Core-annular flow through a horizontal pipe: hydrodynamic counterbalancing of buoyancy force on core

A theoretical investigation has been made of core-annular flow: the flow of a high-viscosity liquid core surrounded by a low-viscosity liquid annular layer through a horizontal pipe. Special attention is paid to the question of how the buoyancy force on the core, caused by a density difference between the core and the annular layer, is counterbalanced. From earlier studies it is known that at the interface between the annular layer and the core waves are present that move with respect to the pipe wall. In the present study the core is assumed to consist of a solid center surrounded by a high-viscosity liquid layer. Using hydrodynamic lubrication theory taking into account the flow in the low-viscosity liquid annular layer and in the high-viscosity liquid core layer the development of the interfacial waves is calculated. They generate pressure variations in the core layer and annular layer that can cause a net force on the core. Steady eccentric core-annular flow is found to be possible

A numerical study on level set based multiphase flow simulation

학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2015. 8. 강명주.This thesis concerns numerical methods for simulating multiphase flow using level set method. The motion of multiphase flow can be expressed as the incompressible Navier-Stokes equation. First, we survey numerical methods that can approximately solve the governing equations. Also, we introduce level set method for describing interface of fluid and show how to combine level set method with the Navier-Stokes equations. Finally, we show numerical simulation by core-annular flow in horizontal pipe problem.Abstract i 1 Introduction 1 2 Mathematical Formulation of Fluid Motion 3 2.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 The Equation of Motion - Navier-Stokes Equa- tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.2 Dimensionless Form of Navier-Stokes Equations 4 2.2 Level Set Method . . . . . . . . . . . . . . . . . . . . . . . 5 3 Numerical Methods 7 3.1 The Projection Method . . . . . . . . . . . . . . . . . . . . 7 3.2 Advection Term . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2.1 ENO/WENO Approximation - For Spatial Dis- cretization . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2.2 TVD Runge Kutta Scheme - For Time Discretiza- tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.2.3 Semi-Lagrangian/BDF mixed Scheme . . . . . . . 17 3.3 Projection Term . . . . . . . . . . . . . . . . . . . . . . . . 18 3.3.1 Poisson's Equation . . . . . . . . . . . . . . . . . . . 18 3.3.2 Variable Coecient Poisson's Equation with Jump Condition: Surface Tension Eect Considered . . 19 3.3.3 Preconditioned Conjugate Gradient Method . . 21 3.4 Viscosity Term . . . . . . . . . . . . . . . . . . . . . . . . . 26 ii CONTENTS 3.4.1 Semi-Implicit Viscosity Solver . . . . . . . . . . . 27 3.5 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 28 3.5.1 Advection/Viscous Terms . . . . . . . . . . . . . . 28 3.5.2 Projection Term . . . . . . . . . . . . . . . . . . . . 30 3.6 Reinitialization . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.7 CFL Condition . . . . . . . . . . . . . . . . . . . . . . . . . 33 4 Numerical experiments 35 4.1 Two-Phase Core-Annular Flow in Crude Oil Trans- portation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.1.1 Parameters for Equations . . . . . . . . . . . . . . 36 4.1.2 Up ow Case for Validation . . . . . . . . . . . . . 37 4.1.3 Horizontal Flow with Gravity Eect . . . . . . . . 38 4.1.4 Time for Computing . . . . . . . . . . . . . . . . . 44 5 Conclusion 49 Abstract (in Korean) 53 Acknowledgement (in Korean) 54Docto