A Numerical Simulation of Swirling Two-Phase Flow in BWR Steam-Water Separator and Its Optimization

2003 ◽  
Author(s):  
Haruo Terasaka ◽  
Sensuke Shimizu ◽  
Minoru Kawahara
Keyword(s):  
Transient Flow ◽  
Fluid Model ◽  
Flow Analysis ◽  
Phase Flow ◽  
Step Size ◽  
Time Step ◽  
Two Phase ◽  
Time Step Size ◽  
Fully Implicit ◽  
Water Separator

An advanced numerical method based on the two-fluid model has been developed. The solution method presented here is an extension of the SIMPLEST scheme, a fully implicit scheme for single-phase flow analysis. It is robust and unconditionally stable, and therefore it enables us to use a very large time step size. This feature is suitable for steady and/or slow transient flow analyses. Furthermore, it enhances numerical stability during rapid transient calculations. By using this method, swirling gas-liquid flow in a steam-water separator of Boiling Water Reactors (BWRs) was calculated and the hydrodynamics characteristics were investigated for optimization.

A Numerical Study of BWR Steam Separator

2002 ◽  
Author(s):  
Haruo Terasaka ◽  
Sensuke Shimizu
Keyword(s):  
Transient Flow ◽  
Numerical Study ◽  
Fluid Model ◽  
Flow Analysis ◽  
Phase Flow ◽  
Step Size ◽  
Time Step ◽  
Two Phase ◽  
Time Step Size ◽  
Steam Separator

An advanced numerical method based on two-fluid model of two-phase flow has been developed to simulate the swirling gas-liquid flow and the phase separation process in a Boiling Water Reactor separator. The goal is to correctly predict the performance of operating steam separator as well as new designs. The solution method present here is an extension of SIMPLEST scheme, a fully implicit scheme for single-phase flow analysis. It is robust and unconditionally stable, therefore enable us to use very large time step size. This feature is suitable for steady and/or slow transient flow analyses. Furthermore, it enhances numerical stability during rapid transient calculations. By employing this method, separator hydrodynamics around swirler were calculated.

scholarly journals Multiscale Time-Splitting Strategy for Multiscale Multiphysics Processes of Two-Phase Flow in Fractured Media

2011 ◽  
Vol 2011 ◽  
pp. 1-24 ◽  
Author(s):  
Jisheng Kou ◽  
Shuyu Sun ◽  
Bo Yu
Keyword(s):  
Porous Media ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Step Size ◽  
Time Step ◽  
Two Phase ◽  
Time Step Size ◽  
Multi Scale ◽  
Rapid Changes ◽  
Time Splitting

The temporal discretization scheme is one important ingredient of efficient simulator for two-phase flow in the fractured porous media. The application of single-scale temporal scheme is restricted by the rapid changes of the pressure and saturation in the fractured system with capillarity. In this paper, we propose a multi-scale time splitting strategy to simulate multi-scale multi-physics processes of two-phase flow in fractured porous media. We use the multi-scale time schemes for both the pressure and saturation equations; that is, a large time-step size is employed for the matrix domain, along with a small time-step size being applied in the fractures. The total time interval is partitioned into four temporal levels: the first level is used for the pressure in the entire domain, the second level matching rapid changes of the pressure in the fractures, the third level treating the response gap between the pressure and the saturation, and the fourth level applied for the saturation in the fractures. This method can reduce the computational cost arisen from the implicit solution of the pressure equation. Numerical examples are provided to demonstrate the efficiency of the proposed method.

scholarly journals Analysis of a Decoupled Time-Stepping Scheme for Evolutionary Micropolar Fluid Flows

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
S. S. Ravindran
Keyword(s):  
Micropolar Fluid ◽  
Stokes Equations ◽  
Fluid Model ◽  
Navier Stokes ◽  
Optimal Order ◽  
Step Size ◽  
Time Step ◽  
Order Error ◽  
Time Step Size ◽  
Time Stepping

Micropolar fluid model consists of Navier-Stokes equations and microrotational velocity equations describing the dynamics of flows in which microstructure of fluid is important. In this paper, we propose and analyze a decoupled time-stepping algorithm for the evolutionary micropolar flow. The proposed method requires solving only one uncoupled Navier-Stokes and one microrotation subphysics problem per time step. We derive optimal order error estimates in suitable norms without assuming any stability condition or time step size restriction.

scholarly journals Accuracy Analysis of a Spectral Element Atmospheric Model Using a Fully Implicit Solution Framework

2010 ◽  
Vol 138 (8) ◽  
pp. 3333-3341 ◽  
Author(s):  
Katherine J. Evans ◽  
Mark A. Taylor ◽  
John B. Drake
Keyword(s):  
Shallow Water Equation ◽  
Time Integration ◽  
Atmospheric Model ◽  
Test Cases ◽  
Implicit Methods ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Fully Implicit ◽  
Stability Limits

Abstract A fully implicit (FI) time integration method has been implemented into a spectral finite-element shallow-water equation model on a sphere, and it is compared to existing fully explicit leapfrog and semi-implicit methods for a suite of test cases. This experiment is designed to determine the time step sizes that minimize simulation time while maintaining sufficient accuracy for these problems. For test cases without an analytical solution from which to compare, it is demonstrated that time step sizes 30–60 times larger than the gravity wave stability limits and 6–20 times larger than the advective-scale stability limits are possible using the FI method without a loss in accuracy, depending on the problem being solved. For a steady-state test case, the FI method produces error within machine accuracy limits as with existing methods, but using an arbitrarily large time step size.

Dynamic Simulation of Gas-Liquid Homogeneous Flow in Natural Gas Pipeline Using Two-Fluid Conservation Equations

2005 ◽  
Author(s):  
Mohammad Abbaspour ◽  
Kirby S. Chapman ◽  
Larry A. Glasgow ◽  
Zhongquan C. Zheng
Keyword(s):  
Natural Gas ◽  
Large Time ◽  
Gas Pipeline ◽  
Phase Flow ◽  
Time Step ◽  
Two Phase ◽  
Natural Gas Pipeline ◽  
Fully Implicit ◽  
Large Time Step ◽  
Two Fluid

Homogeneous two-phase flows are frequently encountered in a variety processes in the petroleum and gas industries. In natural gas pipelines, liquid condensation occurs due to the thermodynamic and hydrodynamic imperatives. During horizontal, concurrent gas-liquid flow in pipes, a variety of flow patterns can exist. Each pattern results from the particular manner by which the liquid and gas distribute in the pipe. The objective of this study is to simulate the non-isothermal, one-dimensional, transient homogenous two-phase flow gas pipeline system using two-fluid conservation equations. The modified Peng-Robinson equation of state is used to calculate the vapor-liquid equilibrium in multi-component natural gas to find the vapor and liquid compressibility factors. Mass transfer between the gas and the liquid phases is treated rigorously through flash calculation, making the algorithm capable of handling retrograde condensation. The liquid droplets are assumed to be spheres of uniform size, evenly dispersed throughout the gas phase. The method of solution is the fully implicit finite difference method. This method is stable for gas pipeline simulations when using a large time step and therefore minimizes the computation time. The algorithm used to solve the nonlinear finite-difference thermo-fluid equations for two phase flow through a pipe is based on the Newton-Raphson method. The results show that the liquid condensate holdup is a strong function of temperature, pressure, mass flow rate, and mixture composition. Also, the fully implicit method has advantages, such as the guaranteed stability for large time step, which is very useful for simulating long-term transients in natural gas pipeline systems.

scholarly journals Diffuse-interface two-phase flow models with different densities: A new quasi-incompressible form and a linear energy-stable method

2018 ◽  
Vol 28 (04) ◽  
pp. 733-770 ◽  
Author(s):  
M. Shokrpour Roudbari ◽  
G. Şimşek ◽  
E. H. van Brummelen ◽  
K. G. van der Zee
Keyword(s):  
Two Phase Flow ◽  
Linear Method ◽  
Diffuse Interface ◽  
Integration Scheme ◽  
Phase Flow ◽  
Time Step ◽  
Two Phase ◽  
Time Step Size ◽  
Mixture Density ◽  
Energy Stable

While various phase-field models have recently appeared for two-phase fluids with different densities, only some are known to be thermodynamically consistent, and practical stable schemes for their numerical simulation are lacking. In this paper, we derive a new form of thermodynamically-consistent quasi-incompressible diffuse-interface Navier–Stokes–Cahn–Hilliard model for a two-phase flow of incompressible fluids with different densities. The derivation is based on mixture theory by invoking the second law of thermodynamics and Coleman–Noll procedure. We also demonstrate that our model and some of the existing models are equivalent and we provide a unification between them. In addition, we develop a linear and energy-stable time-integration scheme for the derived model. Such a linearly-implicit scheme is nontrivial, because it has to suitably deal with all nonlinear terms, in particular those involving the density. Our proposed scheme is the first linear method for quasi-incompressible two-phase flows with non-solenoidal velocity that satisfies discrete energy dissipation independent of the time-step size, provided that the mixture density remains positive. The scheme also preserves mass. Numerical experiments verify the suitability of the scheme for two-phase flow applications with high density ratios using large time steps by considering the coalescence and breakup dynamics of droplets including pinching due to gravity.

scholarly journals An Efficient, Energy Stable Scheme for the Cahn-Hilliard-Brinkman System

2013 ◽  
Vol 13 (4) ◽  
pp. 929-957 ◽  
Author(s):  
Craig Collins ◽  
Jie Shen ◽  
Steven M. Wise
Keyword(s):  
Brinkman Equation ◽  
Implicit Time ◽  
Step Size ◽  
Time Step ◽  
Two Phase ◽  
Time Step Size ◽  
Brinkman System ◽  
Energy Stable ◽  
Nonlinear Multigrid ◽  
Nonlinear Multigrid Method

AbstractWe present an unconditionally energy stable and uniquely solvable finite difference scheme for the Cahn-Hilliard-Brinkman (CHB) system, which is comprised of a Cahn-Hilliard-type diffusion equation and a generalized Brinkman equation mod-eling fluid flow. The CHB system is a generalization of the Cahn-Hilliard-Stokes model and describes two phase very viscous flows in porous media. The scheme is based on a convex splitting of the discrete CH energy and is semi-implicit. The equations at the implicit time level are nonlinear, but we prove that they represent the gradient of a strictly convex functional and are therefore uniquely solvable, regardless of time step size. Owing to energy stability, we show that the scheme is stable in the time and space discrete and norms. We also present an efficient, practical nonlinear multigrid method . comprised of a standard FAS method for the Cahn-Hilliard part, and a method based on the Vanka smoothing strategy for the Brinkman part . for solving these equations. In particular, we provide evidence that the solver has nearly optimal complexity in typical situations. The solver is applied to simulate spinodal decomposition of a viscous fluid in a porous medium, as well as to the more general problems of buoyancy- and boundary-driven flows.

Nonisothermal Transient Flow in Natural Gas Pipeline

2008 ◽  
Vol 75 (3) ◽  
Author(s):  
M. Abbaspour ◽  
K. S. Chapman
Keyword(s):  
Gas Flow ◽  
Transient Flow ◽  
Flow Analysis ◽  
Compressibility Factor ◽  
Momentum Equation ◽  
Gas Pipeline ◽  
Time Step ◽  
Inertia Term ◽  
Fully Implicit ◽  
Energy Equations

The fully implicit finite-difference method is used to solve the continuity, momentum, and energy equations for flow within a gas pipeline. This methodology (1) incorporates the convective inertia term in the conservation of momentum equation, (2) treats the compressibility factor as a function of temperature and pressure, and (3) considers the friction factor as a function of the Reynolds number and pipe roughness. The fully implicit method representation of the equations offers the advantage of guaranteed stability for a large time step, which is very useful for gas pipeline industry. The results show that the effect of treating the gas in a nonisothermal manner is extremely necessary for pipeline flow calculation accuracies, especially for rapid transient process. It also indicates that the convective inertia term plays an important role in the gas flow analysis and cannot be neglected from the calculation.

Two-Phase Flow Analysis in Multi-Channel

2004 ◽  
Author(s):  
Man Yeong Ha ◽  
Cheol Hwan Kim ◽  
Yong Won Jung ◽  
Giho Jeong ◽  
Seong Geun Heo
Keyword(s):  
Two Phase Flow ◽  
Fluid Model ◽  
Flow Analysis ◽  
Flow Characteristics ◽  
Momentum Conservation ◽  
Present Calculation ◽  
Phase Flow ◽  
Two Phase ◽  
Volume Of Fluid Model ◽  
Volume Method

In the present study, we have carried out the experimental and numerical studies for the single- and two- phase flow characteristics and the corresponding pressure drop in the single- and multi-channels. We used the finite volume method to solve the mass and momentum conservation equations. The volume of fluid model is used to predict the two-phase flow in the channel. The calculated results for the single- and two-phase flow are partly compared with the present experimental data, showing relatively good agreement between them. The numerical scheme used in this study predicts well characteristics of single- and two-phase flow in a multi-channel. Thus we expect that system performances could be improved by obtaining the optimal conditions from the present calculation.

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