 
Abstract/Syllabus:

Tan, Choon, and Edward Greitzer, 16.540 Internal Flows in Turbomachines, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed 07 Jul, 2010). License: Creative Commons BYNCSA
Internal Flows in Turbomachines
Spring 2006
The trajectory of particles leaking over a compressor tip, an image from the lecture 'Modeling Fluid Flow'. (Image by MIT OCW, adapted from Furukawa et al.)
Course Highlights
This course features a sample of lecture notes from the class, and a series of concept questions and quizzes in the assignments section.
Course Description
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 threedimensional, sometimes unsteady, and sometimes occurring in noninertial (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 threedimensional 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 inclass 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 midterm exam and an oral final exam will be held. The midterm 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.
Grading criteria.
ACTIVITIES 
PERCENTAGES 
Class participation 
10% 
Concept questions 
10% 
Concept quizzes 
20% 
Team project 
20% 
Midterm exam 
15% 
Final exams 
25% 
Learning Objectives for 16.540

Development of "physical insight" into the phenomena which characterize internal flow in fluid machinery (not just what happened, but why it happened).

Ability to define, in a rigorous manner, the levels of modeling needed for useful descriptions of a number of internal flow situations.

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:

Describe overall principles for developing models of internal flows (inclass discussions, concept quizzes). [KNOWLEDGE, COMPREHENSION, ANALYSIS]

Apply control volume analysis to internal flow situations and evaluate the features and the limitations of the solutions (inclass discussion, concept quizzes). [APPLICATION, SYNTHESIS, EVALUATION]

Apply concepts of vorticity and circulation to describe and quantify the behavior of internal flows (inclass discussions, concept quiz). [COMPREHENSION, APPLICATION, ANALYSIS]

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 nondimensional parameters for describing these flows, develop simplified models to describe and quantify these flows (inclass discussions, concept quiz). [COMPREHENSION, APPLICATION, ANALYSIS]

Describe loss generation metrics and mechanisms in internal flows, identify appropriate nondimensional parameters for assessing mixing and loss in internal flows, develop simplified models to describe and quantify mixing and losses (inclass discussions, concept quiz). [COMPREHENSION, APPLICATION, ANALYSIS]

State and explain one or two examples where unsteady flow plays an important role in the behavior of fluid machinery, identify the appropriate nondimensional parameters for assessing the importance of unsteadiness, describe the general forms of disturbances in flows, develop simplified models to describe and quantify these flows (inclass discussions, concept quiz). [COMPREHENSION, APPLICATION, ANALYSIS]

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 twentyfive 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] 
23 
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


56 
Dynamics of vorticity
Vorticity changes in inviscid and viscous, incompressible and compressible fluids, with uniform and nonuniform density, with conservative and nonconservative 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 nonuniform density, with conservative and nonconservative body forces. Applications to flows of uniform and nonuniform density, creation of circulation in a nonuniform 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, nonheat 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 velocityvorticity relationship, examples for twodimensional 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 nonuniform 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 nonuniform stagnation properties
Mixing loss from fluid injection into a stream
Irreversibility generation in mixing


1314 
Averaging of a nonuniform flow  What is "The" loss
Concepts: Area average, mass average and stream thrust average
Application to a simple flow model
Appropriate averages for a nonuniform 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: Twostream mixing, linear shear flow mixing in diffusers and nozzles, wake mixing
Loss characterization in turbomachinery cascades



Midterm 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
Nondimensional 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 taylorproudman theorem (two different perspectives)
Viscous flows (ekman layers) on rotating surfaces

Concept quiz 5 
18 
Rotating channel flow in constant area straight passages
Twodimensional inviscid flow in a rotating straight channel
Fully developed flow in a rotating straight channel
Boundary layers in rotating straight channels


1920 
Rotating flow in turbomachinery passages
Twodimensional flow in rotating diffusing passages
Threedimensional 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] 
2122 
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!)


2324 
Waves and oscillations in fluid systems
Introduction to selfexcited 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 multidimensional disturbances in fluid systems

Concept quiz 7 
25 
Elements of compressor stability modeling
Loworder description of asymmetric flow in compressors, onset of rotating stall



Final oral exam 



Further Reading:

Readings
This section includes the supplementary reading list which provides a different perspective on the topics covered.
Please read the following sections in the text before class and come prepared to discuss the material. All readings in the table below are from the following text:
Greitzer, E., C. Tan, and M. Graf. Internal Flow: Concepts and Applications. Cambridge, UK: Cambridge University Press, 2004. ISBN: 9780521343930.
Course readings.

LEC #

READINGS

2

2.3, 2.3.1, 2.3.2, 2.4.1, and 2.4.2.

3

2.8 through 2.8.3, 2.9 through 2.9.2, and 2.10 through 2.10.3.

4

3.1 through 3.2.2.

5

3.3 through 3.4.2.

6

3.5 through 3.7.

7

3.8 through 3.10.1.

8

3.12 through 3.14.1.3.

9

9.9 through 9.10.3.

10

5.1 through 5.3.

11

5.4 through 5.4.3.

12

5.5 through 5.5.6.

13

5.6 through 5.6.3.

14

5.6.5 through 5.6.5.1, and 5.7 through 5.7.2.

15

5.9 through 5.11.

16

7.1 through 7.4.1.

17

7.4.2 through 7.4.3.

18

7.6 through 7.6.2.

19

7.8 through 7.9.

20

9.7 through 9.7.3, and 9.8 through 9.8.1.

21

6.1 through 6.3.1.

22

6.4 through 6.4.5.

23

6.5 through 6.5.2.

24

6.6 through 6.6.3, 6.7, and 6.8.2.

25

12.7 through 12.7.1.

Supplemental Readings
Below is a supplementary reading list which provides a different perspective on the topics covered.
Course readings.

PART #

READINGS

II. Some useful basic ideas

Batchelor, G. K. An Introduction to Fluid Dynamics. Cambridge, UK: Cambridge University Press, 2000. ISBN: 9780521663960.
Johnston, J. P. "Internal Flows." In Turbulence. Edited by P. Bradshaw. New York, NY: SpringerVerlag, 1976. ISBN: 9780387077055.
Fay, J. A. Introduction to Fluid Mechanics. Cambridge, MA: MIT Press, 1994. ISBN: 9780262061650.
Sabersky, R., A. Acosta, and E. Hauptmann. Fluid Flow: A First Course in Fluid Mechanics. New York, NY: MacMillan Publishers, 1998. ISBN: 9780135763728.
Schlichting, H. Boundary Layer Theory. New York, NY: McGrawHill, 2004. ISBN: 9783540662709.
White, F. M. Viscous Fluid Flow. New York, NY: McGrawHill, 2005. ISBN: 9780072402315.

III. Vorticity and circulation

Batchelor, G. K. An Introduction to Fluid Dynamics. Cambridge, UK: Cambridge University Press, 2000. ISBN: 9780521663960.
Lighthill, J. An Informal Introduction to Theoretical Fluid Mechanics. Oxford, UK: Oxford University Press, 1988. ISBN: 9780198536307.
National Committee. Illustrated Experiments in Fluid Mechanics. Cambridge, MA: MIT Press, 1972. ISBN: 9780262640121. (See especially the chapter on Vorticity by Shapiro).
Panton, P. Incompressible Flow. New York, NY: Wiley, 2005. ISBN: 9780471261223.
Rosenhead, L., ed. Laminar Boundary Layers. New York, NY: Dover, 1988, chapter 2. ISBN: 9780486656465.
Saffman, P. G. Vortex Dynamics. Cambridge, UK: Cambridge University Press, 1995. ISBN: 9780521477390.
Scorer, R. S. Environmental Aerodynamics. New York, NY: John Wiley & Sons, 1978. ISBN: 9780470992708.
Sherman, F. S. Viscous Flow. New York, NY: McGrawHill, 1990. ISBN: 9780070565791.

IV. Loss sources and loss accounting

Pianko, M., and F. Wazelt. "Suitable Averaging Techniques in Nonuniform Internal Flows." AGARD AR, Propulsion and Energetic Panel Working Group 14, no. 182 (1983).
Cumpsty, N. A. Compressor Aerodynamics. Melbourne, FL: Krieger Publishing, 2004. ISBN: 9781575242477.
Cumpsty, N. A., and J. H. Horlock. "Averaging NonUniform Flow with a Purpose." IGTI Paper GT200568081, 2005.
Denton, J. D. "Loss Mechanisms in Turbomachines." ASME J Turbomachinery 115 (1993): 621656.
Prasad, A. "Calculation of the MixedOut State in Turbomachine Flows." ASME J Turbomachinery 127 (2005): 564572.

V. Flow in rotating passages

Cumpsty, N. A. Compressor Aerodynamics. Melbourne, FL: Krieger Publishing, 2004. ISBN: 9781575242477.
Greenspan, H. P. The Theory of Rotating Fluids. Cambridge, UK: Cambridge University Press, 1968. ISBN: 9780521051477.
Kleppner, D, and R. J. Kolenkow. An Introduction to Mechanics. New York, NY: McGrawHill, 1973. ISBN: 9780070350489. (There are many good dynamics books with discussions of Coriolis forces; this one gives a treatment at an elementary and instructive level.)
Scorer, R. S. Environmental Aerodynamics. New York, NY: John Wiley & Sons, 1978. ISBN: 9780470992708.
Tritton, D. Physical Fluid Dynamics. Oxford, UK: Oxford University Press, 1988. ISBN: 9780198544937.

VI. Unsteady flow

Paduano, J. D., E. M. Greitzer, and A. H. Epstein. "Compression System Stability and Active Control." Annual Review of Fluid Mechanics 33 (2001): 491517.
Horlock, J. H. Axial Flow Compressors: Fluid Mechanics and Thermodynamics, Axial Flow Turbines. Melbourne, FL: Krieger Publishing, 1982. ISBN: 9780882750965.
———. Axial Flow Turbines: Fluid Mechanics and Thermodynamics, Axial Flow Turbines. Melbourne, FL: Krieger Publishing, 1973. ISBN: 9780882750972.
Rosenhead, L., ed. Laminar Boundary Layers. New York, NY: Dover, 1988, chapter 6. ISBN: 9780486656465.
Sabersky, R., A. Acosta, and E. Hauptmann. Fluid Flow: A First Course in Fluid Mechanics. New York, NY: MacMillan Publishers, 1998. ISBN: 9780135763728.
Schlichting, H. Boundary Layer Theory. New York, NY: McGrawHill, 2004. ISBN: 9783540662709.




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