Fluid Mechanics: An Introduction to the Theory of Fluid Flows – Franz Durst – 1st Edition

1. Introduction, Importance and Development of Fluid Mechanics
•1.1 Fluid Flows and their Significance
•1.2 Sub-Domains of Fluid Mechanics
•1.3 Historical Developments
•References
2. Mathematical Basics
•2.1 Introduction and Definitions
•2.2 Tensors of Zero Order (Scalars)
•2.3 Tensors of First Order (Vectors)
•2.4 Tensors of Second Order
•2.5 Field Variables and Mathematical Operations
•2.6 Substantial Quantities and Substantial Derivative
•2.7 Gradient, Divergence, Rotation and Laplace Operators
•2.8 Line, Surface and Volume Integrals
•2.9 Integral Laws of Stokes and Gauss
•2.10 Differential Operators in Curvilinear Orthogonal Coordinates
•2.11 Complex Numbers
o2.11.1 Axiomatic Introduction to Complex Numbers
o2.11.2 Graphical Representation of Complex Numbers
o2.11.3 The Gauss Complex Number Plane
o2.11.4 Trigonometric Representation
o2.11.5 Stereographic Projection
o2.11.6 Elementary Function
•References
3. Physical Basics
•3.1 Solids and Fluids
•3.2 Molecular Properties and Quantities of Continuum Mechanics
•3.3 Transport Processes in Newtonian Fluids
o3.3.1 General Considerations
o3.3.2 Pressure in Gases
o3.3.3 Molecular-Dependent Momentum Transport
o3.3.4 Molecular Transport of Heat and Mass in Gases
•3.4 Viscosity of Fluids
•3.5 Balance Considerations and Conservation Laws
•3.6 Thermodynamic Considerations
•References
4. Basics of Fluid Kinematics
•4.1 General Considerations
•4.2 Substantial Derivatives
•4.3 Motion of Fluid Elements
o4.3.1 Path Lines of Fluid Elements
o4.3.2 Streak Lines of Locally Injected Tracers
•4.4 Kinematic Quantities of Flow Fields
o4.4.1 Stream Lines of a Velocity Field
o4.4.2 Stream Function and Stream Lines of Two-Dimensional Flow Fields
o4.4.3 Divergence of a Flow Field
•4.5 Translation, Deformation and Rotation of Fluid Elements
•4.6 Relative Motions
•References
5. Basic Equations of Fluid Mechanics
•5.1 General Considerations
•5.2 Mass Conservation (Continuity Equation)
•5.3 Newton’s Second Law (Momentum Equation)
•5.4 The Navier–Stokes Equations
•5.5 Mechanical Energy Equation
•5.6 Thermal Energy Equation
•5.7 Basic Equations in Different Coordinate Systems
o5.7.1 Continuity Equation
o5.7.2 Navier–Stokes Equations
•5.8 Special Forms of the Basic Equations
o5.8.1 Transport Equation for Vorticity
o5.8.2 The Bernoulli Equation
o5.8.3 Crocco Equation
o5.8.4 Further Forms of the Energy Equation
•5.9 Transport Equation for Chemical Species
•References
6. Hydrostatics and Aerostatics
•6.1 Hydrostatics
•6.2 Connected Containers and Pressure-Measuring Instruments
o6.2.1 Communicating Containers
o6.2.2 Pressure-Measuring Instruments
•6.3 Free Fluid Surfaces
o6.3.1 Surface Tension
o6.3.2 Water Columns in Tubes and Between Plates
o6.3.3 Bubble Formation on Nozzles
•6.4 Aerostatics
o6.4.1 Pressure in the Atmosphere
o6.4.2 Rotating Containers
o6.4.3 Aerostatic Buoyancy
o6.4.4 Conditions for Aerostatics: Stability of Layers
•References
7. Similarity Theory
•7.1 Introduction
•7.2 Dimensionless Form of the Differential Equations
o7.2.1 General Remarks
o7.2.2 Dimensionless Form of the Differential Equations
o7.2.3 Considerations in the Presence of Geometric and Kinematic Similarities
o7.2.4 Importance of Viscous Velocity, Time and Length Scales
•7.3 Dimensional Analysis and ?-Theorem
•References
8. Integral Forms of the Basic Equations
•8.1 Integral Form of the Continuity Equation
•8.2 Integral Form of the Momentum Equation
•8.3 Integral Form of the Mechanical Energy Equation
•8.4 Integral Form of the Thermal Energy Equation
•8.5 Applications of the Integral Form of the Basic Equations
o8.5.1 Outflow from Containers
o8.5.2 Exit Velocity of a Nozzle
o8.5.3 Momentum on a Plane Vertical Plate
o8.5.4 Momentum on an Inclined Plane Plate
o8.5.5 Jet Deflection by an Edge
o8.5.6 Mixing Process in a Pipe of Constant Cross-Section
o8.5.7 Force on a Turbine Blade in a Viscosity-Free Fluid
o8.5.8 Force on a Periodical Blade Grid
o8.5.9 Euler’s Turbine Equation
o8.5.10 Power of Flow Machines
•References
9. Stream Tube Theory
•9.1 General Considerations
•9.2 Derivations of the Basic Equations
o9.2.1 Continuity Equation
o9.2.2 Momentum Equation
o9.2.3 Bernoulli Equation
o9.2.4 The Total Energy Equation
•9.3 Incompressible Flows
o9.3.1 Hydro-Mechanical Nozzle Flows
o9.3.2 Sudden Cross-Sectional Area Extension
•9.4 Compressible Flows
o9.4.1 Influences of Area Changes on Flows
o9.4.2 Pressure-Driven Flows Through Converging Nozzles
•References
10. Potential Flows
•10.1 Potential and Stream Functions
•10.2 Potential and Complex Functions
•10.3 Uniform Flow
•10.4 Corner and Sector Flows
•10.5 Source or Sink Flows and Potential Vortex Flow
•10.6 Dipole-Generated Flow
•10.7 Potential Flow Around a Cylinder
•10.8 Flow Around a Cylinder with Circulation
•10.9 Summary of Important Potential Flows
•10.10 Flow Forces on Bodies
•References
11. Wave Motions in Non-Viscous Fluids
•11.1 General Considerations
•11.2 Longitudinal Waves: Sound Waves in Gases
•11.3 Transversal Waves: Surface Waves
o11.3.1 General Solution Approach
•11.4 Plane Standing Waves
•11.5 Plane Progressing Waves
•11.6 References to Further Wave Motions
•References
12. Introduction to Gas Dynamics
•12.1 Introductory Considerations
•12.2 Mach Lines and Mach Cone
•12.3 Non-Linear Wave Propagation, Formation of Shock Waves
•12.4 Alternative Forms of the Bernoulli Equation
•12.5 Flow with Heat Transfer (Pipe Flow)
o12.5.1 Subsonic Flow
o12.5.2 Supersonic Flow
•12.6 Rayleigh and Fanno Relations
•12.7 Normal Compression Shock (Rankine–Hugoniot Equation)
•References
13. Stationary, One-Dimensional Fluid Flows of Incompressible, Viscous Fluids
•13.1 General Considerations
o13.1.1 Plane Fluid Flows
o13.1.2 Cylindrical Fluid Flows
•13.2 Derivations of the Basic Equations for Fully Developed Fluid Flows
o13.2.1 Plane Fluid Flows
o13.2.2 Cylindrical Fluid Flows
•13.3 Plane Couette Flow
•13.4 Plane Fluid Flow Between Plates
•13.5 Plane Film Flow on an Inclined Plate
•13.6 Axi-Symmetric Film Flow
•13.7 Pipe Flow (Hagen–Poiseuille Flow)
•13.8 Axial Flow Between Two Cylinders
•13.9 Film Flows with Two Layers
•13.10 Two-Phase Plane Channel Flow
•References
14. Time-Dependent, One-Dimensional Flows of Viscous Fluids
•14.1 General Considerations
•14.2 Accelerated and Decelerated Fluid Flows
o14.2.1 Stokes First Problem
o14.2.2 Diffusion of a Vortex Layer
o14.2.3 Channel Flow Induced by Movements of Plates
o14.2.4 Pipe Flow Induced by the Pipe Wall Motion
•14.3 Oscillating Fluid Flows
o14.3.1 Stokes Second Problem
•14.4 Pressure Gradient-Driven Fluid Flows
o14.4.1 Starting Flow in a Channel
o14.4.2 Starting Pipe Flow
•References
15. Fluid Flows of Small Reynolds Numbers
•15.1 General Considerations
•15.2 Creeping Fluid Flows Between Two Plates
•15.3 Plane Lubrication Films
•15.4 Theory of Lubrication in Roller Bearings
•15.5 The Slow Rotation of a Sphere
•15.6 The Slow Translatory Motion of a Sphere
•15.7 The Slow Rotational Motion of a Cylinder
•15.8 The Slow Translatory Motion of a Cylinder
•15.9 Diffusion and Convection Influences on Flow Fields
•References
16. Flows of Large Reynolds Numbers: Boundary-Layer Flows
•16.1 General Considerations and Derivations
•16.2 Solutions of the Boundary-Layer Equations
•16.3 Flat Plate Boundary Layer (Blasius Solution)
•16.4 Integral Properties of Wall Boundary Layers
•16.5 The Laminar, Plane, Two-Dimensional Free Shear Layer
•16.6 The Plane, Two-Dimensional, Laminar Free Jet
•16.7 Plane, Two-Dimensional Wake Flow
•16.8 Converging Channel Flow
•References
17. Unstable Flows and Laminar-Turbulent Transition
•17.1 General Considerations
•17.2 Causes of Flow Instabilities
o17.2.1 Stability of Atmospheric Temperature Layers
o17.2.2 Gravitationally Caused Instabilities
o17.2.3 Instabilities in Annular Clearances Caused by Rotation
•17.3 Generalized Instability Considerations (Orr–Sommerfeld Equation)
•17.4 Classifications of Instabilities
•17.5 Transitional Boundary-Layer Flows
•References
18. Turbulent Flows
•18.1 General Considerations
•18.2 Statistical Description of Turbulent Flows
•18.3 Basics of Statistical Considerations of Turbulent Flows
o18.3.1 Fundamental Rules of Time Averaging
o18.3.2 Fundamental Rules for Probability Density
o18.3.3 Characteristic Function
•18.4 Correlations, Spectra and Time-Scales of Turbulence
•18.5 Time-Averaged Basic Equations of Turbulent Flows
o18.5.1 The Continuity Equation
o18.5.2 The Reynolds Equation
o18.5.3 Mechanical Energy Equation for the Mean Flow Field
o18.5.4 Equation for the Kinetic Energy of Turbulence
•18.6 Characteristic Scales of Length, Velocity and Time of Turbulent Flows
•18.7 Turbulence Models
o18.7.1 General Considerations
o18.7.2 General Considerations Concerning Eddy Viscosity Models
o18.7.3 Zero-Equation Eddy Viscosity Models
o18.7.4 One-Equation Eddy Viscosity Models
o18.7.5 Two-Equation Eddy Viscosity Models
•18.8 Turbulent Wall Boundary Layers
•References
19. Numerical Solutions of the Basic Equations
•19.1 General Considerations
•19.2 General Transport Equation and Discretization of the Solution Region
•19.3 Discretization by Finite Differences
•19.4 Finite-Volume Discretization
o19.4.1 General Considerations
o19.4.2 Discretization in Space
o19.4.3 Discretization with Respect to Time
o19.4.4 Treatments of the Source Terms
•19.5 Computation of Laminar Flows
o19.5.1 Wall Boundary Conditions
o19.5.2 Symmetry Planes
o19.5.3 Inflow Planes
o19.5.4 Outflow Planes
•19.6 Computations of Turbulent Flows
o19.6.1 Flow Equations to be Solved
o19.6.2 Boundary Conditions for Turbulent Flows
•References
20. Fluid Flows with Heat Transfer
•20.1 General Considerations
•20.2 Stationary, Fully Developed Flow in Channels
•20.3 Natural Convection Flow Between Vertical Plane Plates
•20.4 Non-Stationary Free Convection Flow Near a Plane Vertical Plate
•20.5 Plane-Plate Boundary Layer with Plate Heating at Small Prandtl Numbers
•20.6 Similarity Solution for a Plate Boundary Layer with Wall Heating and Dissipative Warming
•20.7 Vertical Plate Boundary-Layer Flows Caused by Natural Convection
•20.8 Similarity Considerations for Flows with Heat Transfer
•References
21. Introduction to Fluid-Flow Measurement
•21.1 Introductory Considerations
•21.2 Measurements of Static Pressures
•21.3 Measurements of Dynamic Pressures
•21.4 Applications of Stagnation-Pressure Probes
•21.5 Basics of Hot-Wire Anemometry
o21.5.1 Measuring Principle and Physical Principles
o21.5.2 Properties of Hot-Wires and Problems of Application
o21.5.3 Hot-Wire Probes and Supports
o21.5.4 Cooling Laws for Hot-Wire Probes
o21.5.5 Static Calibration of Hot-Wire Probes
•21.6 Turbulence Measurements with Hot-Wire Anemometers
•21.7 Laser Doppler Anemometry
o21.7.1 Theory of Laser Doppler Anemometry
o21.7.2 Optical Systems for Laser Doppler Measurements
o21.7.3 Electronic Systems for Laser Doppler Measurements
o21.7.4 Execution of LDA-Measurements: One-Dimensional LDA Systems
•References