Development of Conservative Form of RELAP5 Thermal Hydraulic Equations: Part II — Numerical Approach and Code Results

2014 ◽  
Author(s):  
Zheng Fu ◽  
Fatih Aydogan ◽  
Richard J. Wagner
Keyword(s):  
Numerical Approach ◽  
Phase System ◽  
Current Version ◽  
Two Phase ◽  
Pressurized Water ◽  
Conservation Equations ◽  
Two Fluids ◽  
Conservative Form ◽  
Energy And Momentum ◽  
Single Pipe

One of the principle features of RELAP5-based system thermal hydraulic codes is the use of a two-fluid, non-equilibrium, non-homogeneous, hydrodynamic model for the transient simulation of the two-phase system behavior. This model includes six governing equations to describe the mass, energy, and momentum of the two fluids. The current version of RELAP-5 uses non-conservative numerical approximation form of conservation equations. The current version of RELAP5 versions have mass and energy errors during time advancements, either resulting in (a) automatic reduction of time steps used in the advancement of the equations and increased run times or (b) the growth of unacceptably large errors in the transient results. Therefore, conservative conservation equations and closure equations were developed to address this problem in the first part of the paper series This part of the series demonstrates the numerical approach to implement the developed conservative conservation equations into RELAP5 and the results of RELAP5 including developed conservative form of conservation equations. RELAP5 versions including conservative and non-conservative conservation equations are compared for various tests from a single pipe to a whole Pressurized Water Reactor (PWR) model.

Development of Conservative Form of RELAP5 Thermal Hydraulic Equations: Part I — Theory

2014 ◽  
Author(s):  
Zheng Fu ◽  
Fatih Aydogan ◽  
Richard J. Wagner
Keyword(s):  
Nuclear Power ◽  
Power Plants ◽  
Numerical Approximation ◽  
Numerical Approach ◽  
Phase System ◽  
Hydraulic Systems ◽  
Governing Equations ◽  
Two Phase ◽  
Current Form ◽  
Two Fluids

The design and analysis of the thermal/hydraulic systems of nuclear power plants necessitates system codes that can be used in the analysis of steady state and transient conditions. RELAP5 is one of the most commonly used system codes in nuclear organizations. RELAP5 is based on a two-fluid, non-equilibrium, non-homogeneous, hydrodynamic model for the transient simulation of the two-phase system behavior. This model includes six governing equations to describe the mass, energy, and momentum of the two fluids. The “non-conservative” numerical approximation form (which is the current form of RELAP5 code versions) is obtained through the manipulation of selected derivative terms in the equations including the linearization of the product terms in the time derivatives of the equations. For non-conservative technique, the truncation errors introduced in the linearization process can produce mass and energy errors for some classes of transients during time advancements, either resulting in (a) automatic reduction of time steps used in the advancement of the equations and increased run times or (b) the growth of unacceptably large errors in the transient results. To eliminate these difficulties, a new, optional numerical approach has been introduced in RELAP/SCDAPSIM/MOD4.0. This new option uses a more consistent set of the “conservative” numerical approximation to solve non-linearized mass and energy governing equations. The RELAP/SCDAPSIM/MOD4.0 code, being developed as part of the international SCDAP (Severe Core Damage Analysis Package) Development and Training Program (SDTP), is the first version of RELAP5 completely rewritten to FORTRAN 90/95/2000 standards. This paper provides an overview of the original RELAP5 numerical approximations and describes the new theoretical approach. Then the second article introduces the solution strategy of conservative approach and presents some examples of transient problems that have been run using this new approach.

scholarly journals Frozen wave simulation by the lattice Boltzmann method

2021 ◽  
pp. 59-68
Author(s):  
I. V. Volodin ◽  
◽  
A. A. Alabuzhev ◽  
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Wave Number ◽  
Phase System ◽  
Layer System ◽  
Two Phase ◽  
Immiscible Liquids ◽  
Two Fluids ◽  
Linear Vibrations ◽  
Boltzmann Method

The dynamics of two-layer system of immiscible liquids under the action of horizontal linear vibrations in the field of gravity was investigated. The numerical simulation was carried out by the lattice Boltzmann method (LBM) with model D2Q9. For the first time LBM was used to achieve the appearance of frozen wave (quasi-stationary relief) at the interface of two fluids. There are two types of boundary conditions for the sidewalls: a periodic condition for comparison with analytical results and no-slip condition for comparison with experiments. Various computational domains were considered. Both cases with the same viscosities of both phases and different viscosity ratios were studied. HCZ model was used to describe two-phase system and the interface of two liquids. The presence of a frozen wave on the interface of liquids was found. The dependence of liquids viscosity on the relief was studied. The obtained critical wave number coincides well with the theoretically predicted value for liquids with the equal viscosity and vanishing viscosity. The results of numerical calculations show a weak viscosity effect for a more viscous lower liquid. However, the destabilizing effect of viscosity is more significant for a more viscous upper liquid.

On the Problem of “Two-Phase” Activated Sludge

1991 ◽  
Vol 24 (7) ◽  
pp. 59-64 ◽  
Author(s):  
R. W. Szetela
Keyword(s):  
Activated Sludge ◽  
Single Phase ◽  
Phase System ◽  
Two Phase ◽  
Wastewater Treatment Process ◽  
Sludge Stabilization ◽  
Technological Advantage ◽  
In Series ◽  
State Models ◽  
Activated Sludge Systems

Steady-state models are presented to describe the wastewater treatment process in two activated sludge systems. One of these makes use of a single complete-mix reactor; the other one involves two complete-mix reactors arranged in series. The in-series system is equivalent to what is known as the “two-phase” activated sludge, a concept which is now being launched throughout Poland in conjunction with the PROMLECZ technology under implementation. Analysis of the mathematical models has revealed the following: (1) treatment efficiency, excess sludge production, energy consumption, and the degree of sludge stabilization are identical in the two systems; (2) there exists a technological equivalence of “two-phase” sludge with “single-phase” sludge; (3) the “two-phase” system has no technological advantage over the “single-phase” system.

Interphase distribution of 2-furylethylenes

1985 ◽  
Vol 50 (8) ◽  
pp. 1642-1647 ◽  
Author(s):  
Štefan Baláž ◽  
Anton Kuchár ◽  
Ernest Šturdík ◽  
Michal Rosenberg ◽  
Ladislav Štibrányi ◽  
...  
Keyword(s):  
Partition Coefficient ◽  
Partition Coefficients ◽  
Transport Rate ◽  
Phase System ◽  
Two Phase ◽  
Interphase Distribution ◽  
Distribution Kinetics ◽  
System 1 ◽  
Kinetics Of

The distribution kinetics of 35 2-furylethylene derivatives in two-phase system 1-octanol-water was investigated. The transport rate parameters in direction water-1-octanol (l1) and backwards (l2) are partition coefficient P = l1/l2 dependent according to equations l1 = logP - log(βP + 1) + const., l2 = -log(βP + 1) + const., const. = -5.600, β = 0.261. Importance of this finding for assesment of distribution of compounds under investigation in biosystems and also the suitability of the presented method for determination of partition coefficients are discussed.

Enhancing the Sensitivity of DNA and Aptamer Probes in the Dextran/PEG Aqueous Two-Phase System

2021 ◽  
Author(s):  
Qiaoshu Chen ◽  
Yanwen Zhang ◽  
Hui Chen ◽  
Jianbo Liu ◽  
Juewen Liu
Keyword(s):  
Phase System ◽  
Two Phase ◽  
Aqueous Two Phase System

Development of an ethanolic two-phase system (ETPS) based on polypropylene glycol 2000 + ethylene glycol + ethanol for separation of hydrophobic compounds

2021 ◽  
Author(s):  
Filipe Smith Buarque ◽  
Cleide Mara Faria Soares ◽  
Ranyere Lucena de Souza ◽  
Matheus Mendonça Pereira ◽  
Álvaro Silva Lima
Keyword(s):  
Ethylene Glycol ◽  
Phase System ◽  
Polypropylene Glycol ◽  
Two Phase ◽  
Hydrophobic Compounds ◽  
Ethanol Content ◽  
Coexisting Phases ◽  
Phase Water ◽  
High Ethanol

Two-phase water-free systems containing high ethanol content in the coexisting phases can selectively partition hydrophobic molecules from natural biomass.

Continuous Purification of an Enveloped and Non-enveloped Viral Particle Using an Aqueous Two-Phase System

2021 ◽  
pp. 118753
Author(s):  
Dylan G. Turpeinen ◽  
Pratik U. Joshi ◽  
Seth A. Kriz ◽  
Supreet Kaur ◽  
Natalie M. Nold ◽  
...  
Keyword(s):  
Viral Particle ◽  
Phase System ◽  
Two Phase ◽  
Aqueous Two Phase System
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