| 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
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| 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
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| 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
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| 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.
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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.
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| 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.
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| 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.
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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
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| 11 |
Boundary layer losses
Entropy generation in boundary layers
Entropy production and dissipation coefficient
Estimation of turbomachinery blade profile losses
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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
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| 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
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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
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Mid-term oral exam |
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| 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
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| 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
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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
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| 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
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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!)
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| 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
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Concept quiz 7 |
| 25 |
Elements of compressor stability modeling
Low-order description of asymmetric flow in compressors, onset of rotating stall
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Final oral exam |
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