Muutke küpsiste eelistusi

Mathematical Modeling for Complex Fluids and Flows 2012 ed. [Kõva köide]

  • Formaat: Hardback, 264 pages, kõrgus x laius: 235x155 mm, kaal: 594 g, XX, 264 p., 1 Hardback
  • Ilmumisaeg: 13-Jan-2012
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 364225294X
  • ISBN-13: 9783642252945
  • Formaat: Hardback, 264 pages, kõrgus x laius: 235x155 mm, kaal: 594 g, XX, 264 p., 1 Hardback
  • Ilmumisaeg: 13-Jan-2012
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 364225294X
  • ISBN-13: 9783642252945
Mathematical Modeling for Complex Fluids and Flows provides researchers and engineering practitioners encountering fluid flows with state-of-the-art knowledge in continuum concepts and associated fluid dynamics. In doing so it supplies the means to design mathematical models of these flows that adequately express the engineering physics involved. It exploits the implicit link between the turbulent flow of classical Newtonian fluids and the laminar and turbulent flow of non-Newtonian fluids such as those required in food processing and polymeric flows.The book develops a descriptive mathematical model articulated through continuum mechanics concepts for these non-Newtonian, viscoelastic fluids and turbulent flows. Each complex fluid and flow is examined in this continuum context as well as in combination with the turbulent flow of viscoelastic fluids. Some details are also explored via kinetic theory, especially viscoelastic fluids and their treatment with the Boltzmann equation. Both solution and modeling strategies for turbulent flows are laid out using continuum concepts, including a description of constructing polynomial representations and accounting for non-inertial and curvature effects.Ranging from fundamental concepts to practical methodology, and including discussion of emerging technologies, this book is ideal for those requiring a single-source assessment of current practice in this intricate yet vital field.

This book provides state-of-the-art knowledge in continuum concepts and associated fluid dynamics. It supplies the means to design mathematical models of these flows that adequately express the engineering physics involved.
1 Introduction
1(20)
1.1 Complex Fluids
2(6)
1.1.1 Physical Considerations
3(2)
1.1.2 Viscoelastic Fluids
5(1)
1.1.3 Viscometric Flows
6(2)
1.2 Complex Flows
8(4)
1.2.1 Physical Considerations: Circular Couette Flow
8(2)
1.2.2 Transitional Flows
10(1)
1.2.3 Turbulent Flows
11(1)
1.3 Elastic Turbulence
12(1)
1.4 Examples of a Complex Fluid and Flow
12(5)
1.4.1 The Kaye Effect: Shear-Thinning Evidence
13(2)
1.4.2 Bouncing Newtonian Jet
15(1)
1.4.3 Turbulent Drag Reduction
15(2)
1.5 The Modeling Map
17(4)
2 Tensor Analysis, Invariants, and Representations
21(26)
2.1 Symmetries and Transformations
23(2)
2.2 Invariants and Traces of Matrix Polynomials
25(6)
2.2.1 Polynomial Invariants
26(2)
2.2.2 Traces of Matrix Polynomials
28(3)
2.3 Integrity Bases for Vectors and Tensors
31(7)
2.3.1 Integrity Basis for Vectors
32(1)
2.3.2 Integrity Bases for Symmetric Second-Order Tensors
32(2)
2.3.3 Integrity Bases for Vectors and Second-Order Tensors
34(4)
2.4 Polynomial Representations for Tensors and Vectors
38(9)
2.4.1 Proper Orthogonal Group
38(4)
2.4.2 Full Orthogonal Group
42(5)
3 Kinematics and Dynamics
47(22)
3.1 Material Elements and Deformation
47(8)
3.1.1 Decomposition of the Deformation
53(1)
3.1.2 Infinitesimal Strain and Rotation
53(2)
3.2 Rate of Deformation
55(6)
3.2.1 Time Rate of Change
55(1)
3.2.2 Strain Rate and Rotation Rate Tensors
56(2)
3.2.3 Dilatation Rate
58(1)
3.2.4 Rivlin-Ericksen Tensors
59(2)
3.3 Reynolds Transport Theorem
61(1)
3.4 Conservation Equations
62(7)
3.4.1 Mass Conservation
63(1)
3.4.2 Momentum Conservation
63(4)
3.4.3 Energy Conservation
67(2)
4 Constitutive Equations: General Principles
69(26)
4.1 Introduction
69(1)
4.2 Methodological Principles
70(5)
4.2.1 Material Stress Field
71(2)
4.2.2 Turbulent Stress Field
73(2)
4.3 Frames, Transformations and Objectivity
75(9)
4.3.1 Transformations and Objectivity
75(4)
4.3.2 Objective Rates of the Stress Tensor
79(5)
4.4 Restrictions on Constitutive Relationships
84(5)
4.4.1 A Thermodynamic Constraint for Constitutive Relationships
84(1)
4.4.2 Objectivity Constraints on Material Constitutive Equations
85(4)
4.5 Deformation and Constant Stretch History Motion
89(6)
4.5.1 Viscometric Flow
92(1)
4.5.2 Extensional Flow
93(1)
4.5.3 Viscometric Functions
94(1)
5 Non-Newtonian and Viscoelastic Fluids
95(54)
5.1 Introduction
95(1)
5.2 Classical and Generalized Newtonian Models
96(2)
5.2.1 Newtonian Fluids
96(1)
5.2.2 Generalized Newtonian Fluids
97(1)
5.3 Linear Viscoelasticity
98(3)
5.3.1 Maxwell Model
99(1)
5.3.2 Kelvin-Voigt Model
100(1)
5.3.3 Jeffreys Model
100(1)
5.4 From a Simple Fluid to Viscoelasticity
101(2)
5.4.1 Reiner-Rivlin Fluid
101(1)
5.4.2 Elasticity as the Limit Case
102(1)
5.4.3 Design of a Viscoelastic Constitutive Equation
103(1)
5.5 Rivlin-Ericksen and Order Fluids
103(2)
5.5.1 Rivlin-Ericksen Fluids
104(1)
5.5.2 Order Fluids
104(1)
5.5.3 Plane Shear Flow of a Second-Order Fluid
105(1)
5.6 Constant Stretch History Flows
105(2)
5.7 Constitutive Equations of the Rate Type
107(8)
5.7.1 Oldroyd-B Models
107(6)
5.7.2 Improved Rate Type Models
113(1)
5.7.3 Relation Between Rate Type and Integral Models
114(1)
5.8 Dumbbell Models
115(6)
5.8.1 Rouse Model
115(1)
5.8.2 The Hookean Dumbbell
116(1)
5.8.3 Drag Force
117(1)
5.8.4 Brownian Motion
118(1)
5.8.5 Dumbbell Stress
119(2)
5.8.6 The Giesekus Model Revisited
121(1)
5.9 Dumbbells and Stochastic Differential Equations
121(7)
5.9.1 The Fokker-Planck Equation
121(2)
5.9.2 Hookean Dumbbell
123(1)
5.9.3 Nonlinear Dumbbells
124(3)
5.9.4 Dumbbells with Hydrodynamic Interactions
127(1)
5.10 The Micro-Macro Description
128(2)
5.10.1 Solving the Fokker-Planck Equation
129(1)
5.10.2 Brownian Configuration Fields
130(1)
5.11 Consequences of Non-affine Motion
130(3)
5.11.1 Dumbbells with Non-affine Motion and the Gordon-Schowalter Model
130(2)
5.11.2 Modeling Polymeric Networks
132(1)
5.12 Modeling of Polymer Melts
133(16)
5.12.1 Doi-Edwards Model
134(3)
5.12.2 Differential Form of the Doi-Edwards Model
137(2)
5.12.3 Pom-Pom Model
139(4)
5.12.4 The Extended Pom-Pom Model
143(2)
5.12.5 Linear Entangled Polymer Chains and the Rolie-Poly Equation
145(4)
6 Turbulent Flows
149(66)
6.1 Homogeneity and the Spectral Cascade
149(3)
6.2 Numerical Solution Methodologies
152(21)
6.2.1 Direct Numerical Simulation (DNS)
154(4)
6.2.2 Scale Resolving Simulations
158(10)
6.2.3 Mean Equation Methods
168(5)
6.3 Mean Equation Closure
173(10)
6.3.1 Reynolds Stress Tensor
175(4)
6.3.2 Dissipation Rate Tensor
179(4)
6.4 Reynolds Stress Transport Equation Closure
183(11)
6.4.1 Pressure-Strain Rate Correlation
184(4)
6.4.2 Turbulent Transport
188(6)
6.5 Polynomial Representations of the Turbulent Stress Tensor
194(18)
6.5.1 Turbulent Stress of a Simple Fluid
195(2)
6.5.2 Turbulent Stress from Invariant Bases
197(13)
6.5.3 Constraints Imposed by Solid Boundaries
210(2)
6.6 Hybrid Methodologies
212(3)
7 The Boltzmann Equation
215(28)
7.1 Kinetic Theory
216(4)
7.1.1 Generalities
216(2)
7.1.2 Continuous Boltzmann Equation
218(1)
7.1.3 Boltzmann-BGK Based Continuous Equations
219(1)
7.2 Hermite Function Approximation
220(2)
7.3 Galerkin Method
222(1)
7.4 Chapman-Enskog Expansion
223(5)
7.4.1 Zero Order Approximation
224(1)
7.4.2 First Order Approximation
224(4)
7.5 Lattice Boltzmann Method
228(5)
7.6 Multiple Relaxation Time Boltzmann Equation
233(2)
7.6.1 Linearized Boltzmann Equation
233(1)
7.6.2 MRT Lattice Boltzmann Method
234(1)
7.7 LBM for Viscoelastic Fluids
235(5)
7.7.1 Advection-Diffusion Equation with a Source Term
236(2)
7.7.2 Computation of the Constitutive Equation
238(1)
7.7.3 Description of the Algorithm
239(1)
7.8 LBM for Turbulent Flows
240(3)
Appendix Properties of the Hermite Polynomials
243(6)
Continuous Case
243(2)
Gauss-Hermite Quadrature Rule
245(1)
Discrete Case
246(3)
References 249(12)
Index 261