The purpose of this book is to construct an efficient robust, and reliable numericalapproach for incompressible gas-liquid two-phase flows. The book focuses attention on capturing interface between fluids with different properties and modeling surface tension effect on the interface. A numerical analysis is presented to demonstrate the possibility of simulations for physically interesting problems in incompressible gas-liq uid two-phase flows in range over a wide field.
Moreover, a study on convection-diffusion problems has also been carried out to understand various finite difference methods for convection-diffusion equations.
Finally, over all conclusions have been drawn.
Preface i
Chapter 1 Introduction
1.1 Classification of Two-Phase Flows
1.2 Classification of Gas-Liquid Two-Phase Flows
1.3 Traditional Techniques for Representing Free Surface
1.3.1 Height Function Method
1.3.2 Line Segment Method
1.3.3 Marker Particle Method
1.3.4 Volume-of-Fluid Method
1.4 Objectives
1.5 Outline
Chapter 2 Study on Convection-Diffusion Problems
2.1 Introduction
2.2 One-Dimensional Linear Convection Equation
2.3 One-Dimensional Diffusion Equation
2.4 One-Dimensional Convection-Diffusion Equation
2.5 Test Problem for One-Dimensional Convection-Diffusion Equa-tion
2.6 Conclusion Chapter 3 Level Set Method
3.1 Level Set Function
3.1.1 Construction of the initial value for φ
3.1.2 Derivation of the equation for φ
3.2 Reinitialization of Level Set Function
3.3 Derivation of Level Set Formulation
3.4 Conclusion
Chapter 4 Mathematical Formulation and Numerical Method
4.1 Governing Equations of Viscous, Incompressible Flows 37
4.2 Non-Dimensionlization of Governing Equations of Viscous, Incompressible Flows
4.3 Numerical Algorithm
4.3.1 Positions of Variables
4.3.2 Discretisation of Navier-Stokes Equation in Space
4.3.3 Poisson Equation Solver
4.3.4 Level Set Function
4.3.5 Discretisation of Convection Equation of Level Set Function
4.3.6 Reinitialization of Level Set Function
4.3.7 Discretisation of Reinitialization of Level Set Function
4.3.8 Smoothing of Interface
4.3.9 Discretisation in Time
4.3.10 Computation of Time Step ∆t
4.3.11 Numerical Procedure
4.4 Conclusion
Chapter 5 Investigation of Effects for Parameters and Operation
5.1 Introduction
5.2 Improvement for reinitialization of level set function
— a new reinitialization approach
5.3 Effect of Reinitialization of Level Set Function
5.3.1 Statement of problem
5.3.2 Initial and boundary conditions
5.3.3 Results
5.4 Effect of Different Density Ratios
5.4.1 Statement of problem
5.4.2 Initial and boundary conditions
5.4.3 Results
5.5 Effect of Surface Tension Force
5.5.1 Statement of problem
5.5.2 Initial and boundary conditions
5.5.3 Results
5.6 Effect of Viscous Terms
5.6.1 Statement of problem
5.6.2 Initial and boundary conditions
5.6.3 Results
5.7 Conclusion
Chapter 6 Fluid Interfacial Motion Induced by Surface Tension Force
6.1 Introduction
6.2 Outline of CSF Model
6.2.1 Surface stress and pressure boundary conditions
6.2.2 A volume reformulation of surface tension force
6.2.3 Treatment of curvature for interface
6.3 Interfacial Motion of an Initially-Square Droplet
6.3.1 Statement of problem
6.3.2 Initial and boundary conditions
6.3.3 Results
6.4 Surface Tension Force Driven Oscillation of a Combined Droplet
6.4.1 Statement of problem
6.4.2 Initial and boundary conditions
6.4.3 Results
6.5 Conclusion
Chapter 7 Study on Colliding Problems
7.1 Introduction
7.2 An improvement on interface definition
7.3 Collision of a Falling Water Droplet with a Solid Surface
7.3.1 Statement of problem
7.3.2 Initial and boundary conditions
7.3.3 Results
7.4 Collision of a Rising Bubble with a Solid Surface
7.4.1 Statement of problem
7.4.2 Initial and boundary conditions
7.4.3 Results
7.5 Collision of Four Water Droplets with Each Other
7.5.1 Statement of problem
7.5.2 Initial and boundary conditions
7.5.3 Results
7.6 Collision of Five Water Droplets with Each Other
7.6.1 Statement of problem
7.6.2 Initial and boundary conditions
7.6.3 Results
Chapter 8 Study on Problems Involving Large Change of Topology in Free Surface Flows
8.1 Introduction
8.2 Dam-Breaking Problem
8.2.1 Statement of problem
8.2.2 Initial and boundary conditions
8.2.3 Results
8.3 Collision of a Falling Droplet with a Liquid Surface
8.3.1 Statement of problem
8.3.2 Initial and boundary conditions
8.3.3 Results
8.4 Conclusion
Chapter 9 Numerical Simulation of Three-Dimensional Gas-Liquid Two-Phase Flows
9.1 Introduction
9.2 Numerical Formulation
9.2.1 Equations of motion; level set formulation
9.2.2 Poisson Equation Solver
9.3 Bubble Rising Problem
9.3.1 Statement of problem
9.3.2 Initial and boundary conditions
9.3.3 Results
9.4 Head-on Collision of Five Droplets
9.4.1 Statement of problem
9.4.2 Initial and boundary conditions
9.4.3 Results
9.5 Head-on Collision of Two Droplets
9.5.1 Statement of problem
9.5.2 Initial and boundary conditions
9.5.3 Results
9.6 Dam-Breaking Problem
9.6.1 Statement of problem
9.6.2 Initial and boundary conditions
9.6.3 Results
9.7 Droplet Falling on a Liquid Surface
9.7.1 Statement of problem
9.7.2 Initial and boundary conditions
9.7.3 Results
9.8 Conclusion
Chapter 10 Conclusions
Bibliography
Liang Ruquan, male, was born on August 1963 from Feicheng, Shandong Provincewith Han nationality.
Academic field: Thermal energy engineering
Professional titles:
Doctor of Engineering, Linyi University. Second-class professor, doctoral tutor ofNortheastern University and master supervisor of Linyi University and University ofScience and Technology Liaoning; Deputy Editor of the international journal Current Chinese Science -Energy, the international journal Current Mechanics and Advanced Materials, the Chinese international journal Mechanical Research, Fluid Mechanics,Metallurgical Engineering, editorial board member.
In 2001, I was awarded as a foreign Research Fellow of Japan Academic Revitalization Association;
From 2002 to 2006, I was a core member of the International Team for thermocapillary convection Model Research at NASA.
In 2011, I won the first prize of Shenyang Natural Science Academic Achievements;
In 2012, I won the title of Liaoning Province hundred Thousand High-end Introduced Talents;
In 2017, I was awarded the title of high-level talents of Shenyang; I was AwardedYimeng Huicai Diamond Card in 2020;
In 2021, I won the Silver Award of Geneva World Invention Expo and Shandong Huicai Card (High-level Talents of Shandong Province). I am the Member of the Fifth National Microgravity Science and Application Committee and Evaluation Expert of Space Science Satellite Joint Fund Meeting of National Natural Science Foundation of China and Chinese Academy of Sciences; I was granted the National Science and Technology Progress Award Evaluation Expert (power energy core group); Dissertation Evaluation Expert of Academic Degree Center of Ministry of Education; Senior Member of China Physics Society;
Since 2018, I worked as a discipline leader, I have applied for and been approvedtwo research platforms of Linyi Energy Conservation and Emission Reduction Research Center and Thermal Energy Engineering Institute of Linyi University.