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E-raamat: Fluid and Thermodynamics: Volume 2: Advanced Fluid Mechanics and Thermodynamic Fundamentals

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Fluid and Thermodynamics: Volume 2: Advanced Fluid Mechanics and Thermodynamic FundamentalsSuurem pilt
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In this book fluid mechanics and thermodynamics (F&T) are approached as interwoven, not disjoint fields. The book starts by analyzing the creeping motion around spheres at rest: Stokes flows, the Oseen correction and the Lagerstrom-Kaplun expansion theories are presented, as is the homotopy analysis. 3D creeping flows and rapid granular avalanches are treated in the context of the shallow flow approximation, and it is demonstrated that uniqueness and stability deliver a natural transition to turbulence modeling at the zero, first order closure level. The difference-quotient turbulence model (DQTM) closure scheme reveals the importance of the turbulent closure schemes" non-locality effects. Thermodynamics is presented in the form of the first and second laws, and irreversibility is expressed in terms of an entropy balance. Explicit expressions for constitutive postulates are in conformity with the dissipation inequality. Gas dynamics offer a first application of combined F&T. The b

ook is rounded out by a chapter on dimensional analysis, similitude, and physical experiments.

Creeping Motion around Spheres at Rest in a Newtonian Fluid.- Three-Dimensional Creeping Flow - Systematic Derivation of the Shallow Flow Approximations.- Shallow Rapid Granular Avalanches.- Uniqueness and Stability.- Turbulent Modeling.- Turbulent Mixing Length Models and Their Applications to Elementary Flow Con gurations.- Thermodynamics - Fundamentals.- Thermodynamics - Field Formulation.- Gas Dynamics.- Dimensional Analysis, Similitude and Physical Experiments at Laboratory Scale.
11 Creeping Motion Around Spheres at Rest in a Newtonian Fluid
1(46)
11.1 Motivation
3(2)
11.2 Mathematical Preliminaries
5(4)
11.3 Stokes Flow Around a Stagnant Sphere
9(13)
11.3.1 Rigid Sphere and No-Slip Condition on the Surface of the Sphere
9(5)
11.3.2 Cunningham's Correction
14(2)
11.3.3 Rigid Infinitely Thin Spherical Shell Filled with a Fluid of Different Viscosity
16(6)
11.4 Oseen's Theory
22(8)
11.4.1 Governing Equations of the Oseen Theory
22(3)
11.4.2 Construction of a Particular Integral of (11.58)
25(2)
11.4.3 `Stokes-Lets' and `Oseen-Lets'
27(3)
11.5 Theory of Lagerstom and Kaplun
30(8)
11.5.1 Motivation
30(2)
11.5.2 Stokes Expansion
32(2)
11.5.3 Oseen Expansion
34(1)
11.5.4 Matching Procedure
35(3)
11.6 Homotopy Analysis Method---The Viscous Drag Coefficient Computed for Arbitrary Reynolds Numbers
38(5)
11.6.1 The Mathematical Concept
39(2)
11.6.2 Selection of ψ0, H, h and Approximate Solution
41(2)
11.7 Conclusions and Discussion
43(4)
References
44(3)
12 Three-Dimensional Creeping Flow---Systematic Derivation of the Shallow Flow Approximations
47(66)
12.1 Introductory Motivation
49(3)
12.2 Model Equations
52(4)
12.2.1 Field Equations
52(2)
12.2.2 Boundary Conditions
54(2)
12.3 Scaling Procedure
56(10)
12.4 Lowest Order Model Equations for Flow Down Steep Slopes (Strong Steep Slope Shallow Flow Approximation)
66(5)
12.5 A Slightly More General Steep Slope Shallow Flow Approximation (Weak Steep Slope Shallow Flow Approximation)
71(3)
12.6 Phenomenological Expressions for Creeping Glacier Ice
74(3)
12.7 Applications to Downhill Creeping Flows
77(7)
12.7.1 Computational Procedure
77(2)
12.7.2 Profiles and Flows for Isothermal Conditions
79(3)
12.7.3 Remarks for Use of the Shallow Flow Approximation for Alpine Glaciers
82(2)
12.8 Free-Surface Gravity-Driven Creep Flow of a Very Viscous Body with Strong Thermomechanical Coupling---A Rigorous Derivation of the Shallow Ice Approximation
84(23)
12.8.1 The Classical Shallow Flow Approximation
84(13)
12.8.2 Applications
97(10)
12.9 Discussion and Conclusions
107(6)
References
108(5)
13 Shallow Rapid Granular Avalanches
113(84)
13.1 Introduction
115(4)
13.2 Distinctive Properties of Granular Materials
119(12)
13.2.1 Dilatancy
120(1)
13.2.2 Cohesion
121(1)
13.2.3 Lubrication
122(3)
13.2.4 Liquefaction
125(4)
13.2.5 Segregation, Inverse Grading, Brazil Nut Effect
129(2)
13.3 Shallow Flow Avalanche Modeling
131(10)
13.3.1 Voellmy's Avalanche Model
132(2)
13.3.2 The SH Model, Reduced to Its Essentials
134(7)
13.4 A Three-Dimensional Granular Avalanche Model
141(24)
13.4.1 Field Equations
141(3)
13.4.2 Curvilinear Coordinates
144(3)
13.4.3 Equations in Dimensionless Form
147(2)
13.4.4 Kinematic Boundary Conditions
149(1)
13.4.5 Traction Free Condition at the Free Surface
150(1)
13.4.6 Coulomb Sliding Law at the Base
150(1)
13.4.7 Depth Integration
151(3)
13.4.8 Ordering Relations
154(1)
13.4.9 Closure Property
155(3)
13.4.10 Nearly Uniform Flow Profile
158(1)
13.4.11 Summary of the Two-Dimensional SH Equations
159(3)
13.4.12 Standard Form of the Differential Equations
162(3)
13.5 Avalanche Simulation and Verification with Experimental Laboratory Data
165(19)
13.5.1 Introduction
165(1)
13.5.2 Classical and High Resolution Shock Capturing Numerical Methods
165(19)
13.6 Attempts of Model Validation and Verification of Earthquake and Typhoon Induced Landslides
184(13)
References
192(5)
14 Uniqueness and Stability
197(30)
14.1 Introduction
198(3)
14.2 Kinetic Energy of the Difference Motion
201(4)
14.3 Uniqueness
205(1)
14.4 Stability
206(4)
14.5 Energy Stability of the Laminar Channel Flow
210(6)
14.6 Linear Stability Analysis of Laminar Channel Flow
216(11)
14.6.1 Basic Concepts
216(2)
14.6.2 The Orr--Sommerfeld and the Rayleigh Equations
218(3)
14.6.3 The Eigenvalue Problem
221(3)
References
224(3)
15 Turbulent Modeling
227(36)
15.1 A Primer on Turbulent Motions
229(7)
15.1.1 Averages and Fluctuations
231(2)
15.1.2 Filters
233(1)
15.1.3 Reynolds Versus Favre Averages
234(2)
15.2 Balance Equations for the Averaged Fields
236(3)
15.3 Turbulent Closure Relations
239(8)
15.3.1 Reynolds Stress Hypothesis and Turbulent Dissipation Rate
239(1)
15.3.2 Averaged Density Field ρ
240(1)
15.3.3 Turbulent Heat Flux qt and Turbulent Species Mass Flux jt
241(4)
15.3.4 One- and Two-Equation Models
245(2)
15.4 k --- ε Model for Density Preserving and Boussinesq Fluids
247(16)
15.4.1 The Balance Equations
247(5)
15.4.2 Boussinesq Fluid Referred to a Non-inertial Frame
252(2)
15.4.3 Summary of the k --- ε Equations
254(2)
15.4.4 Boundary Conditions
256(3)
15.4.5 Closing Remarks
259(1)
References
260(3)
16 Turbulent Mixing Length Models and Their Applications to Elementary Flow Configurations
263(54)
16.1 Motivation/Introduction
265(6)
16.2 The Turbulent Plane Wake
271(7)
16.3 The Axisymmetric Isothermal Steady Jet
278(17)
16.4 Turbulent Round Jet in a Parallel Co-flow
295(5)
16.5 A Study of Turbulent Plane Poiseuille Flow
300(10)
16.6 Discussion
310(7)
Appendix A Prandtl's Mixing Length
313(2)
References
315(2)
17 Thermodynamics---Fundamentals
317(104)
17.1 Concepts and Some Historical Remarks
320(17)
17.2 General Notions and Definitions
337(16)
17.2.1 Thermodynamic System
337(4)
17.2.2 Thermodynamic States, Thermodynamic Processes
341(4)
17.2.3 Extensive, Intensive, Specific and Molar State Variables
345(2)
17.2.4 Adiabatic and Diathermic Walls
347(2)
17.2.5 Empirical Temperature, Gas Temperature and Temperature Scales
349(4)
17.3 Thermal Equations of State
353(9)
17.3.1 Ideal Gas
354(1)
17.3.2 Real Gases
355(2)
17.3.3 The Phenomenological Model of van der Waals
357(5)
17.4 Reversible and Irreversible Thermodynamic Processes
362(4)
17.4.1 Diffusion
362(4)
17.4.2 Reversible Expansion and Compaction of a Gas
366(1)
17.5 First Law of Thermodynamics
366(26)
17.5.1 Mechanical Energies
366(4)
17.5.2 Definitions, Important for the First Law
370(8)
17.5.3 Caloric Equations of State for Fluids and Gases
378(4)
17.5.4 Simple Applications of the First Law
382(8)
17.5.5 Specific Heats of Real Gases
390(2)
17.6 The Second Law of Thermodynamics---Principle of Irreversibility
392(20)
17.6.1 Preamble
392(3)
17.6.2 The Second Law for Simple Adiabatic Systems
395(15)
17.6.3 Generalizations for Non-adiabatic Systems
410(2)
17.7 First Applications of the Second Law of Thermodynamics
412(9)
References
418(3)
18 Thermodynamics---Field Formulation
421(62)
18.1 The Second Law of Thermodynamics for Continuous Systems
423(6)
18.2 Two Popular Forms of the Entropy Principle
429(23)
18.2.1 Entropy Principle 1: Clausius--Duhem Inequality
430(10)
18.2.2 Entropy Principle of Ingo Muller
440(12)
18.3 Thermal and Caloric Equations of State
452(15)
18.3.1 Canonical Equations of State
452(6)
18.3.2 Specific Heats and Other Thermodynamic Quantities
458(6)
18.3.3 Application to Ideal Gases
464(2)
18.3.4 Isentropic Processes in Caloric Ideal Gases
466(1)
18.4 Thermodynamics of an Inviscid, Heat Conducting Compressible Fluid---Toward a Hyperbolic Heat Conduction Equation
467(16)
18.4.1 The Coleman-Noll Approach
468(4)
18.4.2 The Rational Thermodynamics of Ingo Muller
472(7)
Appendix: Proof of Liu's Theorem
479(2)
References
481(2)
19 Gas Dynamics
483(54)
19.1 Introductory Remarks
485(1)
19.2 Propagation of Small Perturbations in a Gas
486(20)
19.2.1 Fundamental Equations
486(7)
19.2.2 Plane and Spherical Waves
493(9)
19.2.3 Eigen Oscillations Determined with Bernoulli's Method
502(4)
19.3 Steady, Isentropic Stream Filament Theory
506(14)
19.4 Theory of Shocks
520(16)
19.4.1 General Concepts
520(3)
19.4.2 Jump Conditions
523(4)
19.4.3 Stationary Shocks in Simple Fluids Under Adiabatic Conditions
527(9)
19.5 Final Remarks
536(1)
References
536(1)
20 Dimensional Analysis, Similitude and Physical Experiments at Laboratory Scale
537(72)
20.1 Introductory Motivation
541(6)
20.1.1 Dimensional Analysis
541(2)
20.1.2 Similitude and Model Experiments
543(2)
20.1.3 Systems of Physical Entities
545(2)
20.2 Theory of Dimensional Equations
547(24)
20.2.1 Dimensional Homogeneity
547(4)
20.2.2 Buckingham's Theorem
551(5)
20.2.3 A Set of Examples from Fluid Mechanics
556(15)
20.3 Theory of Physical Models
571(12)
20.3.1 Analysis of the Downscaling of Physical Processes
571(6)
20.3.2 Applications
577(6)
20.4 Model Theory and Differential Equations
583(8)
20.4.1 Avalanching Motions down Curved and Inclined Surfaces
584(1)
20.4.2 Navier--Stokes--Fourier--Fick Equations
584(2)
20.4.3 Non-dimensionalization of the NSFF Equations
586(5)
20.5 Discussion and Conclusions
591(18)
Appendix A Algebraic Theory of Dimensional Analysis
592(13)
References
605(4)
List of Biographies 609(2)
Name Index 611(6)
Subject Index 617
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