Paper ID #21525 Integrated Teaching Model: A Follow-Up with Fundamental Aerodynamics Dr. Sidaard Gunasekaran, University of Dayton Sid is an Assistant Professor at the Mechanical and Aerospace Department at the University of Dayton. He got his MS and Ph.D. at the University of Dayton as well. During his doctoral studies, Sid developed a knack for teaching using modern pedagogical practices in mechanical and aerospace classes and engaged in diverse research in Low Reynolds number flows. Sid is an active participant in the Dayton/Cincinnati American Institute of Aeronautics and Astronautics (AIAA) section. c American Society for Engineering Education, 2018
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Paper ID #21525
Integrated Teaching Model: A Follow-Up with Fundamental Aerodynamics
Dr. Sidaard Gunasekaran, University of Dayton
Sid is an Assistant Professor at the Mechanical and Aerospace Department at the University of Dayton.He got his MS and Ph.D. at the University of Dayton as well. During his doctoral studies, Sid developed aknack for teaching using modern pedagogical practices in mechanical and aerospace classes and engagedin diverse research in Low Reynolds number flows. Sid is an active participant in the Dayton/CincinnatiAmerican Institute of Aeronautics and Astronautics (AIAA) section.
Once again, welcome to the Fundamental Aerodynamics class. The idea behind this homework is to get
you start writing your portfolio and start thinking about the subject of aerodynamics. It also gives me an idea of
what you already know about the subject. This homework is intentionally abstract and open-ended as advertised
in the syllabus. Please be descriptive in your answers as opposed to one line/one sentence answers. More often
than not, you will get questions like these along with solving numerical open-ended problems. I strongly believe
that by practicing this kind of problems, you will become better thinkers and learners. Always remember that for
numerical or abstract problems, I don’t care much about you getting the “right” answer. I care more about the
approach you take to solve a problem. So focus on the approach. You can turn in the homework via Isidore.
1. Title Page
Please begin your portfolio with a title page. (You can have a content page. However, it is optional.)
2. Setting Big Picture Context
Before you start your portfolio, it is very important to set a big picture context as to why we are doing this. Please
provide a brief reflection on (not necessarily in order)
1. Your goals, aspirations and your interest in the field of aerospace engineering
2. Why are you taking this class in the first place?
3. What are you hoping to learn from this class?
4. How do you think this class helps you in your academic and professional career?
(You don’t have to retype these questions in your portfolio. Your narrative should have answers to these questions.)
3. Questions to Answer in Portfolio (50 Points)
(The three questions posed below, will make a good introduction to the subject of aerodynamics in your portfolio.
Once again, you don’t have to answer these questions in order. Your general narrative should contain answers to the
following questions. Please be descriptive in your answers. Provide enough pictures, graphs, tables, etc.)
1. Select three different applications of aerodynamics we discussed in class. Based on what you know and what
you are aware of, provide a brief description of the role of aerodynamics in each application. Think about the type
of flows experienced by those applications and list the dominant flow parameters (Ex: Pressure, Friction, Lift,
etc,) acting on those objects.
2. What do you think are the similarities and differences among the aerodynamics of insects (Ex: dragonflies),
birds, airplanes, and rockets? Think about the mechanisms used to generate lift, drag and thrust forces in these
applications and talk about how they generate those forces.
3. You will be using a lot of math in class and it is probably good to refresh on some of the basic concepts. Explain
*clearly* what dot product, cross product, divergence, and gradient mean when applied to a scalar and a
vector. I AM NOT LOOKING FOR JUST EQUATIONS. YOU HAVE TO EXPLAIN WHAT THEY MEAN IN PHYSICAL
SPACE. Also, provide one application for each where you use/apply those operators.
4. Provide Global Reflections on the First Week of Classes and Homework 1 (15 Points)
Page 23 of 44
Homework 2
Due: Tuesday 1/31/2017
Dear students,
This homework should get you to think about calculating coefficient of lift, drag, and pressure. Mainly
focusing on the coefficient of pressure. Pretty soon, you will be able to generate the Cp distribution by yourself.
But before that, you should be comfortable dealing with pressure coefficient and understand the significance of
it. That’s what this homework is about. We are building tools and skills required so that we can move forward
with actual simulation.
1. Questions to Answer in Portfolio (85 Points)
(Your general narrative should contain answers to the following questions. Please be descriptive in your answers.
Provide enough pictures, graphs, tables, etc.)
1. To continue from where you left off from the previous homework, state briefly why should we care about
aerodynamic coefficients? You don’t have to explain each and every coefficients in detail but you have to provide
evidence to show WHY coefficients are important.
2. We discussed in class that just by looking at the variation of Coefficient of pressure, you can tell a lot about the
aerodynamics around any object. Give a brief explanation on coefficient of lift. As an example, please look at the
Coefficient of Pressure contours of a D-8 double bubble design and the pressure coefficient of blended wing body
in the power point slide. Based on the pressure coefficient, explain the aerodynamics around these configurations.
In your opinion, which of these configurations produce better aerodynamic efficiency?
3. Please see attached pamphlet on the CGS Hawk Light Weight Sport Airplane. If you read the content, you will
see that the airplane uses semi-symmetrical airfoil when compared to flat-bottom airfoil used in other light-
weight sport airplanes.
1. Run an XFOIL analysis (tutorial given in slide) to determine the pressure distribution on a semi-
symmetrical NACA 2412 airfoil and a flat bottom Clark Y airfoil at the same angle of attack and at the cruise
Reynolds number (consider sea level). Compare the coefficient of pressure distribution between the two
airfoils and find out what advantages you get by having a semi-symmetrical airfoil over a flat-bottom airfoil.
2. According to the given specifications on the sheet, what would be the velocity at which the airplane will
have the longest range? Clearly state the rationale behind the approach you took to solve the problem.
Perform “sanity” check on the answer you get.
(Fun fact: The entire airplane costs around $25000. And with a 15 mph head wind, the airplane could stand still
in air. The pilot even said he was able to fly backwards which stunned some of the F-16 pilots!)
FOR GRADUATE STUDENTS ONLY
4. Consider a circular cylinder in a hypersonic flow, with its axis perpendicular to the flow. Let 𝜙 be the angle
measured between radii drawn to the leading edge (the stagnation point) and to any arbitrary point on the
cylinder. The pressure coefficient distribution along the cylindrical surface is given by 𝐶𝑝 = 2 cos2 𝜙 for 0 ≤ 𝜙 ≤
𝜋/2 and 3𝜋/2 ≤ 𝜙 ≤ 2𝜋 and 𝐶𝑝 = 0 for 𝜋/2 ≤ 𝜙 ≤ 3𝜋/2. Calculate the drag coefficient for the cylinder, based on
the projected frontal area of the cylinder.
2. Provide Global Reflections on the Second Week of Classes and Homework 2 (15 Points)
Page 24 of 44
Page 25 of 44
Homework 3
Due: Tuesday 2/7/2017
Dear students,
This homework should get you started on documenting the literature review for the passion projects. We
will be discussing equations of fluid motion in class today and this homework will give you some experience in
dealing with the equations of fluid motion. These equations are universal and can be applied to almost any fluid
system. You should have some background to these equations from your fluid dynamics class. This homework
will be a good review for you to apply some of the equations, which can give you important aerodynamic
parameters.
1. Questions to Answer in Portfolio (70 Points)
(Your general narrative should contain answers to the following questions. Please be descriptive in your answers.
Provide enough pictures, graphs, tables, etc.)
1. First step in any experimentation is doing a literature review because it will give you a broad background on
the application you are looking at. Document the relevant information you gathered from different resources you
reviewed for your passion project 1. Based on your literature review and independent study, discuss the relevant
aerodynamics involved in the application you will be working on. You have to include relevant graphs, tables,
figures, etc to support your narrative.
2. Momentum equation is one of the most powerful equation in fluid dynamics because applications of it are
endless. Say you are tasked with finding the drag coefficient of a new airfoil design. You don’t have a force balance
to measure the drag force directly. But you found a velocity profile equation in the wake of a similar airfoil from
the literature. Can you estimate the drag coefficient using that velocity profile equation? (State all the assumptions
you make). And what instrument can you use to check the accuracy of the velocity profile in the wake of your new
airfoil?
3. If an incompressible and inviscid fluid flow is free of heat transfer and shaft work, do we need to consider
energy equation in our flow analysis?
2. Provide Global Reflections on the Second Week of Classes and Homework 3 (15 Points)
Page 26 of 44
Homework 4
Due: Tuesday 2/14/2017
Dear students,
In the last homework, you practiced applying conservation of momentum to obtain drag coefficient. In
this homework, you will understand the application of energy equation in incompressible and compressible flows
and how energy is transferred between the different flow variables. This homework should also help you to start
thinking about the test matrix for your experiments (if you haven’t already). And for the first time since we
started, you will use MATLAB to plot flowfields. That is awesome!
1. Questions to Answer in Portfolio (85 Points) (Your general narrative should contain answers to the following questions. Please be descriptive in your answers.
Provide enough pictures, graphs, tables, etc. to support your narrative.)
1. Provide any additional resources to your passion projects that you might have come across in the last week
and tabulate your test matrix for your experimentation. List down the tools and equipment you need to do your
experiment and your plans to obtain them. Please schedule an appointment with me (using google calendar or
email) to discuss and finalize your test matrix and to brainstorm on the tools and equipment necessary to do the
experiment.
2. Determine the temperature increase on the leading surfaces of Cessna 172 and C-130 during cruising and the
Space Shuttle during reentry. Based on the values you obtain, do you think it is reasonable to exclude energy
equation in incompressible flow and not in compressible flows?
3. Given the two-dimensional incompressible flow fields:
a) 𝑢(𝑥, 𝑦) = 𝑥2𝑦 𝑣(𝑥, 𝑦) = −𝑥𝑦2
b) 𝑢(𝑥, 𝑦, 𝑡) = −𝑥𝑡 𝑣(𝑥, 𝑦, 𝑦) = −𝑦𝑡
c) 𝑢(𝑥, 𝑦, 𝑡) = 1/(1 + 𝑡)2 𝑣(𝑥, 𝑦, 𝑡) = −𝑡
Undergraduate students:
Pick any two velocity fields out of three and determine the equations for streamline, streakline and the pathline.
For each flowfield, plot the streamline, streakline, and pathline on the same plot. (If you are ambitious, you can
every try and animate the flowfield with respect to time. However, IT IS NOT REQUIRED.)
Graduate students:
For all the velocity fields given, determine the equations for streamline, streakline and the pathline. For each
flowfield, plot the streamline, streakline, and pathline on the same plot. (If you are ambitious, you can every try
and animate the flowfield with respect to time. However, IT IS NOT REQUIRED.)
2. Provide Global Reflections on Week 4 and Homework 4 (15 Points)
Page 27 of 44
Homework 5
Due: Tuesday 2/21/2017
Dear students,
This homework will give you some experience in applying the aerodynamic tools such as vorticity and
circulation in an actual research problem. Before we proceed, I need to set proper context here. When you look
at the motion of an insect wing, it follows a complex pattern of pitching and plunging motions as shown in the
figure below. Because of this, the aerodynamics of an insect’s wing can be explored by studying the aerodynamics
of pitching and plunging motions separately.
When a wing plunges in air, it forms what is called as a Leading Edge Vortex (LEV) and a Trailing Edge Vortex
(TEV). For this assignment, let us focus only on the LEV because it plays a monumental role in the production of
lift on a plunging wing. To understand the formation and growth of this LEV, experiments were conducted at the
Wright Patterson Air Force base in the Horizontal Free Surface Water Tunnel (HFWT) on a flat plate plunging at
a certain velocity at a fixed angle of attack. Using an optical flow diagnostic technique called Particle Image
Velocimetry (PIV), the velocity components around the leading edge of the flat plate was obtained. You can
download the velocity vector file from Isidore.
The velocity vector file can either be opened in Excel or in Matlab. The file contains four columns – x, y, u and v.
In this homework, you will numerically calculating vorticity and circulation. It is an essential skill to have when
you graduate from this class because these concepts are applied on a day-to-day basis. There is no use of just
knowing these concepts without applying. Since this assignment involves programming, GET STARTED ON THIS
ASSIGNMENT EARLY. Don’t wait till the weekend. Apart from finding vorticity and circulation, you also have to
document any progress you made in your passion project in the last week.
(Your general narrative should contain answers to the following questions. Please be descriptive in your answers.
Provide enough pictures, graphs, tables, etc. to support your narrative.)
1. Document any progress you made regarding your passion project such as finding resources, references and
testing (if you have done it).
2. Plot the U velocity contour, V velocity contour and the velocity magnitude contour for the given experimental
data and discuss the aerodynamics you see from the contours.
3. Determine the vorticity present in the flowfield and plot the vorticity contour. What new information regarding
the relevant aerodynamics did you get by determining vorticity?
4. Explain the concept of circulation and its significance.
Page 29 of 44
Homework 6
Due: Tuesday 2/28/2017
Dear students,
In the last homework, you numerically determined vorticity to see the leading edge vortex around a
plunging plate. In this homework, you will use the same program you wrote to determine the vorticity and
circulation of a wingtip vortex emerging from an aspect ratio 6 ClarkY wing! You will be able to see how the
theoretical concept such as circulation compares to the experimental data. You will also be documenting the wind
tunnel/simulation results from your passion projects in this homework as well. Similar to the last homework,
don’t postpone until the weekend to get started on this homework. Start right away.
1. Questions to Answer in Portfolio (85 Points) (Your general narrative should contain answers to the following questions. Please be descriptive in your answers.
Provide enough pictures, graphs, tables, etc. to support your narrative.)
1. Hopefully, most of you finished your experiments in the wind tunnel. Please document the following:
a) Order of magnitude estimate of the normal and axial forces (before you did the experiment) b) Experimental setup/model with pictures c) Results of your wind tunnel test. (Please don’t include raw data. Plot the results in an appropriate way.)
Note: You don’t have to discuss your results in this homework. You will provide technical explanations
for your results in the next homework. All you are doing in this homework is showing the results you got.
2. Please download the ClarkY wingtip vortex experimental data files from Isidore under the “Homework” tab for
different angles of attack.
a) Use the program you wrote for the last homework to determine the vorticity of the wingtip vortex at
different angles of attack. Identify regions of rotational flow and irrotational flow.
b) Numerically calculate circulation in the wingtip vortex for each angle of attack.
c) Use Kutta-Joukowski theorem to calculate lift and plot the lift as a function of the angle of attack.
d) Compare the lift calculated from wingtip vortex to the lift measured from force balance. The force data is
shown in the back of this page.
3. Consider the incompressible, irrotational, two-dimensional flow, where the stream function is given by,
𝜓 = 2𝑥𝑦
a) What is the velocity at 𝑥 = 1, 𝑦 = 1 and at 𝑥 = 1, 𝑦 =1
2. Do these two points lie along the same streamline?
b) Graph the streamline pattern and discuss the significance of the spacing between the streamlines.
ONLY FOR GRADUATE STUDENTS
c) What is the velocity potential for this flow?
d) Sketch the lines of constant potential. How do the lines of equipotential relate to the streamlines?
2. Provide Global Reflections on Week 6 and Homework 6 (15 Points)
Page 30 of 44
Homework 7
Due: Tuesday 3/14/2017
Dear students,
Hope you all had a good spring break and came back rejuvenated and refreshed. We have been talking
about simulating flows in this class for a while and in this homework, you are going to do just that. Using the
stream function and Laplace equations, you will simulate flow over a cylinder and flow over a lifting cylinder. You
will also be solving a problem related to a real life application using the equations we derived from potential flow
around a cylinder.
1. Questions to Answer in Portfolio (85 Points) (Your general narrative should contain answers to the following questions. Please be descriptive in your answers.
Provide enough pictures, graphs, tables, etc. to support your narrative.)
1. Provide comprehensive technical discussions on the wind tunnel testing/simulation results you included in the
last homework. You may consult with me if you could not figure out the science behind why you see what you
see in your results.
2. Simulate the potential flow around a cylinder along with the velocity components. Show a plot of the stream
function and a plot of the velocity vectors around the cylinder. Assume 𝑉∞ = 1 𝑚/𝑠 and a doublet strength 𝜅 =
−300 𝑚3/𝑠.
3. You are to design a Quonset hut to serve as temporary housing near the seashore. The Quonset hut may be
considered to be a closed (no leaks) semicylinder, whose radius is 2.5 m, as shown in the figure below. Neglect
viscous effects and assume that the flow field over the top of the hut is identical to the flow over the cylinder for
0 ≤ 𝜃 ≤ 𝜋. The air inside the hut is at rest and the pressure is equal to the stagnation pressure 𝑝0. What is the
force required to keep the hut on the ground if the wind speed is around 50 m/s? Consider sea-level conditions.
4. Simulate the potential flow around a spinning cylinder along with the velocity components. Show a plot of the
stream function and a plot of the velocity vectors around the cylinder. Assume 𝑉∞ = 1 𝑚/𝑠, a doublet strength
𝑘 = −300 𝑚3/𝑠 and a vortex strength Γ = 100 𝑚2/𝑠. Determine the pressure distribution along the surface of
the cylinder.
2. Provide Global Reflections on Week 7 and Homework 7 (15 Points)
Page 31 of 44
Homework 8
Due: Tuesday 3/21/2017
Dear students,
In the last homework, you simulated the flow over a stationary cylinder and a lifting cylinder. In this
homework, we are going to kick it up a notch and simulate flow over an airfoil that you design. This is an extremely
important skill to have. You can take this homework and carry it on as passion project as well if you are interested.
You will design the airfoil using Joukowski transformation and simulate the flow using Joukowski transformation
as well.
1. Questions to Answer in Portfolio (75 Points) (Your general narrative should contain answers to the following questions. Please be descriptive in your answers.
Provide enough pictures, graphs, tables, etc. to support your narrative.)
1. Compile the write-up of different sections of the Passion project 1 into one document. Please make sure you
have the following sections in the final report
a) Introduction
b) Literature Review
c) Order of Magnitude Estimate of Forces
d) Experimental Setup
e) Results and Discussion
f) Conclusion
2. Please choose a second passion project to work out of the list of projects listed on the Class 16 powerpoint
presentation. Please note that there are three projects added to the list of projects. You can also come up with a
project you are interested in pursuing.
3. Use conformal mapping to simulate a flow around
a) A symmetrical airfoil
b) A cambered airfoil (ONLY FOR GRADUATE STUDENTS)
Make sure to use the circulation value which satisfies Kutta condition.
Show the following graphs:
1. Joukowski Airfoil
2. Flow around lifting cylinder
3. Flow around the shifted lifting cylinder
4. Flow around the airfoil
2. Provide Global Reflections on Week 8 and Homework 8 (15 Points)
Page 32 of 44
Homework 9
Due: Tuesday 3/28/2017
Dear students,
In the last homework, you simulated flow over airfoil and wrapped up Passion project 1. In this
homework, you will apply the equations you learned in class on thin airfoil theory to predict the coefficient of lift,
coefficient of pitching moment and location of center of pressure for a given camber line. You will also document
the literature review on the project of your interest for the passion project 2.
1. Questions to Answer in Portfolio (85 Points) (Your general narrative should contain answers to the following questions. Please be descriptive in your answers.
Provide enough pictures, graphs, tables, etc. to support your narrative.)
1. Document the relevant information you gathered from different resources you reviewed for your passion
project 2. Based on your literature review and independent study, discuss the relevant aerodynamics involved in
the application you will be working on. You have to include relevant graphs, tables, figures, etc to support your
narrative.
2. Get X, Y coordinates for the cambered airfoil you generated from the last homework using Joukowski
transformation. Input the coordinates into XFOIL or XFLR5 to
a) Determine the coefficient of lift variation with angle of attack and the lift curve slope.
b) Compare the result with lift curve slope predicted by thin airfoil theory and zero lift angle of attack
predicted by thin airfoil theory.
c) Plot the variation of the center of pressure location with angle of attack.
2. Provide Global Reflections on Week 9 and Homework 9 (15 Points)
Page 33 of 44
Homework 10
Due: Tuesday 4/4/2017
Dear students,
In the last homework, you determined the coefficient of lift and the location of center of pressure as a
function of angle of attack using XFLR5 for a cambered airfoil you generated. In this homework, you are going to
program your code to determine the angle of attack of zero lift, coefficient of pitching moment and location of
center of pressure based on the thin airfoil theory equations. You will be comparing the results you got with the
results obtained from XFLR5.
1. Questions to Answer in Portfolio (85 Points) (Your general narrative should contain answers to the following questions. Please be descriptive in your answers.
Provide enough pictures, graphs, tables, etc. to support your narrative.)
1. Provide any additional resources to your passion project 2 that you might have come across in the last week
and tabulate the test matrix for your experimentation. List down the tools and equipment you need to do your
experiment and your plans to obtain them. Please schedule an appointment with me (using google calendar or
email) to discuss and finalize your test matrix and to brainstorm on the tools and equipment necessary to do the
experiment.
2. Use the cambered airfoil you generated in the last homework and determine through thin airfoil theory,
d) The angle of attack at zero lift
e) Coefficient of pitching moment variation about the quarter chord with angle of attack
f) Variation of location of center of pressure with angle of attack
Compare these results with the results obtained from XFLR5 in the last homework.
Steps involved:
1. Determine the camber line from the cambered airfoil you used in the last homework.
2. Use “polyfit” command to get the equation of the camber line. (Use 4th or 5th order polynomial fit)
3. Differentiate the equation of the camber line to get 𝑑𝑧/𝑑𝑥.
4. Convert 𝑑𝑧/𝑑𝑥 in terms of polar coordinates using 𝑥 = 𝑐/2 (1 − cos 𝜃)
5. Substitute in angle of attack at zero lift formula and integrate.
6. Compare the angle of attack at zero lift you get with the result from XFLR5.
7. Do similar procedure to calculate 𝐴0, 𝐴1 and 𝐴2 values you need to determine pitching moment coefficient
and location of center of pressure.
2. Provide Global Reflections on Week 10 and Homework 10 (15 Points)
Page 34 of 44
Homework 11
Due: Tuesday 4/11/2017
Dear students,
In the last few homework, you created your own airfoil, simulated flow around that airfoil and determined
lift coefficients, quarter chord and location of center of pressure using XFLR5 and thin airfoil theory analytical
prediction. What is left is to achieve one of other goals where you can potentially get coefficient of pressure for
any shaped object using panel methods (Basically what XFOIL and XFLR5 does). In this homework, you will
simulate coefficient of pressure over an object using source panel method.
1. Questions to Answer in Portfolio (50 Points) (Your general narrative should contain answers to the following questions. Please be descriptive in your answers.
Provide enough pictures, graphs, tables, etc. to support your narrative.)
1. For your passion project
• Document the order of magnitude estimate for forces/coefficients for your passion project 2
• Begin testing in the UD-LSWT
2. Download “incomplete_sourcepanel.m” file from isidore. Fill in the missing steps and provide comments on the
source panel code. (Hopefully, we will get time to do this in class)
Compare the coefficient of pressure obtained by source panel method with analytical distribution.
Page 35 of 44
Homework 12
Due: Tuesday 4/27/2017
Dear students,
Here we are in the final assignment of the semester! It feels great to look back at the skills you acquired
through these homework assignments. These assignments trained you to use and apply aerodynamic tools such
as vorticity, circulation, KJ theorem and trained you to design your own airfoils using Joukowski transformation.
You also did analysis on the airfoil you generated in XFLR5 and XFOIL and compared with theoretical predictions.
In this homework, you will add on to your skillset by taking the airfoil you designed and converting it into a wing
to perform XFLR5 analysis.
You will also be reflecting on a very important video by Albion Bowers on Prandtl-D. I could not think
about a better way than to finish the theoretical aerodynamics class with the Prandtl-D wing. It is such a
remarkable design which one day could fly in Mars! All that came from the theoretical aerodynamics.
Through these homework assignments, you documented several stages of progress regarding your
passion project. I hope all of these assignments helped you understand the material and I hope the skills that you
learned add value to your work/career wherever you may end up.
1. Questions to Answer in Portfolio (50 Points) (Your general narrative should contain answers to the following questions. Please be descriptive in your answers.
Provide enough pictures, graphs, tables, etc. to support your narrative.)
1. For your passion project 2, provide technical discussion and explanations for the results you generated in the
wind tunnel/simulation. You may consult me regarding the results as well before you write it in your portfolio.
2. Model a 3D wing of AR 4 in XFLR5 using the Joukowski airfoil you created before. Perform viscous analysis on
the wing using “lifting line” or “3D Panels” option in XLFR5 to determine
1. Lift variation with angle of attack and lift curve slope. Compare lift curve slope with Helmbold’s equation.
2. Induced drag variation as a function of angle of attack
3. Span efficiency of the wing (Using Helmbold’s Equation)