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