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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 | |