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Internal Flow Concepts and Applications

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ISBN-10: 0521036720

ISBN-13: 9780521036726

Edition: 2006

Authors: E. M. Greitzer, C. S. Tan, M. B. Graf

List price: $119.99
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Focusing on phenomena important in implementing the performance of a broad range of fluid devices, this work describes the behavior of internal flows encountered in propulsion systems, fluid machinery (compressors, turbines, and pumps) and ducts (diffusers, nozzles and combustion chambers). The book equips students and practicing engineers with a range of new analytical tools. These tools offer enhanced interpretation and application of both experimental measurements and the computational procedures that characterize modern fluids engineering.
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Book details

List price: $119.99
Copyright year: 2006
Publisher: Cambridge University Press
Publication date: 2/26/2007
Binding: Paperback
Pages: 736
Size: 6.50" wide x 9.25" long x 1.50" tall
Weight: 3.080
Language: English

Conventions and nomenclature
Equations of motion
Properties of a fluid and the continuum assumption
Dynamic and thermodynamic principles
The rate of change of quantities following a fluid particle
Mass and momentum conservation for a fluid system
Thermodynamic states and state change processes for a fluid system
First and second laws of thermodynamics for a fluid system
Behavior of the working fluid
Equations of state
Specific heats
Relation between changes in material and fixed volumes: Reynolds's Transport Theorem
Conservation laws for a fixed region (control volume)
Description of stress within a fluid
Integral forms of the equations of motion
Force, torque, and energy exchange in fluid devices
Differential forms of the equations of motion
Conservation of mass
Conservation of momentum
Conservation of energy
Splitting the energy equation: entropy changes in a fluid
Heat transfer and entropy generation sources
Initial and boundary conditions
Boundary conditions at solid surfaces
Inlet and outlet boundary conditions
The rate of strain tensor and the form of the dissipation function
Relationship between stress and rate of strain
The Navier-Stokes equations
Cartesian coordinates
Cylindrical coordinates
Disturbance propagation in a compressible fluid: the speed of sound
Stagnation and static quantities
Relation of stagnation and static quantities in terms of Mach number
Kinematic and dynamic flow field similarity
Incompressible flow
Kinematic similarity
Dynamic similarity
Compressible flow
Limiting forms for low Mach number
Some useful basic ideas
The assumption of incompressible flow
Steady flow
Unsteady flow
Upstream influence
Upstream influence of a circumferentially periodic non-uniformity
Upstream influence of a radial non-uniformity in an annulus
Pressure fields and streamline curvature: equations of motion in natural coordinates
Normal and streamwise accelerations and pressure gradients
Other expressions for streamline curvature
Quasi-one-dimensional steady compressible flow
Corrected flow per unit area
Differential relations between area and flow variables for steady isentropic one-dimensional flow
Steady isentropic one-dimensional channel flow
Shock waves
The entropy rise across a normal shock
Shock structure and entropy generation processes
Effect of exit conditions on steady, isentropic, one-dimensional compressible channel flow
Flow regimes for a converging nozzle
Flow regimes for a converging-diverging nozzle
Applications of the integral forms of the equations of motion
Pressure rise and mixing losses at a sudden expansion
Ejector performance
Fluid force on turbomachinery blading
The Euler turbine equation
Thrust force on an inlet
Thrust of a cylindrical tube with heating or cooling (idealized ramjet)
Oblique shock waves
Boundary layers
Features of boundary layers in ducts
The influence of boundary layers on the flow outside the viscous region
Turbulent boundary layers
Inflow and outflow in fluid devices: separation and the asymmetry of real fluid motions
Qualitative considerations concerning flow separation from solid surfaces
The contrast between flow in and out of a pipe
Flow through a bent tube as an illustration of the principles
Flow through a sharp edged orifice
Vorticity and circulation
Vorticity kinematics
Vortex lines and vortex tubes
Behavior of vortex lines at a solid surface
Vorticity dynamics
Vorticity changes in an incompressible, uniform density, inviscid flow with conservative body force
Examples: Secondary flow in a bend, horseshoe vortices upstream of struts
Vorticity changes and angular momentum changes
Vorticity changes in an incompressible, non-uniform density, inviscid flow
Examples of vorticity creation due to density non-uniformity
Vorticity changes in a uniform density, viscous flow with conservative body forces
Vorticity changes and viscous torques
Diffusion and intensification of vorticity in a viscous vortex
Changes of vorticity in a fixed volume
Summary of vorticity evolution in an incompressible flow
Vorticity changes in a compressible inviscid flow
Kelvin's Theorem
Circulation behavior in an incompressible flow
Uniform density inviscid flow with conservative body forces
Incompressible, non-uniform density, inviscid flow with conservative body forces
Uniform density viscous flow with conservative body forces
Circulation behavior in a compressible inviscid flow
Circulation generation due to shock motion in a non-homogeneous medium
Rate of change of circulation for a fixed contour
Rotational flow descriptions in terms of vorticity and circulation
Behavior of vortex tubes when D[Gamma]/Dt = 0
Evolution of a non-uniform flow through a diffuser or nozzle
Trailing vorticity and trailing vortices
Generation of vorticity at solid surfaces
Generation of vorticity in a two-dimensional flow
Vorticity flux in thin shear layers (boundary layers and free shear layers)
Vorticity generation at a plane surface in a three-dimensional flow
Relation between kinematic and thermodynamic properties in an inviscid, non-heat-conducting fluid: Crocco's Theorem
Applications of Crocco's Theorem
The velocity field associated with a vorticity distribution
Application of the velocity representation to vortex tubes
Application to two-dimensional flow
Surface distributions of vorticity
Some specific velocity fields associated with vortex structures
Numerical methods based on the distribution of vorticity
Boundary layers and free shear layers
Boundary layer behavior and device performance
The boundary layer equations for plane and curved surfaces
Plane surfaces
Extension to curved surfaces
Boundary layer integral quantities and the equations that describe them
Boundary layer integral thicknesses
Integral forms of the boundary layer equations
Laminar boundary layers
Laminar boundary layer behavior in favorable and adverse pressure gradients
Laminar boundary layer separation
Laminar-turbulent boundary layer transition
Turbulent boundary layers
The time mean equations for turbulent boundary layers
The composite nature of a turbulent boundary layer
Introductory discussion of turbulent shear stress
Boundary layer thickness and wall shear stress in laminar and turbulent flow
Vorticity and velocity fluctuations in turbulent flow
Applications of boundary layer analysis: viscous-inviscid interaction in a diffuser
Qualitative description of viscous-inviscid interaction
Quantitative description of viscous-inviscid interaction
Extensions of interactive boundary layer theory to other situations
Turbulent boundary layer separation
Free turbulent flows
Similarity solutions for incompressible uniform-density free shear layers
The mixing layer between two streams
The effects of compressibility on free shear layer mixing
Appropriateness of the similarity solutions
Turbulent entrainment
Jets and wakes in pressure gradients
Loss sources and loss accounting
Losses and entropy change
Losses in a spatially uniform flow through a screen or porous plate
Irreversibility, entropy generation, and lost work
Lost work accounting in fluid components and systems
Loss accounting and mixing in spatially non-uniform flows
Boundary layer losses
Entropy generation in boundary layers on adiabatic walls
The boundary layer dissipation coefficient
Estimation of turbomachinery blade profile losses
Mixing losses
Mixing of two streams with non-uniform stagnation pressure and/or temperature
The limiting case of low Mach number (M[superscript 2] [less than less than] 1) mixing
Comments on loss metrics for flows with non-uniform temperatures
Mixing losses from fluid injection into a stream
Irreversibility in mixing
A caveat: smoothing out of a flow non-uniformity does not always imply loss
Averaging in non-uniform flows: the average stagnation pressure
Representation of a non-uniform flow by equivalent average quantities
Averaging procedures in an incompressible uniform-density flow
Effect of velocity distribution on average stagnation pressure (incompressible, uniform-density flow)
Averaging procedures in compressible flow
Appropriate average values for stagnation quantities in a non-uniform flow
Streamwise evolution of losses in fluid devices
Stagnation pressure averages and integral boundary layer parameters
Comparison of losses within a device to losses from downstream mixing
Effect of base pressure on mixing losses
Effect of pressure level on average properties and mixing losses
Two-stream mixing
Mixing of a linear shear flow in a diffuser or nozzle
Wake mixing
Losses in turbomachinery cascades
Summary concerning loss generation and characterization
Unsteady flow
The inherent unsteadiness of fluid machinery
The reduced frequency
An example of the role of reduced frequency: unsteady flow in a channel
Examples of unsteady flows
Stagnation pressure changes in an irrotational incompressible flow
The starting transient for incompressible flow exiting a tank
Stagnation pressure variations due to the motion of an isolated airfoil
Moving blade row (moving row of bound vortices)
Unsteady wake structure and energy separation
Shear layer instability
Instability of a vortex sheet (Kelvin-Helmholtz instability)
General features of parallel shear layer instability
Waves and oscillation in fluid systems: system instabilities
Transfer matrices (transmission matrices) for fluid components
Examples of unsteady behavior in fluid systems
Nonlinear oscillations in fluid systems
Multi-dimensional unsteady disturbances in a compressible inviscid flow
Examples of fluid component response to unsteady disturbances
Interaction of entropy and pressure disturbances
Interaction of vorticity and pressure disturbances
Disturbance interaction caused by shock waves
Irrotational disturbances and upstream influence in a compressible flow
Summary concerning small amplitude unsteady disturbances
Some Features of unsteady viscous flows
Flow due to an oscillating boundary
Oscillating channel flow
Unsteady boundary layers
Dynamic stall
Turbomachine wake behavior in an unsteady environment
Flow in rotating passages
Equations of motion in a rotating coordinate system
Rotating coordinate systems and Coriolis accelerations
Centrifugal accelerations in a uniform density fluid: the reduced static pressure
Illustrations of Coriolis and centrifugal forces in a rotating coordinate system
Conserved quantities in a steady rotating flow
Phenomena in flows where rotation dominates
Non-dimensional parameters: the Rossby and Ekman numbers
Inviscid flow at low Rossby number: the Taylor-Proudman Theorem
Viscous flow at low Rossby number: Ekman layers
Changes in vorticity and circulation in a rotating flow
Flow in two-dimensional rotating straight channels
Inviscid flow
Coriolis effects on boundary layer mixing and stability
Three-dimensional flow in rotating passages
Generation of cross-plane circulation in a rotating passage
Fully developed viscous flow in a rotating square duct
Comments on viscous flow development in rotating passages
Two-dimensional flow in rotating diffusing passages
Quasi-one-dimensional approximation
Two-dimensional inviscid flow in a rotating diffusing blade passage
Effects of rotation on diffuser performance
Features of the relative flow in axial turbomachine passages
Swirling flow
Incompressible, uniform-density, inviscid swirling flows in simple radial equilibrium
Examples of simple radial equilibrium flows
Rankine vortex flow
Upstream influence in a swirling flow
Effects of circulation and stagnation pressure distributions on upstream influence
Instability in swirling flow
Waves on vortex cores
Control volume equations for a vortex core
Wave propagation in unconfined geometries
Wave propagation and flow regimes in confined geometries: swirl stabilization of Kelvin-Helmholtz instability
Features of steady vortex core flows
Pressure gradients along a vortex core centerline
Axial and circumferential velocity distributions in vortex cores
Applicability of the Rankine vortex model
Vortex core response to external conditions
Unconfined geometries (steady vortex cores with specified external pressure variation)
Confined geometries (steady vortex cores in ducts with specified area variation)
Discontinuous vortex core behavior
Swirling flow boundary layers
Swirling flow boundary layers on stationary surfaces and separation in swirling flow
Swirling flow boundary layers on rotating surfaces
The enclosed rotating disk
Internal flow in gas turbine engine rotating disk cavities
Swirling jets
Recirculation in axisymmetric swirling flow and vortex breakdown
Generation of streamwise vorticity and three-dimensional flow
A basic illustration of secondary flow: a boundary layer in a bend
Qualitative description
A simple estimate for streamwise vorticity generation and cross-flow plane velocity components
A quantitative look at secondary flow in a bend: measurements and three-dimensional computations
Additional examples of secondary flow
Outflow of swirling fluid from a container
Secondary flow in an S-shaped duct
Streamwise vorticity and secondary flow in a two-dimensional contraction
Three-dimensional flow in turbine passages
Expressions for the growth of secondary circulation in an inviscid flow
Incompressible uniform density fluid
Incompressible non-uniform density fluid
Perfect gas with constant specific heats
Applications of secondary flow analyses
Approximations based on convection of vorticity by a primary flow
Flow with large distortion of the stream surfaces
Three-dimensional boundary layers: further remarks on effects of viscosity in secondary flow
Secondary flow in a rotating reference frame
Absolute vorticity as a measure of secondary circulation
Generation of secondary circulation in a rotating reference frame
Expressions for, and examples of, secondary circulation in rotating systems
Non-uniform density flow in rotating passages
Secondary flow in rotating machinery
Radial migration of high temperature fluid in a turbine rotor
Streamwise vorticity and mixing enhancement
Lobed mixers and streamwise vorticity generation
Vortex-enhanced mixing
Additional aspects of mixing enhancement in lobed mixers
Fluid impulse and vorticity generation
Creation of a vortex ring by a distribution of impulses
Fluid impulse and lift on an airfoil
Far field behavior of a jet in cross-flow
Compressible internal flow
Corrected flow per unit area
Generalized one-dimensional compressible flow analysis
Differential equations for one-dimensional flow
Influence coefficient matrix for one-dimensional flow
Effects of shaft work and body forces
Effects of friction and heat addition on compressible channel flow
Constant area adiabatic flow with friction
Constant area frictionless flow with heat addition
Results for area change, friction, and heat addition
Starting and operation of supersonic diffusers and inlets
The problem of starting a supersonic flow
The use of variable geometry to start the flow
Starting of supersonic inlets
Characteristics of supersonic flow in passages and channels
Turbomachinery blade passages
Shock wave patterns in ducts and shock train behavior
Extensions of the one-dimensional concepts - I: axisymmetric compressible swirling flow
Development of equations for compressible swirling flow
Application of influence coefficients for axisymmetric compressible swirling flow
Behavior of connected flow per unit area in a compressible swirling flow
Extensions of the one-dimensional concepts - II: compound-compressible channel flow
Introduction to compound flow: two-stream low Mach number (incompressible) flow in a converging nozzle
Qualitative considerations for multistream compressible flow
Compound-compressible channel flow theory
One-dimensional compound waves
Results for two-stream compound-compressible flows
Flow angle, Mach number, and pressure changes in isentropic supersonic flow
Differential relationships for small angle changes
Relationships for finite angle changes: Prandtl-Meyer flows
Flow field invariance to stagnation temperature distribution: the Munk and Prim substitution principle
Two-dimensional flow
Three-dimensional flow
Flow from a reservoir with non-uniform stagnation temperature
Flow with heat addition
Introduction: sources of heat addition
Heat addition and vorticity generation
Stagnation pressure decrease due to heat addition
Heat addition and flow state changes in propulsion devices
The H-K diagram
Flow processes in ramjet and scramjet systems
An illustration of the effect of condensation on compressible flow behavior
Swirling flow with heat addition
Results for vortex core behavior with heat addition
An approximate substitution principle for viscous heat conducting flow
Equations for flow with heat addition and mixing
Two-stream mixing as a model problem-I: constant area, low Mach number, uniform inlet stagnation pressure
Two-stream mixing as a model problem- II: non-uniform inlet stagnation pressures
Effects of inlet Mach number level
Applications of the approximate principle
Lobed mixer nozzles
Mixing of streams with non-uniform densities
Comments on the approximations
Non-uniform flow in fluid components
An illustrative example of flow modeling: two-dimensional steady non-uniform flow through a screen
elocity and pressure field upstream of the screen
Flow in the downstream region
Matching conditions across the screen
Overall features of the solution
Nonlinear effects
Disturbance length scales and the assumption of inviscid flow
Applications to creation of a velocity non-uniformity using screens
Flow through a uniform inclined screen
Pressure drop and velocity field with partial duct blockage
Enhancing flow uniformity in diffusing passages
Upstream influence and component interaction
Non-axisymmetric (asymmetric) flow in axial compressors
Flow upstream of the compressor
Flow downstream of the compressor
Matching conditions across the compressor
Behavior of the axial velocity and upstream static pressure
Generation of non-uniform flow by circumferentially varying tip clearance
Additional examples of upstream effects in turbomachinery flows
Turbine engine effects on inlet performance
Strut-vane row interaction: upstream influence with two different length scales
Unsteady compressor response to asymmetric flow
Self-excited propagating disturbances in axial compressors and compressor instability
A deeper look at the effects of circumferentially varying tip clearance
Axial compressor response to circumferentially propagating distortions
Nonlinear descriptions of compressor behavior in asymmetric flow
Non-axisymmetric flow in annular diffusers and compressor-component coupling
Quasi-two-dimensional description of non-axisymmetric flow in an annular diffuser
Features of the diffuser inlet static pressure field
Compressor-component coupling
Effects of flow non-uniformity on diffuser performance
Introduction to non-axisymmetric swirling flows
A simple approach for long length scale non-uniformity
Explicit forms of the velocity disturbances
Flow angle disturbances
Relations between stagnation pressure, static pressure, and flow angle disturbances
Overall features of non-axisymmetric swirling flow
A secondary flow approach to non-axisymmetric swirling flow
Supplementary references appearing in figures