
significant.
Table 4: Effect estimates
An ANOVA table is presented in Table 5,
below. This table presents much of the
same information as the previous table.
As with the previous table, the p values for the various factors are
listed. All p values are much larger
than the threshold 0.05 value, indicating none of the factors are significant.
A normal probability plot of the
estimated contrast effects is shown in Figure 9,
below. A normal probability plot is used
to make a relative comparison. Instead
of plotting the sum of squares values, a normal probability plot plots the
estimated contrast effects. These
effects are computed for every contrast, arranged in rank order, and plotted
versus the appropriate percentages on a normal probability chart. Normal probability plots have the property
that a random sample drawn from a normal distribution will yield a straight
line, more or less. (2) Thus, the fact that the data point for this
experiment fall more or less in a straight line suggests none of the effects
are significant.
Figure 9: Normal probability plot of
effects
A scree plot for this experiment
is shown in Figure 10,
below. A scree plot plots the sum of
squares for each contrast in descending order of magnitude, and connects these
points to form the profile of a cliff.
(In the chart, below, the cliff is rotated 90°.) A significant effect would be much taller
than the noise. In this case, none of
the factors stand out significantly, and all fall below the p=0.05 criterion for
significance.
Figure 10: Scree plot of the effects
Discussion
This statistical analysis of the
experimental data suggests that none of the factors have a significant effect
on flame height. While cylindrical
screen height and turntable rotation speed came closest to being significant
factors, both failed to meet the p=0.05 criterion. Thus, one could conclude that flame height is
a function of some other factor, or that the experiment was flawed. Possible flaws in the experiment include
flame height measurement technique, burner lighter fluid charging, turn table
speed, and subgroup size. These items
are discussed below.
Flame Height Measurement
Flame height, the
measured response of the system, was determined by visual inspection. Inasmuch as the flame height fluctuated
widely and rapidly during burn time, employing a videographic system to capture
and assess peak flame height would improve the fidelity of the
measurement. Also, decreasing the
ambient light during the test period may improve the measurements.
Burner Lighter Fluid Charging
In retrospect, it is
hypothesized that the amount of available lighter fluid in the burner is a
significant factor in flame height. The
significance of all other factors could be masked or confounded due to this
single uncontrolled factor. Weighing
each burner before each test run to verify the initial mass / amount of
available fuel is the same every time, would have allowed for a true study of
the significance of lighter fluid, as well as improved the fidelity of the
other data.
Turntable Speed
The turntable was
manually spun at either “fast” or “slow” rates, per the test matrix, with rates
gauged qualitatively by the operator.
While there was an observable difference between the two spin rates,
employing a mechanical system to spin the turntable in a repeatable and steady
manner may increase the ability to determine the significance of this factor.
Increasing Subgroup Size
A subgroup size of
one was used for this experiment to minimize the total number of runs. However, because there was only one observation
per test, 2- and 3-way interactions were not assessed. Adding additional observations would allow
for the affects of interactions to be estimated.
Addressing these or other flaws in the experiment could
result in an improved understanding of the factors that impact flame
height. Additionally, other factors could
be included in the experiment. The
computational work of Battaglia et al. (3) and others
could be queried for additional insights on key factors. While our experiments failed to reveal the
key factors, others have, experimentally, computationally, or otherwise,
determined design parameters such that fire whirls are available commercially,
as discussed in the following section.
Commercial Fire Whirls
Fire whirls are marketed
commercially as patio heaters and displays.
Some of the commercially available fire whirls are driven by electric
exhaust fans while others are naturally aspirated. Most produce the fire whirl within tubes of
borosilicate glass. See the images,
below for examples of the commercially available fire whirls.
Figure 11: Lava Heat fire whirl (4)
Figure 12: Vortex Fires fire whirl (5)
Works Cited
1. Fire whirl. Wikipedia. [Online] April 2,
2012. [Cited: April 10, 2012.] http://en.wikipedia.org/wiki/Fire_whirl.
2. Wheeler, Donald J. Understanding Industrial Experimentation.
Knoxville : SPC Press, Inc., 1990. ISBN 0-945320-09-4.
3. Fire Whirl Simulations. Battaglia, Francine, et al.
Gaithersburg : NIST United States Department of Commerce Technology
Administration, 1998. http://fire.nist.gov/bfrlpubs/fire98/art079.html. NISTIR
6242.
4. Starfire Direct. Lava Heat Patio Heater. Starfire Direct. [Online]
2012. [Cited: April 10, 2012.]
http://www.starfiredirect.com/lava-heat-patio-heater-p-965.html.
5. Moderustic Inc. Home. Moderustic Vortex Fires. [Online]
2011. [Cited: April 10, 2012.] http://www.vortexfires.com/Home.html.
