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 Internal Flows in Turbomachines  posted by  member150_php   on 2/22/2009  Add Courseware to favorites Add To Favorites  
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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 BY-NC-SA

Internal Flows in Turbomachines

Spring 2006

Fluid flow leakage around a compressor tip.
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 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.


ACTIVITIES PERCENTAGES
Class participation 10%
Concept questions 10%
Concept quizzes 20%
Team project 20%
Mid-term exam 15%
Final exams 25%

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.


    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



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