Courses:

Help support MIT OpenCourseWare by shopping at Amazon.com! MIT OpenCourseWare offers direct links to Amazon.com to purchase the books cited in this course. Click on the Amazon logo to the left of any citation and purchase the book from Amazon.com, and MIT OpenCourseWare will receive up to 10% of all purchases you make. Your support will enable MIT to continue offering open access to MIT courses.

In 16.540 we address fluid dynamic phenomena of interest in internal flow situations. The emphasis tends to be on problems that arise in air breathing propulsion, but the application of the concepts covered is more general, and the course is wider in scope, than turbomachines (in spite of the title). Stated more directly, the focus is on the fluid mechanic principles that determine the behavior of a broad class of industrial devices. The material can therefore be characterized, only partly tongue in cheek, as "industrial strength fluid mechanics done in a rigorous manner".

Internal flow exhibits a rich array of phenomena. Further, the topics we will cover are generally not dealt with in subjects or texts about external fluid dynamics; the flows described in 16.540 are generally rotational, often three-dimensional, sometimes unsteady, and sometimes occurring in non-inertial (e.g., rotating) coordinate systems. The aim is to give you an appreciation for, and an ability to quantify, these phenomena.

Much of the content and style of the course can be viewed as the development of flow models and ideas to allow physical insight into the behavior of three-dimensional and unsteady flows. In this sense, the course can be considered to highlight the use of simplified (but conceptually sophisticated) flow modeling as a complement to subjects which address the development of computational techniques. From this perspective, a goal of the course is to provide an increased ability to interpret computational results and hence to effectively extract conclusions about the key features of complex internal flows.

The lecturers for the course are:

Prof. Edward M. Greitzer
Dr. Choon S. Tan

The text for the class is:

Greitzer, E., C. Tan, and M. Graf. Internal Flow: Concepts and Applications. Cambridge, UK: Cambridge University Press, 2004. ISBN: 9780521343930.

Given that a text exists for the course material, it is the intent of the lectures to discuss the material rather than to present it for the first time in class. As such you will be expected to read the material before class and to engage in in-class discussions of the reading material (these may include answering questions, elaborating concepts, etc.). Student class participation will count for 10% of the final course grade.

You will be asked to develop "concept questions" which help to illustrate the physical principles and approximations that are made. This will be done in small (three or four person) teams so you can discuss the questions among yourselves. One of these questions is to be developed each week by each team. They are to be handed in by 6 pm on the Friday before the lectures take place. The concept questions will count for 10% of the final grade.

Approximately eight short (~20 minute) "concept quizzes" will be given during class, roughly equally spaced throughout the term. These may make use of the questions generated by students. The total of these quizzes will count for 20% of the final course grade.

A team project on internal flow modeling will be assigned. The project will be on a topic you choose from a list of topics supplied by the instructors. The team project will count for 20% of the grade each.

An oral mid-term exam and an oral final exam will be held. The mid-term and final exams will count for 15% and 25% of the final course grade respectively.

The instructors reserve the right to alter the percentages slightly, depending on circumstances.

1. Development of "physical insight" into the phenomena which characterize internal flow in fluid machinery (not just what happened, but why it happened).
2. Ability to define, in a rigorous manner, the levels of modeling needed for useful descriptions of a number of internal flow situations.
3. Ability to interpret numerical simulations and experimental results in terms of concepts and principles such as those enumerated below.

Measurable outcomes are just what the name implies, in other words those items that follow directly from the learning objectives and that we can explicitly measure. In the outcomes below the verbs in bold denote the actions that will be carried out, the phrases in italics describe how these will be assessed, and the words in UPPER CASE define the connection with Bloom's taxonomy of knowledge, which is described here:

Bloom's Taxonomy of Knowledge (PDF)

Note there are different levels of engagement with these objectives (and with different aspects of the subject); we do not expect you to be at the highest level in everything that is covered. In some aspects, for example, we expect you to comprehend and be able to use, with the expectation that in the future your engagement with these concepts is such that you will move up the hierarchy.

Measurable Outcomes - at the end of this course, students should be able to:

1. Describe overall principles for developing models of internal flows (in-class discussions, concept quizzes). [KNOWLEDGE, COMPREHENSION, ANALYSIS]
2. Apply control volume analysis to internal flow situations and evaluate the features and the limitations of the solutions (in-class discussion, concept quizzes). [APPLICATION, SYNTHESIS, EVALUATION]
3. Apply concepts of vorticity and circulation to describe and quantify the behavior of internal flows (in-class discussions, concept quiz). [COMPREHENSION, APPLICATION, ANALYSIS]
4. State and explain the principal features of fluid motion in a rotating coordinate system which distinguishes it from fluid motion in inertial coordinate systems, identify the appropriate non-dimensional parameters for describing these flows, develop simplified models to describe and quantify these flows (in-class discussions, concept quiz). [COMPREHENSION, APPLICATION, ANALYSIS]
5. Describe loss generation metrics and mechanisms in internal flows, identify appropriate non-dimensional parameters for assessing mixing and loss in internal flows, develop simplified models to describe and quantify mixing and losses (in-class discussions, concept quiz). [COMPREHENSION, APPLICATION, ANALYSIS]
6. State and explain one or two examples where unsteady flow plays an important role in the behavior of fluid machinery, identify the appropriate non-dimensional parameters for assessing the importance of unsteadiness, describe the general forms of disturbances in flows, develop simplified models to describe and quantify these flows (in-class discussions, concept quiz). [COMPREHENSION, APPLICATION, ANALYSIS]
7. Produce a useful simplified model of an internal flow phenomenon, explain and justify the methods that are applied, discuss the principal results, compare and contrast the model to other methods that have been applied, and make recommendations for modeling similar problems in the future. (modeling projects). [SYNTHESIS, EVALUATION]