Advanced Fluid Mechanics and Heat Transfer for Engineers and Scientists: For Engineers and Scientists

Preface
Contents
Nomenclature
	Symbols
	Greek Symbols, Operators
	Subscripts, Superscripts
1 Introduction
	1.1 Continuum Hypothesis
	1.2 Molecular Viscosity
	1.3 Flow Classification
		1.3.1 Velocity Pattern: Laminar, Intermittent, Turbulent Flow
		1.3.2 Change of Density, Incompressible, Compressible Flow
		1.3.3 Statistically Steady Flow, Unsteady Flow
	1.4 Shear-Deformation Behavior of Fluids
2 Vector and Tensor Analysis, Applications to Fluid Mechanics
	2.1 Tensors in Three-Dimensional Euclidean Space
		2.1.1 Index Notation
	2.2 Vector Operations: Scalar, Vector and Tensor Products
		2.2.1 Scalar Product
		2.2.2 Vector or Cross Product
		2.2.3 Tensor Product
	2.3 Contraction of Tensors
	2.4 Differential Operators in Fluid Mechanics
		2.4.1 Substantial Derivatives
		2.4.2 Differential Operator
	2.5 Operator  Applied to Different Functions
		2.5.1 Scalar Product of  and V
		2.5.2 Vector Product
		2.5.3 Tensor Product of  and V
		2.5.4 Scalar Product of  and a Second Order Tensor
		2.5.5 Eigenvalue and Eigenvector of a Second Order Tensor
	2.6 Problems
3 Kinematics of Fluid Motion
	3.1 Material and Spatial Description of the Flow Field
		3.1.1 Material Description
		3.1.2 Jacobian Transformation Function and its Material Derivative
		3.1.3 Velocity, Acceleration of Material Points
		3.1.4 Spatial Description
	3.2 Translation, Deformation, Rotation
	3.3 Reynolds Transport Theorem
	3.4 Pathline, Streamline, Streakline
	3.5 Problems
4 Differential Balances in Fluid Mechanics
	4.1 Mass Flow Balance in Stationary Frame of Reference
		4.1.1 Incompressibility Condition
	4.2 Differential Momentum Balance in Stationary Frame of Reference
		4.2.1 Relationship Between Stress Tensor and Deformation Tensor
		4.2.2 Navier-Stokes Equation of Motion
		4.2.3 Special Case: Euler Equation of Motion
	4.3 Some Discussions on Navier-Stokes Equations
	4.4 Energy Balance in Stationary Frame of Reference to Fluid Mechanics
		4.4.1 Mechanical Energy
		4.4.2 Thermal Energy Balance
		4.4.3 Total Energy
		4.4.4 Entropy Balance
	4.5 Differential Balances in Rotating Frame of Reference
		4.5.1 Velocity and Acceleration in Rotating Frame
		4.5.2 Continuity Equation in Rotating Frame of Reference
		4.5.3 Equation of Motion in Rotating Frame of Reference
		4.5.4 Energy Equation in Rotating Frame of Reference
	4.6 Problems
5 Integral Balances in Fluid Mechanics
	5.1 Mass Flow Balance
	5.2 Balance of Linear Momentum
	5.3 Balance of Moment of Momentum
	5.4 Balance of Energy
		5.4.1 Energy Balance Special Case 1: Steady Flow
		5.4.2 Energy Balance Special Case 2: Steady Flow, Constant Mass Flow
	5.5 Application of Energy Balance to Engineering Components and Systems
		5.5.1 Application: Pipe, Diffuser, Nozzle
		5.5.2 Application: Combustion Chamber
		5.5.3 Application: Turbo-shafts, Energy Extraction, Consumption
	5.6 Irreversibility, Entropy Increase, Total Pressure Loss
		5.6.1 Application of Second Law to Engineering Components
	5.7 Theory of Thermal Turbomachinery Stages
		5.7.1 Energy Transfer in Turbomachinery Stages
		5.7.2 Energy Transfer in Relative Systems
		5.7.3 Unified Treatment of Turbine and Compressor Stages
	5.8 Dimensionless Stage Parameters
		5.8.1 Simple Radial Equilibrium to Determine r
		5.8.2 Effect of Degree of Reaction on the Stage Configuration
		5.8.3 Effect of Stage Load Coefficient on Stage Power
	5.9 Unified Description of a Turbomachinery Stage
		5.9.1 Unified Description of Stage with Constant Mean Diameter
	5.10 Turbine and Compressor Cascade Flow Forces
		5.10.1 Blade Force in an Inviscid Flow Field
		5.10.2 Blade Forces in a Viscous Flow Field
		5.10.3 Effect of Solidity on Blade Profile Losses
	5.11 Problems, Project
6 Inviscid Potential Flows
	6.1 Incompressible Potential Flows
	6.2 Complex Potential for Plane Flows
		6.2.1 Elements of Potential Flow
	6.3 Superposition of Potential Flow Elements
		6.3.1 Superposition of a Uniform Flow and a Source
		6.3.2 Superposition of a Translational Flow and a Dipole
		6.3.3 Superposition of a Translational Flow,  a Dipole and a Vortex
		6.3.4 Superposition of a Uniform Flow, Source, and Sink
		6.3.5 Superposition of a Source and a Vortex
		6.3.6 Blasius Theorem
	6.4 Kutta-Joukowski Theorem
	6.5 Conformal Transformation
		6.5.1 Conformal Transformation, Basic Principles
		6.5.2 Kutta-Joukowsky Transformation
		6.5.3 Joukowsky Transformation
	6.6 Vortex Theorems
		6.6.1 Thomson Theorem
		6.6.2 Generation of Circulation
		6.6.3 Helmholtz Theorems
		6.6.4 Induced Velocity Field, Law of Bio-Savart
		6.6.5 Induced Drag Force
	6.7 Problems
7 Viscous Laminar Flow
	7.1 Steady Viscous Flow Through a Curved Channel
		7.1.1 Case I: Conservation Laws
		7.1.2 Case I: Solution of the Navier-Stokes Equation
		7.1.3 Case I: Curved Channel, Negative Pressure Gradient
		7.1.4 Case I: Curved Channel, Positive Pressure Gradient
		7.1.5 Case II: Radial Flow, Positive Pressure Gradient
	7.2 Temperature Distribution
		7.2.1 Case I: Solution of Energy Equation
		7.2.2 Case I: Curved Channel, Negative Pressure Gradient
		7.2.3 Case I: Curved Channel, Positive Pressure Gradient
		7.2.4 Case II: Radial Flow, Positive Pressure Gradient
	7.3 Steady Parallel Flows
		7.3.1 Couette Flow Between Two Parallel Walls
		7.3.2 Couette Flow Between Two Concentric Cylinders
		7.3.3 Hagen-Poiseuille Flow
	7.4 Unsteady Laminar Flows
		7.4.1 Flow Near Oscillating Flat Plate, Stokes-Rayleigh Problem
		7.4.2 Influence of Viscosity on Vortex Decay
	7.5 Problems
8 Laminar-Turbulent Transition
	8.1 Stability of Laminar Flow
	8.2 Laminar-Turbulent Transition
	8.3 Stability of Laminar Flows
		8.3.1 Stability of Small Disturbances
		8.3.2 The Orr-Sommerfeld Stability Equation
		8.3.3 Orr-Sommerfeld Eigenvalue Problem
		8.3.4 Solution of Orr-Sommerfeld Equation
		8.3.5 Numerical Results
	8.4 Physics of an Intermittent Flow, Transition
		8.4.1 Identification of Intermittent Behavior of Statistically Steady Flows
		8.4.2 Turbulent/Non-turbulent Decisions
		8.4.3 Intermittency Modeling for Steady Flow at Zero Pressure Gradient
		8.4.4 Identification of Intermittent Behavior of Periodic Unsteady Flows
		8.4.5 Intermittency Modeling for Periodic Unsteady Flow
	8.5 Implementation of Intermittency into Navier Stokes Equations
		8.5.1 Reynolds-Averaged Equations for Fully Turbulent Flow
		8.5.2 Intermittency Implementation in RANS
	8.6 Problems and Projects
9 Turbulent Flow, Modeling
	9.1 Fundamentals of Turbulent Flows
		9.1.1 Type of Turbulence
		9.1.2 Correlations, Length and Time Scales
		9.1.3 Spectral Representation of Turbulent Flows
		9.1.4 Spectral Tensor, Energy Spectral Function
	9.2 Averaging Fundamental Equations of Turbulent Flow
		9.2.1 Averaging Conservation Equations
		9.2.2 Equation of Turbulence Kinetic Energy
		9.2.3 Equation of Dissipation of Kinetic Energy
	9.3 Turbulence Modeling
		9.3.1 Algebraic Model: Prandtl Mixing Length Hypothesis
		9.3.2 Algebraic Model: Cebeci–Smith Model
		9.3.3 Baldwin–Lomax Algebraic Model
		9.3.4 One-Equation Model by Prandtl
		9.3.5 Two-Equation Models
	9.4 Grid Turbulence
	9.5 Numerical Simulation Examples
		9.5.1 Examples of Steady Flow Simulations with Two-Equation Models
		9.5.2 Case Study: Flow Simulation in a Rotating Turbine
		9.5.3 Results, Discussion
		9.5.4 RANS-Shortcomings, Closing Remark
	9.6 Problems and Projects
10 Free Turbulent Flow
	10.1 Types of Free Turbulent Flows
	10.2 Fundamental Equations of Free Turbulent Flows
	10.3 Free Turbulent Flows at Zero-Pressure Gradient
		10.3.1 Plane Free Jet Flows
		10.3.2 Straight Wake at Zero Pressure Gradient
		10.3.3 Free Jet Boundary
	10.4 Wake Flow at Non-zero Lateral Pressure Gradient
		10.4.1 Wake Flow in Engineering, Applications, General Remarks
		10.4.2 Theoretical Concept, an Inductive Approach
		10.4.3 Nondimensional Parameters
		10.4.4 Near Wake, Far Wake Regions
		10.4.5 Utilizing the Wake Characteristics
	10.5 Computational Projects
11 Boundary Layer Aerodynamics
	11.1 Boundary Layer Approximations
	11.2 Exact Solutions of Laminar Boundary Layer Equations
		11.2.1 Laminar Boundary Layer, Flat Plate
		11.2.2 Wedge Flows
		11.2.3 Polhausen Approximate Solution
	11.3 Boundary Layer Theory Integral Method
		11.3.1 Boundary Layer Thicknesses
		11.3.2 Boundary Layer Integral Equation
	11.4 Turbulent Boundary Layers
		11.4.1 Universal Wall Functions
		11.4.2 Velocity Defect Function
	11.5 Boundary Layer, Differential Treatment
		11.5.1 Solution of Boundary Layer Equations
	11.6 Measurement of Boundary Layer Flow
	11.7 Design Facilities for Boundary Layer Research
		11.7.1 Facilities for Boundary Layer Research in Stationary Frame
		11.7.2 Facilities for Boundary Layer Research in Rotating Frame
	11.8 Instrumentation and Data Acquisition
		11.8.1 How to Measure Boundary Layer Velocity with HWA
		11.8.2 HWA Averaging, Sampling Data
		11.8.3 Data Sampling Rate
	11.9 Experimental Verification, Steady Flow
	11.10 Case Studies
		11.10.1 Case Study 1: Curved Test Section
		11.10.2 Unsteady Turbulence Activities, Calm Regions
	11.11 Case Study 2: Aircraft Engine
		11.11.1 Parameter Variations, General Remarks
		11.11.2 Flow Unsteadiness: Kinematics of Periodic Wakes
		11.11.3 Variation of Pressure Gradient
		11.11.4 Velocity Distribution
		11.11.5 Velocity and Its Fluctuations
		11.11.6 Time Averaged Velocity, Unsteadiness
		11.11.7 Time Averaged Fluctuation, Unsteadiness
		11.11.8 Combined Effects of Wakes and Turbulence
		11.11.9 Impact of Wake Frequency on Flow Separation
		11.11.10 Dynamics of Separation Bubbles
		11.11.11 Variation of Tu
		11.11.12 Variation of Tu at Constant Wake Frequency
		11.11.13 Quantifying the Combined Effects on Aerodynamics
	11.12 Numerical Simulation
12 Boundary Layer Heat Transfer
	12.1 Introduction
	12.2 Equations for Heat Transfer Calculation
	12.3 Instrumentation for Temperature Measurement
	12.4 Heat Transfer Calculation Procedures
	12.5 Experimental Heat Transfer
	12.6 Local Heat Transfer Coefficient Distribution on Concave Surface
		12.6.1 Heat Transfer Coefficient Distribution
	12.7 Case Study, Heat Transfer
	12.8 Boundary Layer Parameters
		12.8.1 Parameter Variation at Steady Inlet Flow Condition
		12.8.2 Parameter Variation at Unsteady Inlet Flow Condition
	12.9 Temperature Measurement in Rotating Frame
		12.9.1 PSP: Working Principle, Calibration
	12.10 Case Studies, Heat Transfer in Rotating Frame
		12.10.1 Rotating Heat Transfer, Case I
		12.10.2 Rotating Heat Transfer, Case II
		12.10.3 Rotating Heat Transfer, Case III
13 Compressible Flow
	13.1 Steady Compressible Flow
		13.1.1 Speed of Sound, Mach Number
		13.1.2 Fluid Density, Mach Number, Critical State
		13.1.3 Effect of Cross-Section Change on Mach Number
		13.1.4 Supersonic Flow
	13.2 Unsteady Compressible Flow
		13.2.1 One-Dimensional Approximation
	13.3 Numerical Treatment
		13.3.1 Unsteady Compressible Flow: Example: Shock Tube
		13.3.2 Shock Tube Dynamic Behavior
	13.4 Problems and Projects
14 Flow Measurement Techniques, Calibration
	14.1 Measurement of Time Dependent Flow  Field Using HWA
		14.1.1 Probe Type, Wire, Film Arrangements
		14.1.2 Energy Balance of HW Probes
		14.1.3 Heat Transfer of HW Probes
		14.1.4 Calibration Facility
		14.1.5 Calibration of Single Hot Wire Probes
		14.1.6 Calibration of Single Hot Wire Probes
	14.2 Measurement of Time Averaged Flow Quantities Using Five-Hole Probes
		14.2.1 Flow Field Measurement Using Five Hole Probes
		14.2.2 Calibration Procedure of Five-Hole Probes
15 Heat Transfer
	15.1 Heat Transfer Measurement, Calibration
		15.1.1 Infrared Thermal Imaging
		15.1.2 Film Cooling Effectiveness Measurement with Infrared Camera
		15.1.3 Film Cooling Effectiveness
		15.1.4 Working Principle of IR-Thermography
	15.2 Temperature Measurement Using LC
		15.2.1 Working Principle of Liquid Crystals
		15.2.2 Calibration of Liquid Crystals
		15.2.3 How to Measure Surface Temperature with LC
		15.2.4 Case Studies with LC-Measurement
		15.2.5 Flat Plate LC Cover
		15.2.6 Curved Plate Exposed to a Periodic Unsteady Flow
		15.2.7 Curved Plate Concave Side Heat Transfer
		15.2.8 Curved Plate Convex Side Heat Transfer
		15.2.9 Turbine Blade
	15.3 Boundary Layer Parameters
		15.3.1 Parameter Variation at Steady Inlet Flow Condition
		15.3.2 Parameter Variation at Unsteady Inlet Flow Condition
	15.4 Temperature Measurement in Rotating Frame
	15.5 Case Studies, Heat Transfer in Rotating Frame
		15.5.1 Rotating Heat Transfer, Case I
		15.5.2 Rotating Heat Transfer, Case II
		15.5.3 Rotating Heat Transfer, Case III
Appendix A Tensor Operations in Orthogonal Curvilinear Coordinate Systems
A.1  Change of Coordinate System
A.2  Co- and Contravariant Base Vectors, Metric Coefficients
A.3  Physical Components of a Vector
A.4  Derivatives of the Base Vectors, Christoffel Symbols
A.5  Spatial Derivatives in Curvilinear Coordinate System
A.5.1  Application of  to Tensor Functions
A.6  Application Example 1: Inviscid Incompressible Flow Motion
A.6.1  Equation of Motion in Curvilinear Coordinate Systems
A.6.2  Special Case: Cylindrical Coordinate System
A.6.3  Base Vectors, Metric Coefficients
A.6.4  Christoffel Symbols
A.6.5  Introduction of Physical Components
A.7  Application Example 2: Viscous Flow Motion
A.7.1  Equation of Motion in Curvilinear Coordinate Systems
A.7.2  Special Case: Cylindrical Coordinate System
Appendix B Physical Properties of Dry Air
Appendix  References
Index