| Preface | p. xvii |
| Acknowledgements | p. xx |
| Conventions and nomenclature | p. xxii |
| Equations of motion | p. 1 |
| Introduction | p. 1 |
| Properties of a fluid and the continuum assumption | p. 2 |
| Dynamic and thermodynamic principles | p. 2 |
| The rate of change of quantities following a fluid particle | p. 3 |
| Mass and momentum conservation for a fluid system | p. 4 |
| Thermodynamic states and state change processes for a fluid system | p. 4 |
| First and second laws of thermodynamics for a fluid system | p. 6 |
| Behavior of the working fluid | p. 8 |
| Equations of state | p. 8 |
| Specific heats | p. 9 |
| Relation between changes in material and fixed volumes: Reynolds's Transport Theorem | p. 11 |
| Conservation laws for a fixed region (control volume) | p. 13 |
| Description of stress within a fluid | p. 15 |
| Integral forms of the equations of motion | p. 19 |
| Force, torque, and energy exchange in fluid devices | p. 19 |
| Differential forms of the equations of motion | p. 20 |
| Conservation of mass | p. 24 |
| Conservation of momentum | p. 25 |
| Conservation of energy | p. 26 |
| Splitting the energy equation: entropy changes in a fluid | p. 26 |
| Heat transfer and entropy generation sources | p. 27 |
| Initial and boundary conditions | p. 28 |
| Boundary conditions at solid surfaces | p. 29 |
| Inlet and outlet boundary conditions | p. 30 |
| The rate of strain tensor and the form of the dissipation function | p. 31 |
| Relationship between stress and rate of strain | p. 34 |
| The Navier-Stokes equations | p. 37 |
| Cartesian coordinates | p. 38 |
| Cylindrical coordinates | p. 39 |
| Disturbance propagation in a compressible fluid: the speed of sound | p. 40 |
| Stagnation and static quantities | p. 41 |
| Relation of stagnation and static quantities in terms of Mach number | p. 42 |
| Kinematic and dynamic flow field similarity | p. 43 |
| Incompressible flow | p. 43 |
| Kinematic similarity | p. 44 |
| Dynamic similarity | p. 44 |
| Compressible flow | p. 45 |
| Limiting forms for low Mach number | p. 46 |
| Some useful basic ideas | p. 48 |
| Introduction | p. 48 |
| The assumption of incompressible flow | p. 48 |
| Steady flow | p. 49 |
| Unsteady flow | p. 51 |
| Upstream influence | p. 51 |
| Upstream influence of a circumferentially periodic non-uniformity | p. 52 |
| Upstream influence of a radial non-uniformity in an annulus | p. 54 |
| Pressure fields and streamline curvature: equations of motion in natural coordinates | p. 56 |
| Normal and streamwise accelerations and pressure gradients | p. 56 |
| Other expressions for streamline curvature | p. 57 |
| Quasi-one-dimensional steady compressible flow | p. 60 |
| Corrected flow per unit area | p. 61 |
| Differential relations between area and flow variables for steady isentropic one-dimensional flow | p. 63 |
| Steady isentropic one-dimensional channel flow | p. 65 |
| Shock waves | p. 65 |
| The entropy rise across a normal shock | p. 66 |
| Shock structure and entropy generation processes | p. 68 |
| Effect of exit conditions on steady, isentropic, one-dimensional compressible channel flow | p. 71 |
| Flow regimes for a converging nozzle | p. 72 |
| Flow regimes for a converging-diverging nozzle | p. 74 |
| Applications of the integral forms of the equations of motion | p. 76 |
| Pressure rise and mixing losses at a sudden expansion | p. 76 |
| Ejector performance | p. 78 |
| Fluid force on turbomachinery blading | p. 80 |
| The Euler turbine equation | p. 83 |
| Thrust force on an inlet | p. 84 |
| Thrust of a cylindrical tube with heating or cooling (idealized ramjet) | p. 86 |
| Oblique shock waves | p. 87 |
| Boundary layers | p. 89 |
| Features of boundary layers in ducts | p. 89 |
| The influence of boundary layers on the flow outside the viscous region | p. 91 |
| Turbulent boundary layers | p. 94 |
| Inflow and outflow in fluid devices: separation and the asymmetry of real fluid motions | p. 94 |
| Qualitative considerations concerning flow separation from solid surfaces | p. 94 |
| The contrast between flow in and out of a pipe | p. 96 |
| Flow through a bent tube as an illustration of the principles | p. 98 |
| Flow through a sharp edged orifice | p. 100 |
| Vorticity and circulation | p. 104 |
| Introduction | p. 104 |
| Vorticity kinematics | p. 105 |
| Vortex lines and vortex tubes | p. 107 |
| Behavior of vortex lines at a solid surface | p. 110 |
| Vorticity dynamics | p. 111 |
| Vorticity changes in an incompressible, uniform density, inviscid flow with conservative body force | p. 112 |
| Examples: Secondary flow in a bend, horseshoe vortices upstream of struts | p. 114 |
| Vorticity changes and angular momentum changes | p. 117 |
| Vorticity changes in an incompressible, non-uniform density, inviscid flow | p. 119 |
| Examples of vorticity creation due to density non-uniformity | p. 121 |
| Vorticity changes in a uniform density, viscous flow with conservative body forces | p. 122 |
| Vorticity changes and viscous torques | p. 124 |
| Diffusion and intensification of vorticity in a viscous vortex | p. 125 |
| Changes of vorticity in a fixed volume | p. 127 |
| Summary of vorticity evolution in an incompressible flow | p. 128 |
| Vorticity changes in a compressible inviscid flow | p. 128 |
| Circulation | p. 130 |
| Kelvin's Theorem | p. 130 |
| Circulation behavior in an incompressible flow | p. 132 |
| Uniform density inviscid flow with conservative body forces | p. 132 |
| Incompressible, non-uniform density, inviscid flow with conservative body forces | p. 134 |
| Uniform density viscous flow with conservative body forces | p. 135 |
| Circulation behavior in a compressible inviscid flow | p. 135 |
| Circulation generation due to shock motion in a non-homogeneous medium | p. 135 |
| Rate of change of circulation for a fixed contour | p. 137 |
| Rotational flow descriptions in terms of vorticity and circulation | p. 138 |
| Behavior of vortex tubes when D[Gamma]/Dt = 0 | p. 139 |
| Evolution of a non-uniform flow through a diffuser or nozzle | p. 140 |
| Trailing vorticity and trailing vortices | p. 142 |
| Generation of vorticity at solid surfaces | p. 144 |
| Generation of vorticity in a two-dimensional flow | p. 145 |
| Vorticity flux in thin shear layers (boundary layers and free shear layers) | p. 149 |
| Vorticity generation at a plane surface in a three-dimensional flow | p. 151 |
| Relation between kinematic and thermodynamic properties in an inviscid, non-heat-conducting fluid: Crocco's Theorem | p. 152 |
| Applications of Crocco's Theorem | p. 153 |
| The velocity field associated with a vorticity distribution | p. 156 |
| Application of the velocity representation to vortex tubes | p. 158 |
| Application to two-dimensional flow | p. 159 |
| Surface distributions of vorticity | p. 159 |
| Some specific velocity fields associated with vortex structures | p. 160 |
| Numerical methods based on the distribution of vorticity | p. 163 |
| Boundary layers and free shear layers | p. 166 |
| Introduction | p. 166 |
| Boundary layer behavior and device performance | p. 167 |
| The boundary layer equations for plane and curved surfaces | p. 170 |
| Plane surfaces | p. 170 |
| Extension to curved surfaces | p. 173 |
| Boundary layer integral quantities and the equations that describe them | p. 173 |
| Boundary layer integral thicknesses | p. 173 |
| Integral forms of the boundary layer equations | p. 176 |
| Laminar boundary layers | p. 177 |
| Laminar boundary layer behavior in favorable and adverse pressure gradients | p. 177 |
| Laminar boundary layer separation | p. 179 |
| Laminar-turbulent boundary layer transition | p. 182 |
| Turbulent boundary layers | p. 184 |
| The time mean equations for turbulent boundary layers | p. 184 |
| The composite nature of a turbulent boundary layer | p. 187 |
| Introductory discussion of turbulent shear stress | p. 189 |
| Boundary layer thickness and wall shear stress in laminar and turbulent flow | p. 191 |
| Vorticity and velocity fluctuations in turbulent flow | p. 193 |
| Applications of boundary layer analysis: viscous-inviscid interaction in a diffuser | p. 195 |
| Qualitative description of viscous-inviscid interaction | p. 197 |
| Quantitative description of viscous-inviscid interaction | p. 198 |
| Extensions of interactive boundary layer theory to other situations | p. 201 |
| Turbulent boundary layer separation | p. 201 |
| Free turbulent flows | p. 202 |
| Similarity solutions for incompressible uniform-density free shear layers | p. 202 |
| The mixing layer between two streams | p. 205 |
| The effects of compressibility on free shear layer mixing | p. 208 |
| Appropriateness of the similarity solutions | p. 210 |
| Turbulent entrainment | p. 211 |
| Jets and wakes in pressure gradients | p. 212 |
| Loss sources and loss accounting | p. 217 |
| Introduction | p. 217 |
| Losses and entropy change | p. 218 |
| Losses in a spatially uniform flow through a screen or porous plate | p. 218 |
| Irreversibility, entropy generation, and lost work | p. 220 |
| Lost work accounting in fluid components and systems | p. 222 |
| Loss accounting and mixing in spatially non-uniform flows | p. 225 |
| Boundary layer losses | p. 227 |
| Entropy generation in boundary layers on adiabatic walls | p. 227 |
| The boundary layer dissipation coefficient | p. 230 |
| Estimation of turbomachinery blade profile losses | p. 233 |
| Mixing losses | p. 234 |
| Mixing of two streams with non-uniform stagnation pressure and/or temperature | p. 234 |
| The limiting case of low Mach number (M[superscript 2] [less than less than] 1) mixing | p. 237 |
| Comments on loss metrics for flows with non-uniform temperatures | p. 239 |
| Mixing losses from fluid injection into a stream | p. 239 |
| Irreversibility in mixing | p. 241 |
| A caveat: smoothing out of a flow non-uniformity does not always imply loss | p. 242 |
| Averaging in non-uniform flows: the average stagnation pressure | p. 244 |
| Representation of a non-uniform flow by equivalent average quantities | p. 244 |
| Averaging procedures in an incompressible uniform-density flow | p. 245 |
| Effect of velocity distribution on average stagnation pressure (incompressible, uniform-density flow) | p. 248 |
| Averaging procedures in compressible flow | p. 250 |
| Appropriate average values for stagnation quantities in a non-uniform flow | p. 253 |
| Streamwise evolution of losses in fluid devices | p. 258 |
| Stagnation pressure averages and integral boundary layer parameters | p. 258 |
| Comparison of losses within a device to losses from downstream mixing | p. 261 |
| Effect of base pressure on mixing losses | p. 262 |
| Effect of pressure level on average properties and mixing losses | p. 267 |
| Two-stream mixing | p. 267 |
| Mixing of a linear shear flow in a diffuser or nozzle | p. 269 |
| Wake mixing | p. 273 |
| Losses in turbomachinery cascades | p. 274 |
| Summary concerning loss generation and characterization | p. 277 |
| Unsteady flow | p. 279 |
| Introduction | p. 279 |
| The inherent unsteadiness of fluid machinery | p. 279 |
| The reduced frequency | p. 281 |
| An example of the role of reduced frequency: unsteady flow in a channel | p. 282 |
| Examples of unsteady flows | p. 286 |
| Stagnation pressure changes in an irrotational incompressible flow | p. 286 |
| The starting transient for incompressible flow exiting a tank | p. 286 |
| Stagnation pressure variations due to the motion of an isolated airfoil | p. 288 |
| Moving blade row (moving row of bound vortices) | p. 290 |
| Unsteady wake structure and energy separation | p. 292 |
| Shear layer instability | p. 297 |
| Instability of a vortex sheet (Kelvin-Helmholtz instability) | p. 298 |
| General features of parallel shear layer instability | p. 300 |
| Waves and oscillation in fluid systems: system instabilities | p. 303 |
| Transfer matrices (transmission matrices) for fluid components | p. 305 |
| Examples of unsteady behavior in fluid systems | p. 310 |
| Nonlinear oscillations in fluid systems | p. 315 |
| Multi-dimensional unsteady disturbances in a compressible inviscid flow | p. 321 |
| Examples of fluid component response to unsteady disturbances | p. 324 |
| Interaction of entropy and pressure disturbances | p. 324 |
| Interaction of vorticity and pressure disturbances | p. 328 |
| Disturbance interaction caused by shock waves | p. 334 |
| Irrotational disturbances and upstream influence in a compressible flow | p. 334 |
| Summary concerning small amplitude unsteady disturbances | p. 336 |
| Some Features of unsteady viscous flows | p. 337 |
| Flow due to an oscillating boundary | p. 337 |
| Oscillating channel flow | p. 338 |
| Unsteady boundary layers | p. 340 |
| Dynamic stall | p. 343 |
| Turbomachine wake behavior in an unsteady environment | p. 344 |
| Flow in rotating passages | p. 347 |
| Introduction | p. 347 |
| Equations of motion in a rotating coordinate system | p. 347 |
| Rotating coordinate systems and Coriolis accelerations | p. 349 |
| Centrifugal accelerations in a uniform density fluid: the reduced static pressure | p. 353 |
| Illustrations of Coriolis and centrifugal forces in a rotating coordinate system | p. 353 |
| Conserved quantities in a steady rotating flow | p. 355 |
| Phenomena in flows where rotation dominates | p. 357 |
| Non-dimensional parameters: the Rossby and Ekman numbers | p. 357 |
| Inviscid flow at low Rossby number: the Taylor-Proudman Theorem | p. 358 |
| Viscous flow at low Rossby number: Ekman layers | p. 359 |
| Changes in vorticity and circulation in a rotating flow | p. 363 |
| Flow in two-dimensional rotating straight channels | p. 365 |
| Inviscid flow | p. 365 |
| Coriolis effects on boundary layer mixing and stability | p. 367 |
| Three-dimensional flow in rotating passages | p. 369 |
| Generation of cross-plane circulation in a rotating passage | p. 369 |
| Fully developed viscous flow in a rotating square duct | p. 373 |
| Comments on viscous flow development in rotating passages | p. 378 |
| Two-dimensional flow in rotating diffusing passages | p. 380 |
| Quasi-one-dimensional approximation | p. 380 |
| Two-dimensional inviscid flow in a rotating diffusing blade passage | p. 382 |
| Effects of rotation on diffuser performance | p. 384 |
| Features of the relative flow in axial turbomachine passages | p. 385 |
| Swirling flow | p. 389 |
| Introduction | p. 389 |
| Incompressible, uniform-density, inviscid swirling flows in simple radial equilibrium | p. 390 |
| Examples of simple radial equilibrium flows | p. 391 |
| Rankine vortex flow | p. 393 |
| Upstream influence in a swirling flow | p. 394 |
| Effects of circulation and stagnation pressure distributions on upstream influence | p. 397 |
| Instability in swirling flow | p. 404 |
| Waves on vortex cores | p. 406 |
| Control volume equations for a vortex core | p. 406 |
| Wave propagation in unconfined geometries | p. 408 |
| Wave propagation and flow regimes in confined geometries: swirl stabilization of Kelvin-Helmholtz instability | p. 410 |
| Features of steady vortex core flows | p. 411 |
| Pressure gradients along a vortex core centerline | p. 411 |
| Axial and circumferential velocity distributions in vortex cores | p. 414 |
| Applicability of the Rankine vortex model | p. 414 |
| Vortex core response to external conditions | p. 416 |
| Unconfined geometries (steady vortex cores with specified external pressure variation) | p. 416 |
| Confined geometries (steady vortex cores in ducts with specified area variation) | p. 420 |
| Discontinuous vortex core behavior | p. 422 |
| Swirling flow boundary layers | p. 426 |
| Swirling flow boundary layers on stationary surfaces and separation in swirling flow | p. 426 |
| Swirling flow boundary layers on rotating surfaces | p. 431 |
| The enclosed rotating disk | p. 433 |
| Internal flow in gas turbine engine rotating disk cavities | p. 434 |
| Swirling jets | p. 437 |
| Recirculation in axisymmetric swirling flow and vortex breakdown | p. 440 |
| Generation of streamwise vorticity and three-dimensional flow | p. 446 |
| Introduction | p. 446 |
| A basic illustration of secondary flow: a boundary layer in a bend | p. 446 |
| Qualitative description | p. 446 |
| A simple estimate for streamwise vorticity generation and cross-flow plane velocity components | p. 448 |
| A quantitative look at secondary flow in a bend: measurements and three-dimensional computations | p. 451 |
| Additional examples of secondary flow | p. 451 |
| Outflow of swirling fluid from a container | p. 451 |
| Secondary flow in an S-shaped duct | p. 455 |
| Streamwise vorticity and secondary flow in a two-dimensional contraction | p. 456 |
| Three-dimensional flow in turbine passages | p. 457 |
| Expressions for the growth of secondary circulation in an inviscid flow | p. 461 |
| Incompressible uniform density fluid | p. 461 |
| Incompressible non-uniform density fluid | p. 463 |
| Perfect gas with constant specific heats | p. 464 |
| Applications of secondary flow analyses | p. 465 |
| Approximations based on convection of vorticity by a primary flow | p. 465 |
| Flow with large distortion of the stream surfaces | p. 466 |
| Three-dimensional boundary layers: further remarks on effects of viscosity in secondary flow | p. 469 |
| Secondary flow in a rotating reference frame | p. 472 |
| Absolute vorticity as a measure of secondary circulation | p. 472 |
| Generation of secondary circulation in a rotating reference frame | p. 473 |
| Expressions for, and examples of, secondary circulation in rotating systems | p. 474 |
| Non-uniform density flow in rotating passages | p. 477 |
| Secondary flow in rotating machinery | p. 477 |
| Radial migration of high temperature fluid in a turbine rotor | p. 478 |
| Streamwise vorticity and mixing enhancement | p. 481 |
| Lobed mixers and streamwise vorticity generation | p. 481 |
| Vortex-enhanced mixing | p. 484 |
| Additional aspects of mixing enhancement in lobed mixers | p. 491 |
| Fluid impulse and vorticity generation | p. 494 |
| Creation of a vortex ring by a distribution of impulses | p. 495 |
| Fluid impulse and lift on an airfoil | p. 497 |
| Far field behavior of a jet in cross-flow | p. 499 |
| Compressible internal flow | p. 506 |
| Introduction | p. 506 |
| Corrected flow per unit area | p. 506 |
| Generalized one-dimensional compressible flow analysis | p. 509 |
| Differential equations for one-dimensional flow | p. 509 |
| Influence coefficient matrix for one-dimensional flow | p. 512 |
| Effects of shaft work and body forces | p. 512 |
| Effects of friction and heat addition on compressible channel flow | p. 517 |
| Constant area adiabatic flow with friction | p. 517 |
| Constant area frictionless flow with heat addition | p. 518 |
| Results for area change, friction, and heat addition | p. 519 |
| Starting and operation of supersonic diffusers and inlets | p. 522 |
| The problem of starting a supersonic flow | p. 522 |
| The use of variable geometry to start the flow | p. 524 |
| Starting of supersonic inlets | p. 525 |
| Characteristics of supersonic flow in passages and channels | p. 527 |
| Turbomachinery blade passages | p. 527 |
| Shock wave patterns in ducts and shock train behavior | p. 528 |
| Extensions of the one-dimensional concepts - I: axisymmetric compressible swirling flow | p. 532 |
| Development of equations for compressible swirling flow | p. 533 |
| Application of influence coefficients for axisymmetric compressible swirling flow | p. 537 |
| Behavior of connected flow per unit area in a compressible swirling flow | p. 544 |
| Extensions of the one-dimensional concepts - II: compound-compressible channel flow | p. 546 |
| Introduction to compound flow: two-stream low Mach number (incompressible) flow in a converging nozzle | p. 546 |
| Qualitative considerations for multistream compressible flow | p. 549 |
| Compound-compressible channel flow theory | p. 551 |
| One-dimensional compound waves | p. 554 |
| Results for two-stream compound-compressible flows | p. 556 |
| Flow angle, Mach number, and pressure changes in isentropic supersonic flow | p. 564 |
| Differential relationships for small angle changes | p. 565 |
| Relationships for finite angle changes: Prandtl-Meyer flows | p. 567 |
| Flow field invariance to stagnation temperature distribution: the Munk and Prim substitution principle | p. 569 |
| Two-dimensional flow | p. 570 |
| Three-dimensional flow | p. 572 |
| Flow from a reservoir with non-uniform stagnation temperature | p. 573 |
| Flow with heat addition | p. 575 |
| Introduction: sources of heat addition | p. 575 |
| Heat addition and vorticity generation | p. 577 |
| Stagnation pressure decrease due to heat addition | p. 579 |
| Heat addition and flow state changes in propulsion devices | p. 582 |
| The H-K diagram | p. 582 |
| Flow processes in ramjet and scramjet systems | p. 586 |
| An illustration of the effect of condensation on compressible flow behavior | p. 590 |
| Swirling flow with heat addition | p. 592 |
| Results for vortex core behavior with heat addition | p. 596 |
| An approximate substitution principle for viscous heat conducting flow | p. 599 |
| Equations for flow with heat addition and mixing | p. 599 |
| Two-stream mixing as a model problem-I: constant area, low Mach number, uniform inlet stagnation pressure | p. 601 |
| Two-stream mixing as a model problem- II: non-uniform inlet stagnation pressures | p. 604 |
| Effects of inlet Mach number level | p. 605 |
| Applications of the approximate principle | p. 607 |
| Lobed mixer nozzles | p. 607 |
| Jets | p. 609 |
| Ejectors | p. 610 |
| Mixing of streams with non-uniform densities | p. 613 |
| Comments on the approximations | p. 614 |
| Non-uniform flow in fluid components | p. 615 |
| Introduction | p. 615 |
| An illustrative example of flow modeling: two-dimensional steady non-uniform flow through a screen | p. 616 |
| elocity and pressure field upstream of the screen | p. 617 |
| Flow in the downstream region | p. 620 |
| Matching conditions across the screen | p. 620 |
| Overall features of the solution | p. 622 |
| Nonlinear effects | p. 625 |
| Disturbance length scales and the assumption of inviscid flow | p. 625 |
| Applications to creation of a velocity non-uniformity using screens | p. 628 |
| Flow through a uniform inclined screen | p. 628 |
| Pressure drop and velocity field with partial duct blockage | p. 629 |
| Enhancing flow uniformity in diffusing passages | p. 631 |
| Upstream influence and component interaction | p. 634 |
| Non-axisymmetric (asymmetric) flow in axial compressors | p. 637 |
| Flow upstream of the compressor | p. 638 |
| Flow downstream of the compressor | p. 639 |
| Matching conditions across the compressor | p. 640 |
| Behavior of the axial velocity and upstream static pressure | p. 641 |
| Generation of non-uniform flow by circumferentially varying tip clearance | p. 644 |
| Additional examples of upstream effects in turbomachinery flows | p. 645 |
| Turbine engine effects on inlet performance | p. 645 |
| Strut-vane row interaction: upstream influence with two different length scales | p. 647 |
| Unsteady compressor response to asymmetric flow | p. 648 |
| Self-excited propagating disturbances in axial compressors and compressor instability | p. 651 |
| A deeper look at the effects of circumferentially varying tip clearance | p. 653 |
| Axial compressor response to circumferentially propagating distortions | p. 654 |
| Nonlinear descriptions of compressor behavior in asymmetric flow | p. 655 |
| Non-axisymmetric flow in annular diffusers and compressor-component coupling | p. 658 |
| Quasi-two-dimensional description of non-axisymmetric flow in an annular diffuser | p. 661 |
| Features of the diffuser inlet static pressure field | p. 663 |
| Compressor-component coupling | p. 666 |
| Effects of flow non-uniformity on diffuser performance | p. 668 |
| Introduction to non-axisymmetric swirling flows | p. 673 |
| A simple approach for long length scale non-uniformity | p. 675 |
| Explicit forms of the velocity disturbances | p. 677 |
| Flow angle disturbances | p. 677 |
| Relations between stagnation pressure, static pressure, and flow angle disturbances | p. 678 |
| Overall features of non-axisymmetric swirling flow | p. 678 |
| A secondary flow approach to non-axisymmetric swirling flow | p. 682 |
| References | p. 683 |
| Supplementary references appearing in figures | p. 698 |
| Index | p. 700 |
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