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".

Syllabus

Overall Course Content and Scope

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.

Lectures

The lecturers for the course are:

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

Text

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.

Course Grading and Assignments

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.

Learning Objectives for 16.540

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 for 16.540

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

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]

   Calendar

   The calendar of the class is presented below. Six major topics are covered in twenty-five lectures. For each topic, the instructor is given. EG refers to Prof. Edward Greitzer, and CT refers to Dr. Choon Tan.

   
   

   Course calendar.

   LEC #	TOPICS	KEY DATES
   I. Structure and content of the course, introduction to flow regimes [EG, CT]
   1	Course introduction Learning objectives and measurable outcomes for the course Discussion of prerequisites Conduct of the course Purpose and development of concept questions, "what is a concept question" Concepts of modeling: Utility, levels of fidelity
   II. Some useful basic ideas [EG]
   2-3	Basic ideas Pressure fields and streamline curvature: Equations of motion in natural coordinates Upstream influence in turbomachines Applications of the integral forms of the equations of motion; control volume description of fluid machinery and propulsion systems, applications Features of boundary layers in ducts and channels Inflow and outflow to fluid devices: The asymmetry of real fluid motions
   III. Vorticity and circulation [EG]
   4	Introduction - Useful concepts Definition of vorticity Perspective on utility of the concepts Kinematics of vorticity; vortex lines and vortex tubes; behavior of vortex lines at a solid surface
   5-6	Dynamics of vorticity Vorticity changes in inviscid and viscous, incompressible and compressible fluids, with uniform and non-uniform density, with conservative and non-conservative body forces. Connection with rigid body dynamics. Applications to secondary flow in bends and turbomachinery blade rows, horseshoe vortices.	Concept quiz 1
   7	Circulation changes in fluid motion Circulation changes in inviscid and viscous, incompressible and compressible fluids, with uniform and non-uniform density, with conservative and non-conservative body forces. Applications to flows of uniform and non-uniform density, creation of circulation in a non-uniform density flow.
   8	Rotational flow descriptions in terms of vorticity and circulation Rotational flow in fluid components (nozzles, diffusers, blade rows). Relation between kinematic and thermodynamic properties in an inviscid, non-heat conducting flow; Crocco's theorem; applications in fluid machinery. Viscosity and the generation of vorticity at solid surfaces. Velocity field associated with a vorticity distribution, numerical methods based on the velocity-vorticity relationship, examples for two-dimensional and axisymmetric flow.
   9	Further applications of the concepts Mixing enhancement due to streamwise vorticity, lobed mixer nozzles. Fluid impulse and the generation of vorticity, streamwise vorticity structure and the evolution of a jet in crossflow.	Concept quiz 2
   IV. Loss sources and loss accounting [CT]
   10	Introduction to concepts, metrics for loss Introduction: Appropriate metrics for loss Lost work, entropy generation, and irreversibility Losses in spatially uniform and non-uniform flow
   11	Boundary layer losses Entropy generation in boundary layers Entropy production and dissipation coefficient Estimation of turbomachinery blade profile losses	Concept quiz 3
   12	Mixing losses Introduction to mixing losses - Control volume analysis Mixing of two streams with non-uniform stagnation properties Mixing loss from fluid injection into a stream Irreversibility generation in mixing
   13-14	Averaging of a non-uniform flow - What is "The" loss Concepts: Area average, mass average and stream thrust average Application to a simple flow model Appropriate averages for a non-uniform flow, "averaging for a purpose" Boundary layer losses versus downstream mixing losses	Concept quiz 4
   15	Further aspects of mixing loss, examples, and applications Effect of pressure level on average properties and mixing losses Examples: Two-stream mixing, linear shear flow mixing in diffusers and nozzles, wake mixing Loss characterization in turbomachinery cascades
   	Mid-term oral exam
   V. Flow in rotating passages [EG]
   16	Useful concepts Coriolis and centrifugal forces in a rotating coordinate system Velocity fields in the inertial and the rotating coordinate systems Equations of motion in a rotating coordinate system Non-dimensional parameters in a rotating flow Conserved quantities in a steady rotating flow The role of the reduced static pressure
   17	Phenomena in flows where rotation dominates Conditions in which effects of rotation dominate The taylor-proudman theorem (two different perspectives) Viscous flows (ekman layers) on rotating surfaces	Concept quiz 5
   18	Rotating channel flow in constant area straight passages Two-dimensional inviscid flow in a rotating straight channel Fully developed flow in a rotating straight channel Boundary layers in rotating straight channels
   19-20	Rotating flow in turbomachinery passages Two-dimensional flow in rotating diffusing passages Three-dimensional flow and the "relative eddy" Changes in vorticity and circulation in rotating passages Generation of streamwise vorticity and secondary flow in rotating blade rows; radial migration of high temperature fluid in a turbine rotor	Concept quiz 6
   VI. Unsteady flow [CT]
   21-22	Introduction - Useful concepts The inherent unsteadiness of fluid machinery The reduced Frequency Examples of unsteady flows and the role of the reduced frequency Stagnation pressure changes in an unsteady flow (the basic mechanism for turbomachinery operation!)
   23-24	Waves and oscillations in fluid systems Introduction to self-excited disturbances; shear layer instability Unsteady disturbances in fluid systems Lumped parameter modeling and transmission matrices for components and fluid systems Actuator disk models of fluid components System instabilities Waves and multi-dimensional disturbances in fluid systems	Concept quiz 7
   25	Elements of compressor stability modeling Low-order description of asymmetric flow in compressors, onset of rotating stall
   	Final oral exam