Accuracy of the Operator Splitting Technique for Two-Phase Flow With Stiff Source Terms

2002 ◽  
Author(s):  
Iztok Tiselj ◽  
Andrej Horvat
Keyword(s):  
Two Phase Flow ◽  
Fluid Model ◽  
Operator Splitting ◽  
Splitting Method ◽  
Water Hammer ◽  
Phase Flow ◽  
Hydraulic Systems ◽  
Source Terms ◽  
Two Phase ◽  
Splitting Technique

Code for analysis of the water hammer in thermal-hydraulic systems is being developed within the WAHALoads project founded by the European Commission [1]. Code will be specialized for the simulations of the two-phase water hammer phenomena with the two-fluid model of two-phase flow. The proposed numerical scheme is a two-step second-order accurate scheme with operator splitting; i.e. convection and sources are treated separately. Operator splitting technique is a very simple and “easy-to-use” tool, however, when the source terms are stiff, operator splitting method becomes a source of a specific non-accuracy, which behaves as a numerical diffusion. This type of error is analyzed in the present paper.

scholarly journals Natural modes of the two-fluid model of two-phase flow

2021 ◽  
Vol 33 (3) ◽  
pp. 033324
Author(s):  
Alejandro Clausse ◽  
Martín López de Bertodano
Keyword(s):  
Two Phase Flow ◽  
Fluid Model ◽  
Phase Flow ◽  
Two Phase ◽  
Natural Modes ◽  
Two Fluid Model ◽  
Two Fluid

Numerical Analysis of Two-Phase Pipe Flow of Liquid Helium Using Multi-Fluid Model

2001 ◽  
Vol 123 (4) ◽  
pp. 811-818 ◽  
Author(s):  
Jun Ishimoto ◽  
Mamoru Oike ◽  
Kenjiro Kamijo
Keyword(s):  
Phase Transition ◽  
Gas Phase ◽  
Liquid Helium ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Numerical Results ◽  
Phase Flow ◽  
Two Dimensional ◽  
Two Phase ◽  
Normal Fluid

The two-dimensional characteristics of the vapor-liquid two-phase flow of liquid helium in a pipe are numerically investigated to realize the further development and high performance of new cryogenic engineering applications. First, the governing equations of the two-phase flow of liquid helium based on the unsteady thermal nonequilibrium multi-fluid model are presented and several flow characteristics are numerically calculated, taking into account the effect of superfluidity. Based on the numerical results, the two-dimensional structure of the two-phase flow of liquid helium is shown in detail, and it is also found that the phase transition of the normal fluid to the superfluid and the generation of superfluid counterflow against normal fluid flow are conspicuous in the large gas phase volume fraction region where the liquid to gas phase change actively occurs. Furthermore, it is clarified that the mechanism of the He I to He II phase transition caused by the temperature decrease is due to the deprivation of latent heat for vaporization from the liquid phase. According to these theoretical results, the fundamental characteristics of the cryogenic two-phase flow are predicted. The numerical results obtained should contribute to the realization of advanced cryogenic industrial applications.

A Physically Based, One-Dimensional Two-Fluid Model for Direct Contact Condensation of Steam Jets Submerged in Subcooled Water

2015 ◽  
Vol 1 (2) ◽  
Author(s):  
David Heinze ◽  
Thomas Schulenberg ◽  
Lars Behnke
Keyword(s):  
Direct Contact ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Interfacial Area ◽  
Phase Flow ◽  
Two Phase ◽  
One Dimensional ◽  
Two Fluid Model ◽  
Contact Condensation ◽  
Two Fluid

A simulation model for the direct contact condensation of steam in subcooled water is presented that allows determination of major parameters of the process, such as the jet penetration length. Entrainment of water by the steam jet is modeled based on the Kelvin–Helmholtz and Rayleigh–Taylor instability theories. Primary atomization due to acceleration of interfacial waves and secondary atomization due to aerodynamic forces account for the initial size of entrained droplets. The resulting steam-water two-phase flow is simulated based on a one-dimensional two-fluid model. An interfacial area transport equation is used to track changes of the interfacial area density due to droplet entrainment and steam condensation. Interfacial heat and mass transfer rates during condensation are calculated using the two-resistance model. The resulting two-phase flow equations constitute a system of ordinary differential equations, which is solved by means of the explicit Runge–Kutta–Fehlberg algorithm. The simulation results are in good qualitative agreement with published experimental data over a wide range of pool temperatures and mass flow rates.

Eulerian Two-Phase Flow Modeling of Steam Direct Contact Condensation for the Fukushima Accident Investigation

2014 ◽  
Author(s):  
Marco Pellegrini ◽  
Giulia Agostinelli ◽  
Hidetoshi Okada ◽  
Masanori Naitoh
Keyword(s):  
Two Phase Flow ◽  
Volume Fraction ◽  
Fluid Model ◽  
Fluid Dynamic ◽  
Interfacial Region ◽  
Phase Flow ◽  
Two Phase ◽  
Fukushima Accident ◽  
Average Cell Size ◽  
Average Cell

Steam condensation is characterized by a relatively large interfacial region between gas and liquid which, in computational fluid dynamic (CFD) analyses, allows the creation of a discretized domain whose average cell size is larger than the interface itself. For this reason generally one fluid model with interface tracking (e.g. volume of fluid method, VOF) is employed for its solution in CFD, since the solution of the interface requires a reasonable amount of cells, reducing the modeling efforts. However, for some particular condensation applications, requiring the computation of long transients or the steam ejected through a large number of holes, one-fluid model becomes computationally too expensive for providing engineering information, and a two-fluid model (i.e. Eulerian two-phase flow) is preferable. Eulerian two-phase flow requires the introduction of closure terms representing the interactions between the two fluids in particular, in the condensation case, drag and heat transfer. Both terms involve the description of the interaction area whose definition is different from the typical one adopted in the boiling analyses. In the present work a simple but effective formulation for the interaction area is given based on the volume fraction gradient and then applied to a validation test case of steam bubbling in various subcooling conditions. It has been shown that this method gives realistic values of bubble detachment time, bubble penetration for the cases of interest in the nuclear application and in the particular application to the Fukushima Daiichi accident.

Analysis of Flow-Induced Vibration Due to Stratified Wavy Two-Phase Flow

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
Shuichiro Miwa ◽  
Takashi Hibiki ◽  
Michitsugu Mori
Keyword(s):  
Two Phase Flow ◽  
Dynamic Properties ◽  
Fluid Model ◽  
Dominant Frequency ◽  
Phase Flow ◽  
Flow Induced Vibration ◽  
Two Phase ◽  
Pipe Bend ◽  
Experimental Database ◽  
Force Fluctuation

Fluctuating force induced by horizontal gas–liquid two-phase flow on 90 deg pipe bend at atmospheric pressure condition is considered. Analysis was conducted to develop a model which is capable of predicting the peak force fluctuation frequency and magnitudes, particularly at the stratified wavy two-phase flow regime. The proposed model was developed from the local instantaneous two-fluid model, and adopting guided acoustic theory and dynamic properties of one-dimensional (1D) waves to consider the collisional force due to the interaction between dynamic waves and structure. Comparing the developed model with experimental database, it was found that the main contribution of the force fluctuation due to stratified wavy flow is from the momentum and pressure fluctuations, and collisional effects. The collisional effect is due to the fluid–solid interaction of dynamic wave, which is named as the wave collision force. Newly developed model is capable of predicting the force fluctuations and dominant frequency range with satisfactory accuracy for the flow induced vibration (FIV) caused by stratified wavy two-phase flow in 52.5 mm inner diameter (ID) pipe bend.

Viscous Two-Phase Flow in Porous Media Driven by Source Terms: Analysis and Numerics

2019 ◽  
Vol 51 (6) ◽  
pp. 5103-5140 ◽  
Author(s):  
Yangyang Qiao ◽  
Huanyao Wen ◽  
Steinar Evje
Keyword(s):  
Porous Media ◽  
Two Phase Flow ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Source Terms ◽  
Two Phase
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