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Preface | |

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Acknowledgements | |

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Conventions and nomenclature | |

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Equations of motion | |

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Introduction | |

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Properties of a fluid and the continuum assumption | |

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Dynamic and thermodynamic principles | |

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The rate of change of quantities following a fluid particle | |

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Mass and momentum conservation for a fluid system | |

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Thermodynamic states and state change processes for a fluid system | |

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First and second laws of thermodynamics for a fluid system | |

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Behavior of the working fluid | |

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Equations of state | |

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Specific heats | |

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Relation between changes in material and fixed volumes: Reynolds's Transport Theorem | |

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Conservation laws for a fixed region (control volume) | |

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Description of stress within a fluid | |

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Integral forms of the equations of motion | |

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Force, torque, and energy exchange in fluid devices | |

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Differential forms of the equations of motion | |

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Conservation of mass | |

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Conservation of momentum | |

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Conservation of energy | |

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Splitting the energy equation: entropy changes in a fluid | |

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Heat transfer and entropy generation sources | |

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Initial and boundary conditions | |

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Boundary conditions at solid surfaces | |

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Inlet and outlet boundary conditions | |

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The rate of strain tensor and the form of the dissipation function | |

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Relationship between stress and rate of strain | |

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The Navier-Stokes equations | |

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Cartesian coordinates | |

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Cylindrical coordinates | |

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Disturbance propagation in a compressible fluid: the speed of sound | |

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Stagnation and static quantities | |

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Relation of stagnation and static quantities in terms of Mach number | |

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Kinematic and dynamic flow field similarity | |

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Incompressible flow | |

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Kinematic similarity | |

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Dynamic similarity | |

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Compressible flow | |

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Limiting forms for low Mach number | |

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Some useful basic ideas | |

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Introduction | |

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The assumption of incompressible flow | |

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Steady flow | |

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Unsteady flow | |

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Upstream influence | |

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Upstream influence of a circumferentially periodic non-uniformity | |

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Upstream influence of a radial non-uniformity in an annulus | |

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Pressure fields and streamline curvature: equations of motion in natural coordinates | |

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Normal and streamwise accelerations and pressure gradients | |

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Other expressions for streamline curvature | |

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Quasi-one-dimensional steady compressible flow | |

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Corrected flow per unit area | |

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Differential relations between area and flow variables for steady isentropic one-dimensional flow | |

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Steady isentropic one-dimensional channel flow | |

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Shock waves | |

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The entropy rise across a normal shock | |

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Shock structure and entropy generation processes | |

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Effect of exit conditions on steady, isentropic, one-dimensional compressible channel flow | |

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Flow regimes for a converging nozzle | |

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Flow regimes for a converging-diverging nozzle | |

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Applications of the integral forms of the equations of motion | |

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Pressure rise and mixing losses at a sudden expansion | |

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Ejector performance | |

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Fluid force on turbomachinery blading | |

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The Euler turbine equation | |

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Thrust force on an inlet | |

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Thrust of a cylindrical tube with heating or cooling (idealized ramjet) | |

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Oblique shock waves | |

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Boundary layers | |

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Features of boundary layers in ducts | |

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The influence of boundary layers on the flow outside the viscous region | |

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Turbulent boundary layers | |

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Inflow and outflow in fluid devices: separation and the asymmetry of real fluid motions | |

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Qualitative considerations concerning flow separation from solid surfaces | |

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The contrast between flow in and out of a pipe | |

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Flow through a bent tube as an illustration of the principles | |

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Flow through a sharp edged orifice | |

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Vorticity and circulation | |

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Introduction | |

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Vorticity kinematics | |

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Vortex lines and vortex tubes | |

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Behavior of vortex lines at a solid surface | |

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Vorticity dynamics | |

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Vorticity changes in an incompressible, uniform density, inviscid flow with conservative body force | |

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Examples: Secondary flow in a bend, horseshoe vortices upstream of struts | |

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Vorticity changes and angular momentum changes | |

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Vorticity changes in an incompressible, non-uniform density, inviscid flow | |

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Examples of vorticity creation due to density non-uniformity | |

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Vorticity changes in a uniform density, viscous flow with conservative body forces | |

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Vorticity changes and viscous torques | |

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Diffusion and intensification of vorticity in a viscous vortex | |

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Changes of vorticity in a fixed volume | |

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Summary of vorticity evolution in an incompressible flow | |

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Vorticity changes in a compressible inviscid flow | |

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Circulation | |

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Kelvin's Theorem | |

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Circulation behavior in an incompressible flow | |

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Uniform density inviscid flow with conservative body forces | |

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Incompressible, non-uniform density, inviscid flow with conservative body forces | |

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Uniform density viscous flow with conservative body forces | |

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Circulation behavior in a compressible inviscid flow | |

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Circulation generation due to shock motion in a non-homogeneous medium | |

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Rate of change of circulation for a fixed contour | |

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Rotational flow descriptions in terms of vorticity and circulation | |

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Behavior of vortex tubes when D[Gamma]/Dt = 0 | |

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Evolution of a non-uniform flow through a diffuser or nozzle | |

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Trailing vorticity and trailing vortices | |

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Generation of vorticity at solid surfaces | |

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Generation of vorticity in a two-dimensional flow | |

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Vorticity flux in thin shear layers (boundary layers and free shear layers) | |

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Vorticity generation at a plane surface in a three-dimensional flow | |

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Relation between kinematic and thermodynamic properties in an inviscid, non-heat-conducting fluid: Crocco's Theorem | |

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Applications of Crocco's Theorem | |

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The velocity field associated with a vorticity distribution | |

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Application of the velocity representation to vortex tubes | |

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Application to two-dimensional flow | |

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Surface distributions of vorticity | |

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Some specific velocity fields associated with vortex structures | |

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Numerical methods based on the distribution of vorticity | |

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Boundary layers and free shear layers | |

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Introduction | |

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Boundary layer behavior and device performance | |

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The boundary layer equations for plane and curved surfaces | |

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Plane surfaces | |

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Extension to curved surfaces | |

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Boundary layer integral quantities and the equations that describe them | |

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Boundary layer integral thicknesses | |

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Integral forms of the boundary layer equations | |

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Laminar boundary layers | |

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Laminar boundary layer behavior in favorable and adverse pressure gradients | |

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Laminar boundary layer separation | |

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Laminar-turbulent boundary layer transition | |

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Turbulent boundary layers | |

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The time mean equations for turbulent boundary layers | |

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The composite nature of a turbulent boundary layer | |

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Introductory discussion of turbulent shear stress | |

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Boundary layer thickness and wall shear stress in laminar and turbulent flow | |

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Vorticity and velocity fluctuations in turbulent flow | |

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Applications of boundary layer analysis: viscous-inviscid interaction in a diffuser | |

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Qualitative description of viscous-inviscid interaction | |

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Quantitative description of viscous-inviscid interaction | |

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Extensions of interactive boundary layer theory to other situations | |

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Turbulent boundary layer separation | |

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Free turbulent flows | |

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Similarity solutions for incompressible uniform-density free shear layers | |

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The mixing layer between two streams | |

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The effects of compressibility on free shear layer mixing | |

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Appropriateness of the similarity solutions | |

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Turbulent entrainment | |

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Jets and wakes in pressure gradients | |

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Loss sources and loss accounting | |

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Introduction | |

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Losses and entropy change | |

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Losses in a spatially uniform flow through a screen or porous plate | |

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Irreversibility, entropy generation, and lost work | |

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Lost work accounting in fluid components and systems | |

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Loss accounting and mixing in spatially non-uniform flows | |

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Boundary layer losses | |

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Entropy generation in boundary layers on adiabatic walls | |

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The boundary layer dissipation coefficient | |

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Estimation of turbomachinery blade profile losses | |

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Mixing losses | |

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Mixing of two streams with non-uniform stagnation pressure and/or temperature | |

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The limiting case of low Mach number (M[superscript 2] [less than less than] 1) mixing | |

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Comments on loss metrics for flows with non-uniform temperatures | |

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Mixing losses from fluid injection into a stream | |

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Irreversibility in mixing | |

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A caveat: smoothing out of a flow non-uniformity does not always imply loss | |

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Averaging in non-uniform flows: the average stagnation pressure | |

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Representation of a non-uniform flow by equivalent average quantities | |

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Averaging procedures in an incompressible uniform-density flow | |

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Effect of velocity distribution on average stagnation pressure (incompressible, uniform-density flow) | |

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Averaging procedures in compressible flow | |

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Appropriate average values for stagnation quantities in a non-uniform flow | |

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Streamwise evolution of losses in fluid devices | |

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Stagnation pressure averages and integral boundary layer parameters | |

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Comparison of losses within a device to losses from downstream mixing | |

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Effect of base pressure on mixing losses | |

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Effect of pressure level on average properties and mixing losses | |

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Two-stream mixing | |

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Mixing of a linear shear flow in a diffuser or nozzle | |

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Wake mixing | |

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Losses in turbomachinery cascades | |

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Summary concerning loss generation and characterization | |

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Unsteady flow | |

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Introduction | |

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The inherent unsteadiness of fluid machinery | |

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The reduced frequency | |

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An example of the role of reduced frequency: unsteady flow in a channel | |

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Examples of unsteady flows | |

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Stagnation pressure changes in an irrotational incompressible flow | |

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The starting transient for incompressible flow exiting a tank | |

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Stagnation pressure variations due to the motion of an isolated airfoil | |

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Moving blade row (moving row of bound vortices) | |

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Unsteady wake structure and energy separation | |

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Shear layer instability | |

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Instability of a vortex sheet (Kelvin-Helmholtz instability) | |

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General features of parallel shear layer instability | |

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Waves and oscillation in fluid systems: system instabilities | |

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Transfer matrices (transmission matrices) for fluid components | |

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Examples of unsteady behavior in fluid systems | |

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Nonlinear oscillations in fluid systems | |

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Multi-dimensional unsteady disturbances in a compressible inviscid flow | |

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Examples of fluid component response to unsteady disturbances | |

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Interaction of entropy and pressure disturbances | |

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Interaction of vorticity and pressure disturbances | |

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Disturbance interaction caused by shock waves | |

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Irrotational disturbances and upstream influence in a compressible flow | |

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Summary concerning small amplitude unsteady disturbances | |

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Some Features of unsteady viscous flows | |

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Flow due to an oscillating boundary | |

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Oscillating channel flow | |

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Unsteady boundary layers | |

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Dynamic stall | |

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Turbomachine wake behavior in an unsteady environment | |

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Flow in rotating passages | |

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Introduction | |

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Equations of motion in a rotating coordinate system | |

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Rotating coordinate systems and Coriolis accelerations | |

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Centrifugal accelerations in a uniform density fluid: the reduced static pressure | |

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Illustrations of Coriolis and centrifugal forces in a rotating coordinate system | |

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Conserved quantities in a steady rotating flow | |

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Phenomena in flows where rotation dominates | |

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Non-dimensional parameters: the Rossby and Ekman numbers | |

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Inviscid flow at low Rossby number: the Taylor-Proudman Theorem | |

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Viscous flow at low Rossby number: Ekman layers | |

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Changes in vorticity and circulation in a rotating flow | |

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Flow in two-dimensional rotating straight channels | |

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Inviscid flow | |

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Coriolis effects on boundary layer mixing and stability | |

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Three-dimensional flow in rotating passages | |

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Generation of cross-plane circulation in a rotating passage | |

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Fully developed viscous flow in a rotating square duct | |

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Comments on viscous flow development in rotating passages | |

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Two-dimensional flow in rotating diffusing passages | |

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Quasi-one-dimensional approximation | |

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Two-dimensional inviscid flow in a rotating diffusing blade passage | |

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Effects of rotation on diffuser performance | |

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Features of the relative flow in axial turbomachine passages | |

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Swirling flow | |

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Introduction | |

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Incompressible, uniform-density, inviscid swirling flows in simple radial equilibrium | |

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Examples of simple radial equilibrium flows | |

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Rankine vortex flow | |

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Upstream influence in a swirling flow | |

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Effects of circulation and stagnation pressure distributions on upstream influence | |

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Instability in swirling flow | |

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Waves on vortex cores | |

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Control volume equations for a vortex core | |

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Wave propagation in unconfined geometries | |

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Wave propagation and flow regimes in confined geometries: swirl stabilization of Kelvin-Helmholtz instability | |

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Features of steady vortex core flows | |

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Pressure gradients along a vortex core centerline | |

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Axial and circumferential velocity distributions in vortex cores | |

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Applicability of the Rankine vortex model | |

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Vortex core response to external conditions | |

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Unconfined geometries (steady vortex cores with specified external pressure variation) | |

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Confined geometries (steady vortex cores in ducts with specified area variation) | |

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Discontinuous vortex core behavior | |

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Swirling flow boundary layers | |

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Swirling flow boundary layers on stationary surfaces and separation in swirling flow | |

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Swirling flow boundary layers on rotating surfaces | |

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The enclosed rotating disk | |

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Internal flow in gas turbine engine rotating disk cavities | |

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Swirling jets | |

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Recirculation in axisymmetric swirling flow and vortex breakdown | |

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Generation of streamwise vorticity and three-dimensional flow | |

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Introduction | |

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A basic illustration of secondary flow: a boundary layer in a bend | |

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Qualitative description | |

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A simple estimate for streamwise vorticity generation and cross-flow plane velocity components | |

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A quantitative look at secondary flow in a bend: measurements and three-dimensional computations | |

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Additional examples of secondary flow | |

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Outflow of swirling fluid from a container | |

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Secondary flow in an S-shaped duct | |

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Streamwise vorticity and secondary flow in a two-dimensional contraction | |

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Three-dimensional flow in turbine passages | |

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Expressions for the growth of secondary circulation in an inviscid flow | |

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Incompressible uniform density fluid | |

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Incompressible non-uniform density fluid | |

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Perfect gas with constant specific heats | |

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Applications of secondary flow analyses | |

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Approximations based on convection of vorticity by a primary flow | |

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Flow with large distortion of the stream surfaces | |

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Three-dimensional boundary layers: further remarks on effects of viscosity in secondary flow | |

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Secondary flow in a rotating reference frame | |

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Absolute vorticity as a measure of secondary circulation | |

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Generation of secondary circulation in a rotating reference frame | |

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Expressions for, and examples of, secondary circulation in rotating systems | |

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Non-uniform density flow in rotating passages | |

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Secondary flow in rotating machinery | |

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Radial migration of high temperature fluid in a turbine rotor | |

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Streamwise vorticity and mixing enhancement | |

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Lobed mixers and streamwise vorticity generation | |

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Vortex-enhanced mixing | |

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Additional aspects of mixing enhancement in lobed mixers | |

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Fluid impulse and vorticity generation | |

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Creation of a vortex ring by a distribution of impulses | |

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Fluid impulse and lift on an airfoil | |

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Far field behavior of a jet in cross-flow | |

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Compressible internal flow | |

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Introduction | |

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Corrected flow per unit area | |

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Generalized one-dimensional compressible flow analysis | |

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Differential equations for one-dimensional flow | |

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Influence coefficient matrix for one-dimensional flow | |

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Effects of shaft work and body forces | |

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Effects of friction and heat addition on compressible channel flow | |

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Constant area adiabatic flow with friction | |

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Constant area frictionless flow with heat addition | |

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Results for area change, friction, and heat addition | |

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Starting and operation of supersonic diffusers and inlets | |

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The problem of starting a supersonic flow | |

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The use of variable geometry to start the flow | |

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Starting of supersonic inlets | |

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Characteristics of supersonic flow in passages and channels | |

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Turbomachinery blade passages | |

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Shock wave patterns in ducts and shock train behavior | |

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Extensions of the one-dimensional concepts - I: axisymmetric compressible swirling flow | |

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Development of equations for compressible swirling flow | |

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Application of influence coefficients for axisymmetric compressible swirling flow | |

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Behavior of connected flow per unit area in a compressible swirling flow | |

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Extensions of the one-dimensional concepts - II: compound-compressible channel flow | |

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Introduction to compound flow: two-stream low Mach number (incompressible) flow in a converging nozzle | |

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Qualitative considerations for multistream compressible flow | |

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Compound-compressible channel flow theory | |

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One-dimensional compound waves | |

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Results for two-stream compound-compressible flows | |

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Flow angle, Mach number, and pressure changes in isentropic supersonic flow | |

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Differential relationships for small angle changes | |

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Relationships for finite angle changes: Prandtl-Meyer flows | |

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Flow field invariance to stagnation temperature distribution: the Munk and Prim substitution principle | |

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Two-dimensional flow | |

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Three-dimensional flow | |

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Flow from a reservoir with non-uniform stagnation temperature | |

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Flow with heat addition | |

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Introduction: sources of heat addition | |

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Heat addition and vorticity generation | |

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Stagnation pressure decrease due to heat addition | |

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Heat addition and flow state changes in propulsion devices | |

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The H-K diagram | |

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Flow processes in ramjet and scramjet systems | |

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An illustration of the effect of condensation on compressible flow behavior | |

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Swirling flow with heat addition | |

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Results for vortex core behavior with heat addition | |

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An approximate substitution principle for viscous heat conducting flow | |

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Equations for flow with heat addition and mixing | |

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Two-stream mixing as a model problem-I: constant area, low Mach number, uniform inlet stagnation pressure | |

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Two-stream mixing as a model problem- II: non-uniform inlet stagnation pressures | |

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Effects of inlet Mach number level | |

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Applications of the approximate principle | |

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Lobed mixer nozzles | |

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Jets | |

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Ejectors | |

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Mixing of streams with non-uniform densities | |

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Comments on the approximations | |

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Non-uniform flow in fluid components | |

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Introduction | |

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An illustrative example of flow modeling: two-dimensional steady non-uniform flow through a screen | |

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elocity and pressure field upstream of the screen | |

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Flow in the downstream region | |

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Matching conditions across the screen | |

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Overall features of the solution | |

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Nonlinear effects | |

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Disturbance length scales and the assumption of inviscid flow | |

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Applications to creation of a velocity non-uniformity using screens | |

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Flow through a uniform inclined screen | |

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Pressure drop and velocity field with partial duct blockage | |

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Enhancing flow uniformity in diffusing passages | |

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Upstream influence and component interaction | |

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Non-axisymmetric (asymmetric) flow in axial compressors | |

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Flow upstream of the compressor | |

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Flow downstream of the compressor | |

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Matching conditions across the compressor | |

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Behavior of the axial velocity and upstream static pressure | |

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Generation of non-uniform flow by circumferentially varying tip clearance | |

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Additional examples of upstream effects in turbomachinery flows | |

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Turbine engine effects on inlet performance | |

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Strut-vane row interaction: upstream influence with two different length scales | |

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Unsteady compressor response to asymmetric flow | |

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Self-excited propagating disturbances in axial compressors and compressor instability | |

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A deeper look at the effects of circumferentially varying tip clearance | |

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Axial compressor response to circumferentially propagating distortions | |

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Nonlinear descriptions of compressor behavior in asymmetric flow | |

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Non-axisymmetric flow in annular diffusers and compressor-component coupling | |

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Quasi-two-dimensional description of non-axisymmetric flow in an annular diffuser | |

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Features of the diffuser inlet static pressure field | |

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Compressor-component coupling | |

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Effects of flow non-uniformity on diffuser performance | |

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Introduction to non-axisymmetric swirling flows | |

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A simple approach for long length scale non-uniformity | |

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Explicit forms of the velocity disturbances | |

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Flow angle disturbances | |

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Relations between stagnation pressure, static pressure, and flow angle disturbances | |

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Overall features of non-axisymmetric swirling flow | |

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A secondary flow approach to non-axisymmetric swirling flow | |

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References | |

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Supplementary references appearing in figures | |

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Index | |