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Two-Fluid Model Stability, Simulation and Chaos 1st ed. 2017 [Kõva köide]

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  • Formaat: Hardback, 358 pages, kõrgus x laius: 235x155 mm, kaal: 6919 g, 60 Illustrations, color; 14 Illustrations, black and white; XX, 358 p. 74 illus., 60 illus. in color., 1 Hardback
  • Ilmumisaeg: 17-Nov-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319449672
  • ISBN-13: 9783319449678
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Two-Fluid Model Stability, Simulation and Chaos 1st ed. 2017Suurem pilt
  • Formaat: Hardback, 358 pages, kõrgus x laius: 235x155 mm, kaal: 6919 g, 60 Illustrations, color; 14 Illustrations, black and white; XX, 358 p. 74 illus., 60 illus. in color., 1 Hardback
  • Ilmumisaeg: 17-Nov-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319449672
  • ISBN-13: 9783319449678
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319449678.html
Märksõnad:
This book addresses the linear and nonlinear two-phase stability of the one-dimensional Two-Fluid Model (TFM) material waves and the numerical methods used to solve it. The TFM fluid dynamic stability is a problem that remains open since its inception more than forty years ago. The difficulty is formidable because it involves the combined challenges of two-phase topological structure and turbulence, both nonlinear phenomena. The one dimensional approach permits the separation of the former from the latter. The authors first analyze the kinematic and Kelvin-Helmholtz instabilities with the simplified one-dimensional Fixed-Flux Model (FFM). They then analyze the density wave instability with the well-known Drift-Flux Model. They demonstrate that the Fixed-Flux and Drift-Flux assumptions are two complementary TFM simplifications that address two-phase local and global linear instabilities separately. Furthermore, they demonstrate with a well-posed FFM and a DFM two cases of nonlinear

two-phase behavior that are chaotic and Lyapunov stable. On the practical side, they also assess the regularization of an ill-posed one-dimensional TFM industrial code. Furthermore, the one-dimensional stability analyses are applied to obtain well-posed CFD TFMs that are either stable (RANS) or Lyapunov stable (URANS), with the focus on numerical convergence.

1 Introduction Nomenclature PART 1: HORIZONTAL AND NEAR HORIZONTAL WAVY FLOW 2 Fixed-Flux Model 3 Two-Fluid Model 4 Fixed-Flux Model Chaos PART 2: VERTICAL BUBBLY FLOW 5 Fixed-Flux Model 6 Drift-Flux Model 7 Drift-Flux Model Non-linear Dynamics and Chaos 8 RELAP5 Two-Fluid Model 9 Two-Fluid Model CFD APPENDIX A One-Dimensional Two-Fluid Model APPENDIX B Mathematical BACKGROUND 
1 Introduction
1(10)
1.1 Summary
1(5)
1.2 Outline of Contents
6(5)
References
8(3)
Part I Horizontal and Near Horizontal Wavy Flow
2 Fixed-Flux Model
11(54)
2.1 Introduction
11(2)
2.2 Compressible Two-Fluid Model
13(4)
2.2.1 One-Dimensional Model Equations
13(1)
2.2.2 Characteristics
14(3)
2.3 Incompressible Two-Fluid Model
17(6)
2.3.1 One-Dimensional Model Equations
17(2)
2.3.2 Derivation of the Fixed-Flux Model
19(4)
2.4 Linear Stability
23(12)
2.4.1 Dispersion Relation for the Kelvin--Helmholtz Instability (F = 0)
23(5)
2.4.2 Dispersion Relation for the SWT Instability (F ≠ 0)
28(5)
2.4.3 Sheltering Effect
33(2)
2.5 Numerical Stability
35(14)
2.5.1 Obtaining a Well-Posed Numerical Model
35(1)
2.5.2 First-Order Semi-Implicit Scheme (Inviscid)
35(7)
2.5.3 First-Order Semi-Implicit Scheme (with Viscous Terms)
42(2)
2.5.4 First-Order Fully Implicit Scheme (with Viscous Terms)
44(2)
2.5.5 Second-Order Semi-Implicit Scheme
46(3)
2.6 Verification
49(10)
2.6.1 Kreiss--Ystrom Equations
49(1)
2.6.2 Characteristic Analysis
49(2)
2.6.3 Dispersion Relation
51(2)
2.6.4 Method of Manufactured Solutions
53(4)
2.6.5 Water Faucet Problem
57(2)
2.7 Kelvin--Helmholtz Instability
59(2)
2.8 Summary and Discussion
61(4)
References
62(3)
3 Two-Fluid Model
65(42)
3.1 Introduction
65(1)
3.2 Incompressible Two-Fluid Model
66(2)
3.3 Linear Stability
68(5)
3.3.1 Characteristics
68(2)
3.3.2 Dispersion Analysis
70(1)
3.3.3 KH Instability
71(2)
3.4 Numerical Stability
73(14)
3.4.1 TFIT Two-Fluid Model
74(1)
3.4.2 Staggered Cell Structure
74(3)
3.4.3 First-Order Semi-Implicit Scheme
77(1)
3.4.4 Implicit Pressure Poisson Equation
78(1)
3.4.5 von Neumann Analysis
79(3)
3.4.6 Numerical Regularization
82(2)
3.4.7 Second-Order Semi-implicit Scheme
84(3)
3.5 Verification
87(6)
3.5.1 Sine Wave
87(1)
3.5.2 Water Faucet Problem
88(3)
3.5.3 Modified Water Faucet Problem
91(1)
3.5.4 Convergence
92(1)
3.6 Nonlinear Simulations
93(10)
3.6.1 Thorpe Experiment
93(2)
3.6.2 Viscous Stresses
95(1)
3.6.3 Wall Shear
96(1)
3.6.4 Interfacial Shear
97(1)
3.6.5 Single Nonlinear Wave
97(1)
3.6.6 Thorpe Experiment Validation
98(2)
3.6.7 Convergence
100(3)
3.7 Summary and Discussion
103(4)
References
104(3)
4 Fixed-Flux Model Chaos
107(34)
4.1 Introduction
108(1)
4.2 Chaos and the Kreiss and Ystrom Equations
109(13)
4.2.1 Nonlinear Simulations
109(2)
4.2.2 Sensitivity to Initial Conditions
111(1)
4.2.3 Lyapunov Exponent
112(2)
4.2.4 Fractal Dimension
114(2)
4.2.5 The Route to Chaos
116(4)
4.2.6 Numerical Convergence
120(2)
4.3 Fixed-Flux Model Chaos
122(12)
4.3.1 Nonlinear Simulations with the FFM
122(1)
4.3.2 Extension of Thorpe Experiment into Chaos
122(2)
4.3.3 Fixed-Flux Model for Fully Developed Laminar Flow in a Pipe
124(4)
4.3.4 Kelvin--Helmholtz Instability
128(2)
4.3.5 Nonlinear Simulations
130(2)
4.3.6 Lyapunov Exponent
132(1)
4.3.7 Numerical Convergence
133(1)
4.3.8 Fractal Dimension
134(1)
4.4 Summary and Discussion
134(7)
References
137(4)
Part II Vertical Bubbly Flow
5 Fixed-Flux Model
141(22)
5.1 Introduction
141(1)
5.2 Compressible Two-Fluid Model
142(2)
5.2.1 Compressible Model Equations
142(1)
5.2.2 Virtual Mass Force
143(1)
5.3 Incompressible Two-Fluid Model
144(4)
5.3.1 Interfacial Pressure
145(1)
5.3.2 Fixed-Flux Model Derivation
145(3)
5.4 Linear Stability
148(7)
5.4.1 Characteristic Analysis
148(1)
5.4.2 Collision Force
149(2)
5.4.3 Dispersion Relation: Kinematic Instability
151(1)
5.4.4 Drag Force
152(3)
5.5 Nonlinear Simulations
155(6)
5.5.1 Stable Wave Evolution
155(3)
5.5.2 Kinematically Unstable Waves in Guinness
158(3)
5.6 Summary and Discussion
161(2)
References
161(2)
6 Drift-Flux Model
163(32)
6.1 Introduction
163(2)
6.2 Void Propagation Equation
165(2)
6.3 Applications of Void Propagation Equation
167(6)
6.3.1 Level Swell
167(3)
6.3.2 Drainage
170(2)
6.3.3 Propagation of Material Shocks
172(1)
6.4 Dynamic Drift-Flux Model
173(6)
6.4.1 Mixture Momentum Equation
173(3)
6.4.2 Integral Momentum Equation
176(3)
6.5 Delay Drift-Flux Model
179(5)
6.6 Flow Excursion
184(3)
6.6.1 Homogeneous Equilibrium Model
184(2)
6.6.2 Drift-Flux Model
186(1)
6.7 Density Wave Instability
187(5)
6.7.1 Homogeneous Equilibrium Model
187(2)
6.7.2 Transfer Function
189(3)
6.7.3 Drift-Flux Model
192(1)
6.8 Summary and Discussion
192(3)
References
192(3)
7 Drift-Flux Model Nonlinear Dynamics and Chaos
195(30)
7.1 Introduction
195(2)
7.2 Nonlinear Mapping of the Boiling Channel Dynamics
197(5)
7.3 Model of a Boiling Channel with Moving Nodes
202(7)
7.4 Dynamics of a Boiling Channel with an Adiabatic Riser
209(12)
7.4.1 Summary of MNM Equations for the Channel-Riser System
211(2)
7.4.2 Low Power Oscillations at Low Fr Numbers in a Heated Channel with Adiabatic Riser
213(5)
7.4.3 Experimental Validation of Quasi-periodic Oscillations
218(3)
7.5 Summary and Discussion
221(4)
References
222(3)
8 RELAP5 Two-Fluid Model
225(22)
8.1 Introduction
225(1)
8.2 Material Waves
226(7)
8.2.1 RELAP5 Adiabatic Two-Fluid Model
226(2)
8.2.2 Characteristics
228(2)
8.2.3 Bernier's Experiment
230(3)
8.3 Low Pass Filter Regularization of the TFM
233(10)
8.3.1 Dispersion Analysis
234(2)
8.3.2 Numerical Viscosity
236(4)
8.3.3 Artificial Viscosity Model
240(2)
8.3.4 Water Faucet Problem
242(1)
8.4 Summary and Discussion
243(4)
References
244(3)
9 Two-Fluid Model CFD
247(46)
9.1 Introduction
247(1)
9.2 Incompressible Multidimensional TFM
248(5)
9.2.1 Model Equations
248(1)
9.2.2 Interfacial Momentum Transfer
249(1)
9.2.3 Drag Force
249(1)
9.2.4 Lift Force
250(1)
9.2.5 Wall Force
251(1)
9.2.6 Laminar Pipe Flow
252(1)
9.3 RANS Two-Fluid Model
253(18)
9.3.1 Reynolds Stress Stabilization
253(1)
9.3.2 Single-Phase k--ε Model
253(3)
9.3.3 Two-Phase k--ε Model
256(1)
9.3.4 Decay of Grid Generated Turbulence
257(4)
9.3.5 Turbulent Pipe Flow
261(4)
9.3.6 Turbulent Diffusion Force
265(2)
9.3.7 Bubbly Jet
267(4)
9.4 Near-Wall Two-Fluid Model
271(9)
9.4.1 Wall Boundary Conditions
271(1)
9.4.2 Two-Phase Logarithmic Law of the Wall of Marie et al. (1997)
271(2)
9.4.3 Near-Wall Averaging
273(2)
9.4.4 Laminar Pipe Flow Revisited
275(1)
9.4.5 Turbulent Bubbly Boundary Layer
276(2)
9.4.6 Turbulent Pipe Flow Revisited
278(2)
9.5 URANS Two-Fluid Model
280(7)
9.5.1 Stability
280(1)
9.5.2 Constitutive Relations
281(1)
9.5.3 Plane Bubble Plume
281(6)
9.6 Summary and Discussion
287(6)
References
288(5)
Appendix A One-Dimensional Two-Fluid Model 293(6)
Appendix B Mathematical Background 299(48)
References 347(4)
Index 351
Martín López de Bertodano is Associate Professor of Nuclear Engineering at Purdue University.William D. Fullmer is a graduate student, specializing in computational fluid dynamics and computational multiphase flow, at Purdue University.Alejandro Clausse, Universidad Nacional del Centro, Tandil, Argentina.Victor H. Ransom is Professor Emeritus in the School of Nuclear Engineering at Purdue University.