MAE 434
Pure Axial Vortex Characterization
Krystal Dillon, Trevor Davis, & Kristen Patrick
Date of Submission: December 8th, 2011
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Abstract:
The purpose of this experiment is to measure the static pressure distribution and the
velocity field in the core of a pure axial vortex (Landman). The vortex will be created in the
ODU Low Speed Wind tunnel using a custom vortex generator involving two wings. The
students will design the vortex generator and assist in the wind tunnel testing.
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Table of Contents:
Introductions…………………………………………………………...………………………….4
Proposed Approach………………………………………………………………………………..5
Organization…………………………………………………………….………………………..13
Cost Consideration……………………………………………………………………………….15
Summary………………………………………………………...……………………………….16
Appendix:
List of References……………………………………………………..…………………17
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Introduction:
Vortices are a naturally occurring phenomenon. One such instance is a tornado. Tornados
create a pressure drop, which storm chasers constantly use instruments to measure (Edwards,
2011). According to Bernoulli’s theorem, a vortex should cause a reduction in pressure. The
largest pressure drop being found in the core of the tornado. The theorem is an equilibrium
relation of the dynamic and static pressure of the fluid at two comparative states. In a vortex,
there is an increase in the velocity of the fluid flow. It is often difficult to accurately measure the
pressure drop in a real tornado. This is due to the fact that often times the instruments are
damaged at the time of measurement (Edwards, 2011). Some of the measurements are much
larger than that which would be predicted using Bernoulli’s theorem. Therefore, to try and
replicate some of the measurements seen from real tornados, this project will attempt to create an
axial vortex in a controlled environment.
Wing tip vortices off of two wings will be used in a wind tunnel to create the axial vortex
(Landman). A pressure transducer will be used to measure the pressure drop across the vortex.
From there, a Particle Image Velocimeter may be used to measure and model the velocity of the
flow in the vortex.
The objective of this project is to create a computer model of the dual wing vortex
generator, calculate the amount of load acting on the generator, assist in test design, and assist in
testing (Landman). It is anticipated that the benefits of the results can verify that the actual
pressure drop that occurs in a vortex is greater than what is predicted by Bernoulli’s theorem.
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Proposed Approach:
The vortex generator works by utilizing the principles of finite length wing aerodynamics. The
interaction between two wings at opposing angles of attack is the general cause of the creation of
the vortex, but before this can be explained the airflow around one wing needs to be understood.
When a wing is subjected to airflow with a positive angle of attack, or the angle between the
centerline of the airfoil and the direction of the airflow, a force called lift is applied to the wing.
The force is the result of the pressure differences between the top side of the wing and the
bottom side. With a positive angle of attack, the pressure on the underside of the wing is high
and the pressure on the top side is low. This results in an upward lift. Because this is a wing of
finite length, there are airflow effects at the tip of the wing. The air at high pressure under the
wing wants to flow towards the low pressure air above the wing, so there is an inherent flow
around the tip of the wing from the bottom to the top. (Shown below)
Figure 1: The pressure difference between the top and bottom side of the wing results in lift.
This flow around the tip causes the air to move in a circular motion. As the freestream airflow
moves past the wing (or the wing moves through the free air), the air that gained the circular
motion momentum continues to move in circular motion behind the wing, creating what is called
a trailing wingtip vortex.
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The reason that one wing cannot be used as a vortex generator is that a single trailing
wingtip vortex is very erratic and does not travel in a uniform axial line behind the wingtip. For
this reason, the model being used in the experiment had to be designed to align a vortex in an
axial direction behind the model.
The vortex generator being used for this experiment has been adapted from a design used
in a NASA experiment originally done by Promode R. Bandyopadhyay (Bandyopadhyay, Stead,
Ash, 1990). The generator consists of two wings with finite length using the NACA 0012 airfoil
profile. These two wings are to be set at opposing yet equal in magnitude angles of attack of 4, 6,
8, and 10 degrees. The “tips” of these two wings are at the center of the model (rather than on the
outermost points) and are separated by a flow aligned cylinder. The trailing wingtip vortices
produced by these two wings will appear behind the center of the model. Since the two wings are
at opposite angles of attack, the direction of the circular flow of each vortex will be the same,
creating one strong vortex behind the model. The flow aligned cylinder works to combat the
erratic nature of trailing vortices. The trailing vortex initially wraps around the cylinder and is
aligned into an axial flow direction that is kept constant behind the cylinder, creating a single
pure axial vortex. Effects from the wake of the cylinder are minimal and can be neglected
because the wake is dissipated before the vortex is fully formed.
The vortex generator is going to be mounted in the high speed test section of the ODU
low speed wind tunnel (shown on the following page).
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Figure 2: The ODU Low Speed Windtunnel
The model is 3 feet in length and will be mounted vertically in the test section. The experiment
will be run with wind speeds of no more than 40 m/s.
The main goal of the experiment is to measure the static pressure distribution inside the
vortex created by the model. In order to do this, a cylindrical probe with two self cancelling
static pressure taps is to be manufactured and used (Landman). This probe is able to measure
static pressure even if the airflow is not linearly aligned up to 20 degrees in either direction. This
is because as the airflow strays from the nominal direction, one tap sees an increase in pressure
and the other an equal decrease in pressure. Taking the average of the two tap readings will give
the static pressure. This probe will be installed in the ODU wind tunnel, which has several
pressure measurement acquisition modules with an accurate range for this probe. How this probe
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will be mounted and moved within the tunnel has not yet been determined. Picture of probe
design is shown below.
Figure 3: The cylindrical pressure probe that will be used to measure the static pressure
distribution. (Landman)
To create the vortex we are going to duplicate the wing design from AIAA 90-1625: The
Organized Nature of a Turbulent Trailing Vortex (Bandyopadhyay et al.,1990). The design is
shown in figure below
Figure 4: The wing design used in The Organized Nature of a Turbulent Trailing Vortex report.
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First we had to find a material that could run through the wing that would be strong enough to
handle the forces created from the wing. In Figure () you can see the shear and moment diagrams
for how much force the rod will need to handle.
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Shear (lbs) and Moment (in-lbs)
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Sh…
5
0
0
3
6
9
12
15
18
21
24
27
30
33
36
-5
-10
-15
Figure 5: The Shear and Moment diagram based on lift.
Then we used stress calculations to find that a steel rod could run through the wings and be able
to support the load while having a large factor of safety. Then we duplicated the image from the
report into Solid Works. We made a few changes from the original design to make it easier to
machine and to make it fit our experiment better. The new wing will consist of ten different
components. There will be a steel rod that will run through the whole system. There will be a
brass tube to support the wings and make it possible for the wings to rotate about the steel rod.
The wings are going to be NACA 0012 and will be of foam and will have aluminum ends. The
two pieces will be attached together with a fiber glass cloth with resin. The aluminum end will
have a hold placed that will be used to set the angle of attack. There will be a flow aligned
cylinder made of aluminum that will between the two wings. To mount the wings to the wing
tunnel that will be a mounting plate that will be set in the wind tunnel and it will hold the steel
bar and have holes to put the wings at the necessary angle of attack. A spring pin will be used
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between the mountain plate and aluminum wing end to set the angle of attach. Then we will
other little necessary parts to make the parts stay together. In Figure () you can see the assembly
drawing of apparatus that will be mounted in the wing tunnel.
Figure 6: The assembly drawing of the vortex generator.
Sample Calculations of the stresses that will be on the beam:
Airfoil – 0012
Angle of attack, α = 10°
Span, b =17.5 in
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Chord, c = 4 in
Thickness, t = (12%)*c = (0.12)*(4 in) = 0.48 in
ρ = 0.00237 lbs*s2/ft4
Vmax = 40 m/sec = 1.3123(102) ft/sec
Aspect Ratio, AR =
Note:
CL = (CLα)*(α)
Where
Where
(Dynamic Pressure)
Solve for L to get the amount of Lift acting on the wing.
Steel Rod:
d
d = 0.3125 in
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For Angle of Attack, α = 10°, where L = 7.5 lbf and Mmax = 16.4063 lbf*in:
For Carbon 1144 Stressproof Cold Drawn Round (Steel Rod)
Sy = 100,000 psi (www.onlinemetals.com)
Factor of safety:
Brass Tube:
OD
ID
OD = 0.375 in
ID = 0.315 in
For Angle of Attack, α = 10°, where L = 7.5 lbf and Mmax = 16.4063 lbf*in:
For Brass Tube Brass (C260 Cartridge Brass):
Sy = 52,200 psi (www.onlinemetals.com)
Factor of safety:
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Organization:
The majority of tasks will be a collaboration between all team members. The team leader of the
project is Trevor Davis. The Solidworks (Computer Modeling) specialist is Krystal Dillon. The
stress calculations portion is being led by Kristen Patrick. Bellow can be found a table of the task
list. The Gantt Chart (or timeline of the project) can also be found below in figures 4, 5, and 6.
Task:
Duration:
Start Time:
Research & Planning
21 days
Modeling
14 days
Stress Calculations
Ordering, Manufacturing, & Receiving
Material
Assembly
Design and Manufacture Pressure Probe
Testing
Analysis & Report Writing
14 days
10/20/2011
8:00
11/18/2011
8:00
11/18/2011
8:00
27 days
10 days
25 days
30 days
17 days
12/8/2011 8:00
1/16/2012 8:00
1/9/2012 8:00
2/13/2012 8:00
3/26/2012 8:00
Table 1: Task List
Figure 1: Part 1 of the Current Gantt Chart (Current as of 12/8/11)
End Time:
11/17/2011
17:00
12/7/2011 17:00
12/7/2011 17:00
1/13/2012 17:00
1/27/2012 17:00
2/10/2012 17:00
3/23/2012 17:00
4/17/2012 17:00
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Figure 2: Part 2 of the Current Gantt Chart (Current as of 12/8/11)
Figure 3: Part 3 of the Current Gantt Chart (Current as of 12/8/11)
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Cost Consideration:
Below is an itemized budget of the materials that must be purchased for the
project. Note there is a miscellaneous section that is to account for shipping, taxes,
and unknown expenditures that may occur while completing the project.
Item:
Quantity: Unit Price:
NACA 0012 Wing (4 in Chord, 17.5 in Span)
Brass Tube (60 in Length, 0.375 in OD, 0.315 in ID)
Carbon 1144 Stressproof Cold Drawn Round
0.3125" Diameter, 48" Length (Steel Rod)
Aluminum 2011-T3 Bare Cold Finish Round 0.5" D,
24 in Length
Aluminum 6061-T651 Bare Plate (8 in x 8 in sheet,
0.5 in thick)
18-8 Stainless Steel Key Stock Undersized (1/8" x
1/8", 12" Length)
One-Piece Clamp-on Shaft Collar Black-Oxide Steel,
5/16" Bore, 11/16" OD, 5/16" W
18-8 Stainless Steel Slotted Spring Pin 1/8"
Diameter, 1/2" Length, Packs of 100
Total:
2
$45.00
$90.00
1
$7.99
$7.99
1
$4.31
$4.31
1
$4.82
$4.82
1
$19.76
$19.76
1
$2.08
$2.08
2
$1.74
$3.48
1
$4.48
$4.48
Miscellaneous (Shipping, Tax, etc.)
$30.00
Total:
Table 2: Budget
(www.McMaster.com; www.Onlinemetals.com)
$166.92
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Summary:
In order to create a pure axial vortex, a vortex generator design has been adapted
for the ODU Low Speed Wind Tunnel and is in the manufacturing process due to
be completed by the start of the Spring 2012 semester. The current focus of the
Senior Design students' experiment is to assemble the model, manufacture a
pressure probe, and run wind tunnel tests so that pressure data can be analyzed by
the end of the semester.
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Appendix:
References:
Edwards, R. (2011, October 29). The Online Tornado FAQ. Retrieved December 4, 2011, from
http://www.spc.noaa.gov/faq/tornado/
Landman, D., Pure Axial Vortex Characterization. Retrieved November 30, 2011, from
http://www.mem.odu.edu/ugrad/designproject_pure_axial_vortex.pdf
McMaster-Carr. Retrieved December 4, 2011, from www.mcmaster.com
OnlineMetals.com and plastics too!. Retrieved December 4, 2011, from www.onlinemetals.com
Bandyopadhyay, P., Stead, D., and Ash, R. AIAA 90-1625: The Organized Nature of a Turbulent
Trailing Vortex. 1990.