The current book, Advanced Fluid Mechanics and Heat Transfer is based on author's four decades of industrial and academic research in the area of thermofluid sciences including fluid mechanics, aero-thermodynamics, heat transfer and their applications to engineering systems. Fluid mechanics and heat transfer are inextricably intertwined and both are two integral parts of one physical discipline. No problem from fluid mechanics that requires the calculation of the temperature can be solved using the system of Navier-Stokes and continuity equations only. Conversely, no heat transfer problem can be solved using the energy equation only without using the Navier-Stokes and continuity equations. The fact that there is no book treating this physical discipline as a unified subject in a single book that considers the need of the engineering and physics community, motivated the author to write this book. It is primarily aimed at students of engineering, physics and those practicing professionals who perform aero-thermo-heat transfer design tasks in the industry and would like to deepen their knowledge in this area. The contents of this new book covers the material required in Fluid Mechanics and Heat Transfer Graduate Core Courses in the US universities. It also covers the major parts of the Ph.D-level elective courses Advanced Fluid Mechanics and Heat Transfer that the author has been teaching at Texas A&M University for the past three decades.
Author(s): Meinhard T. Schobeiri
Publisher: Springer
Year: 2022
Language: English
Pages: 609
City: Cham
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
