16.540 | Spring 2006 | Graduate

Internal Flows in Turbomachines

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  

Course Info

As Taught In
Spring 2006
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Lecture Notes