16.100 Aerodynamics Fall 2024 Syllabus

Course Information

16.100 Aerodynamics, Fall 2024

Units: 3-1-8

Lectures: Mon/Wed/Friday, 11-12 EST in Room 33-419

Labs: Fri, 1-2pm EST, 2-3pm EST

Course website: https://canvas.mit.edu/courses/27310

• Registered students can also access by logging onto mit.edu with MIT credentials/certificates, and searching for “16.100” in the Courses tab

Piazza Forum:  https://piazza.com/mit/fall2024/16100 

• To correspond with the 16.100 instructors/peers and to ask any questions about the course, we encourage you to use Piazza.
• Also accessible via the Canvas course website
• Please sign up using https://piazza.com/mit/fall2024/16100 as soon as possible 

Lecture notes: 16.100 Aerodynamics Fall 2024

 

Staff

 

Instructor: Professor Qiqi Wang Pronouns: he/him/his qiqi@mit.edu Office hours: Mondays 12-1 PM in Seamans' lounge (first floor of building 33)	Graduate teaching assistant: Yuenong Ling Pronouns: he/him/his lingyn@mit.edu Office hours: Tuesdays 4-5 PM in Seamans' lounge
Administrative assistant: Douglas Purdy Pronouns: he/him/his dgpurdy@mit.edu

Course Description

Welcome to this intermediate-level course on aerodynamics!  Aerodynamics is the study of the flow of air about a body. In our case, the body will be an airplane, but much of the aerodynamics in this course is relevant to a wide variety of applications, from sailboats to automobiles to birds.  Building on the fundamental concepts that you have learned in the introductory course on fluid mechanics (for example, 16.003 Unified Engineering, Fluid Dynamics), we will explore more complex yet practical and useful aerodynamic models in this course.  You will learn to properly select and apply these models to analyzing airplane wings and bodies, which is a key skill in designing flight vehicles ranging from RC airplanes and multicopters to advanced urban mobility aircraft and next-generation airliners. 

The subsonic/supersonic/transonic speed regimes are the current focus since they are relevant to most aviation endeavors to date. Applied topics covered include (1) Applications of aerodynamic forces (2) Drag and energy consumption (3) Lift induced drag (4) Airfoil shape and lift (5) Aerodynamic stability (6) High lift airfoils (7) Transonic and supersonic flight (8) Aeroacoustics. Understanding these topics will require the coverage of substantial theoretical knowledge, including Fluid Kinematics, Forces, Conservation laws, Non-dimensionalization, Sensitivity Analysis, Order of Magnitude Analysis, Flow regimes, Potential flow modeling, Vorticity dynamics, Viscous flow, Boundary Layer Theory, Theories of Compressible flow, and Unsteady flows.

 

Prerequisites

Working knowledge of basic fluid mechanics and thermodynamics at a level of completing 16.003 Unified Fluids and 16.004 Unified Thermodynamics (including the perquisites therein on Calculus and physics) or their equivalents.

 

Learning Objectives

16.100 has a set of learning objectives that you should always keep in your thoughts as the semester progresses. The entire course is structured to (hopefully) help you achieve these objectives. Specifically, by the end of this course, you will be able to:

• Formulate and apply aerodynamic models to predict aerodynamic performance (lift, drag, energy consumption, stability) of two-/three-dimensional flying objects (e.g. airfoil, wing)
• Identify and explain the applicability and trade-offs of particular aerodynamic models for different applications, and estimate the modeling errors both qualitatively and quantitatively
• Collaborate with members of a team and gain hands-on experience on a practical project of aerodynamic analysis and design using computational and experimental methods

Comment on aerodynamic models: An aerodynamic model is simply a method to estimate the aerodynamic performance (e.g., the lift or drag) of an object (e.g., an airfoil, wing, or airplane). An aerodynamic model could be based on experiments, computation, or theory but often takes a middle path—using a judicious combination of all three approaches. For example, an aerodynamic model might be incompressible thin airfoil theory; or, an aerodynamic model might be incompressible thin airfoil theory with a skin friction drag estimate, or an aerodynamic model might be a wind tunnel experiment at low speed with theoretical corrections for wall effects and higher speed flight conditions. In 16.100, a variety of aerodynamic models will be covered, which could then be combined to produce a more complex model as dictated by the application. Specific aerodynamic models that students will encounter may vary slightly from semester to semester but will generally include: 2D/3D potential flows (incompressible to supersonic) including panel and vortex lattice methods; boundary layer methods including the effects of transition and turbulence; coupled inviscid-viscous models; 2D/3D Euler & Navier-Stokes computations; and wind tunnel testing.

 

Course Structure and Measurable Outcomes

We will analyze and model a wide range of aerodynamic flows which embody various representative flow features.  To address a particular set of salient features, an aerodynamic model often makes certain approximations whereby are categorized by the following properties: (1) incompressible and compressible, (2) inviscid and viscous, (3) two-dimensional (2D) and three-dimensional (3D), and (4) subsonic/transonic/supersonic/hypersonic flow regimes.  Based on these categories of models, this course is organized into the following modules:

1. Fundamental Concepts
2. Incompressible Potential Flow
3. Viscous and Compressible Flow

Upon the completion of 16.100, you will be able to:

 

Module 1: Fundamental Concepts

1. Explain what is lift and drag, identify aerodynamic forces in various applications, and design aerodynamic devices that use lift and drag (homework, exams, project).
2. Explain the motion and deformation of a fluid element using kinematics including the definition of shear strain, normal strain, vorticity, divergence, and the material derivative (homework, exams).
3. (a) Derive the integral form of the compressible Navier-Stokes equations on a fixed control volume using the principles of conservation of mass, momentum, and energy (homework, exams); and (b) relate the terms of the differential form of these equations to physical effects considered in the conservation laws by applying the integral form to an infinitesimal fluid element (homework, exams).
4. Apply flow similarity, non-dimensional coefficients such as the lift and drag coefficient, and non-dimensional parameters such as the Mach number and Reynolds number in aerodynamic modeling of realistic configurations (homework, project, exams).
5. Explain the use of wind tunnel testing in aerodynamic modeling, focusing on the importance of flow similarity in scale testing and on the typical corrections (e.g., wall corrections) required to simulate flight conditions (homework, projects, exams).
6. Assess the ability and limitations of an aerodynamic model to estimate lift and drag (separated into friction, induced, wave and pressure drag contributions) for a specific application (homework, project, exams).
7. Contribute substantially as an individual to the design and execution of computational and experimental aerodynamic analysis of realistic 3-D configuration together with members of a team (project).
8. Explain the sources of friction drag, induced drag, wave drag, and pressure drag (homework, exams)

 

Module 2: Incompressible Potential Flow Aerodynamics

1. Explain and sketch the pressure distribution on an airfoil based on streamline curvature, with emphasis on the understanding of the leading-edge and trailing-edge region, as well as the effects of camber and thickness (homework, project, exams).
2. (a) Explain the basic elements of thin airfoil potential flow models for 2-D subsonic and supersonic flows (homework, exams), and (b) Apply thin airfoil potential flow models to estimate the forces on airfoils in 2-D subsonic and supersonic flows (homework, exams).
3. Explain the basic elements of 2-D panel methods.
4. Explain the basic elements of the lifting line model for high aspect ratio wings (homework, project, exams); (b) Describe the dependence of lift and induced drag on geometry and performance parameters (e.g., aspect ratio, twist, camber distribution, wing loading, flight speed, etc.) using the lifting line model (homework, project, exams); and (c) Apply the lifting line model to estimate lift, induced drag, and roll moments on high aspect ratio wings (homework, project, exams).
5. Relate induced drag to the kinetic energy in the wake (homework, project, exam).
6. Explain the basic elements of 3-D vortex lattice methods (homework, exams).

 

Module 3: Viscous and Compressible Aerodynamics

2. (a) Explain the concept of a laminar boundary layer, including the definition of the displacement thickness and the skin friction coefficient and the importance of the Reynolds number in determining the presence and behavior of a boundary layer (homework, exams); (b) Describe the balance of pressure forces, viscous forces, and momentum change that occurs in a boundary layer (homework, exams); and (c) Describe laminar boundary layer separation and the factors which contribute to it (homework, exams).
3. Explain transition, i.e., the onset of turbulence in a boundary layer, and describe the dependence of transition on Reynolds number and pressure gradient (homework, exams).
4. Explain the qualitative effects of turbulence on boundary layer evolution, including its impact on velocity profile, skin friction coefficient, boundary layer thickness, and separation. Explain the Reynolds averaging of turbulent flows and use the Reynolds stresses to explain the qualitative behavior of turbulent boundary layers (homework, exams).
5. Estimate friction drag on 2-D and 3-D configurations by decomposing the geometry into patches and assuming appropriate local values of skin friction coefficients including the possibility of laminar or turbulent boundary layer conditions (homework, project, exams).
6. (a) Explain the relationship between sound propagation and shock waves (exams); (b) Describe the qualitative change in flow conditions (Mach number, pressure, temperature, total pressure, etc.) across shocks and expansion fans (exams); (c) Estimate the change in flow conditions across shocks and expansion fans using shock-expansion theory (homework, exams).
7. Explain the lift and drag on a supersonic configuration based on shocks and expansion fans (homework, exams).
8. Explain transonic drag rise including the critical Mach number and the use of wing sweep to delay drag rise (homework, project, exams).

Comment on basic elements: The “basic elements” of a model include the critical features that produce a valuable predictive method. For example, consider a 2D panel method. The basic elements would include all of the underlying assumptions of incompressible, potential flow; the discretization of an airfoil geometry into a set of line segments on which potential flow solutions are distributed; the satisfaction of flow tangency at panel control points; the global influence of an individual panel on all other panels; the imposition of the Kutta condition; etc. However, the basic elements would not include the more detailed aspects of the method, which—while important—are not critical to understanding how the method works. The 2D panel method example, would not include the details of the calculation of the influence coefficient of a general source/vortex/doublet panel, the solution of the large linear system of equations, and so on.

 

Course Materials

Course materials will be distributed via the Canvas course site.  The following book is the main textbook of reference for this course:

John D. Anderson, Fundamentals of Aerodynamics, 6th Edition, McGraw Hill (2016). Note: Any edition from the 4^th onwards is completely fine!

The textbook is available at MIT libraries. Obtaining a copy yourself, if possible, may be a valuable investment and is recommended for would-be aerodynamicists.

In addition, the Unified Fluids notes from previous years will be a good resource. Also, the textbook written by Professor Mark Drela for the graduate subject 16.110 Flight Vehicle Aerodynamics will occasionally be used and is an excellent resource generally on all of the topics in 16.100. This electronic copy of this book can be accessed online via MIT Libraries (by searching in lib.mit.edu with MIT login credentials/certificates and via VPN if not on an MIT network).

• Drela, M. (2014). Flight Vehicle Aerodynamics. Cambridge, MA, USA: The MIT Press.

The following books are optional and might also be helpful for the course:

• K. Kundu, I. M. Cohen, and D. R. Dowling, Fluid Mechanics, 5^th Edition, Elsevier (2012).
• James A. Fay, Introduction to Fluid Mechanics, MIT Press (1994).
• Frank M. White, Fluid Mechanics, McGraw Hill (2010).
• Kuethe and Chow, Foundation of Aerodynamics, Wiley (1997).
• Jack Moran, An Introduction to Theoretical and Computational Aerodynamics, Dover (2003).
• John Anderson, Introduction to Flight, McGraw Hill (2011).

 

Recitation Sessions

Weekly recitations will be held on Fridays, 1-2pm and 2-3pm. Students must register for either of the two recitation sessions, and attendance is mandatory. During recitation, we will engage in active problem-solving sessions, reinforce key concepts from the lecture, and discuss the use of aerodynamic modeling tools such as XFOIL, AVL, and computational fluid dynamics (CFD) software.

 

Homework (35% grade)

The homework will be largely based on the assigned reading materials with some problems based on challenging materials from previous reading and lectures.  Homework will be submitted electronically on the Canvas course site. 

Homework is an individual effort; while students are encouraged to discuss homework problems with each other, what is turned in must represent the student’s own understanding of the material.

Past-due homework will generally not be accepted. Only for extremely unusual and unavoidable circumstances could an exception be permitted. In such circumstances, advance notice is crucial. Please request an extension by contacting the Professor and TA via email as soon as you are aware of an issue that will make it impossible to complete homework on time. If you email with only a few days’ notice, a negative response is most likely.

Grades for each homework problem will be given using letter grades, including modifiers. The following scale will be used: (A+, A, A-) = (5.25, 5, 4.75); (B+, B, B-) = (4.25, 4, 3.75); (C+, C, C-) = (3.25, 3, 2.75); D = 2; F = 0. The meaning of a letter grade is MIT’s standard letter grade definition (see below). The overall homework letter grade for the semester will be the mean of all the homework grades, rounded down to the highest letter grade, including modifiers.

 

Project (35% grade)

Starting in the middle of November, students will tackle a project centered on the aerodynamic analysis and redesign of a battery electric airplane. The project will involve using analytical and numerical tools to evaluate the aerodynamic performance of an airplane. Students will then propose and test modifications to the nominal design in order to improve certain performance characteristics. The project may be partitioned into several pieces, with small intermediate assignments due before the final project report.

Before and during the project, we may perform some aerodynamic simulations and flow visualizations using computational fluid dynamics (CFD) tools.

Once the project begins, the regular MW lectures and the recitation sessions will convert to a “project session” wherein the instructor and TA will guide the students through the completion of project assignments, provide software tutorials, give short lectures on relevant topics, and generally answer questions as they arise.

The project assignments will be completed in teams of three to five students; the team assignment will be arranged before the beginning of the project and depend on how many students are enrolled in the class. The total individual student grade on the project will be based on a team project grade (40%) and an individual contribution grade (60%). The individual contribution will be assessed from two sources: (1) instructor interactions with the teams and (2) delineation within the written report of an individual’s contributions.

 

Exams (30% grade)

During the semester, two exams will be held. The first exam will occur on Wednesday, Oct 16th. The second will be on Wednesday, November 13th. There will be no final exam this semester.

 

Final grade

The final subject letter grade will be determined as follows. Letter grades (including +/- modifiers) will be given to the two exams, the project, and the homework. To receive a final subject letter grade, students must have received that grade or better on most of the three individual letter grades (e.g., to receive an A in the subject, you generally will need three As and one B). Substantial deviations below the higher grades will likely result in a final letter grade below these higher grades (e.g., three As and one C+ will probably result in a B+). In other words, the final letter grade represents consistent performance at or above that level.

Please note the following description of subject letter grades from MIT’s grading guidelines:

• A: Exceptionally good performance demonstrating a superior understanding of the subject matter, a foundation of extensive knowledge, and skillful use of concepts and/or materials.
• B: Good performance demonstrating the capacity to use the appropriate concepts, a good understanding of the subject matter, and an ability to handle the problems and materials encountered in the subject.
• C: Adequate performance demonstrating an adequate understanding of the subject matter, an ability to handle relatively simple problems, and adequate preparation for moving on to more advanced work in the field.
• D: Minimally acceptable performance demonstrating at least partial familiarity with the subject matter and some capacity to deal with relatively simple problems, but also demonstrating deficiencies serious enough to make it inadvisable to proceed further in the field without additional work.

 

Inclusivity Statement

MIT values an inclusive environment, and so do we as the 16.100 teaching staff.  We hope to foster a sense of community in this classroom, one that supports a diversity of thoughts, perspectives, and experiences. We welcome and encourage participation by individuals of all backgrounds, beliefs, ethnicities, national origins, gender identities, sexual orientations, religious and political affiliations – and other visible and invisible differences. All members of this class are expected to contribute to a respectful, welcoming, and inclusive class environment and to make sure that all voices have space to be heard. We are still in the process of learning about diverse perspectives and identities, as are we all. If something is said in class that makes you feel uncomfortable, please do not hesitate to talk to us about it.

 

Academic Integrity Statement

In this course, we will hold you to the high standard of academic integrity expected of all students at the Institute. The rationale is two-fold. First, it is essential to the learning process that you are the one doing the work.  We have structured the assignments in this course to enable you to gain a mastery of the course material. Failing to do the work yourself will result in a lesser understanding of the content and, therefore a less meaningful education for you. Second, it is important that there be a level playing field for all students in this course and at the Institute so that the rigor and integrity of the Institute’s educational program are maintained.

Violating the Academic Integrity policy (integrity.mit.edu) in any way (e.g., plagiarism, unauthorized collaboration, cheating, etc.) will result in official Institute sanction. Possible sanctions include receiving a failing grade on the assignment or exam, being assigned a failing grade in the course, having a formal notation of disciplinary action placed on your MIT record, suspension from the Institute, and expulsion from the Institute for very serious cases.

Please review the Academic Integrity policy and related resources (e.g., working under pressure; how to paraphrase, summarize, and quote; etc.) and contact me if you have any questions about appropriate citation methods, the degree of collaboration that is permitted, or anything else related to the Academic Integrity of this course.^[1]

 

Special Accommodations and Disability Support Services

If you need disability-related accommodations, we encourage you to meet and contact the staff early in the semester. If you have not yet been approved for accommodations, please contact Student Disability Services at sds-all@mit.edu.  We look forward to working with you to assist you with your approved accommodations.

 

Mental Health

As a student, you may experience a range of challenges that can interfere with learning, such as strained relationships, increased anxiety, substance use, feeling down, difficulty concentrating, and/or lack of motivation. These mental health concerns or stressful events may impact your ability to attend class, concentrate, complete work, take an exam, or participate in daily activities.  Please discuss this with Student Support Services (S3). You may consult with Student Support Services at 5-104 or at 617-253-4861.  For urgent or after-hours concerns, please contact MIT or your local police.

 

^[1] Office of Student Citizenship, W20-507, (617) 258-8423​