Four-equation Drift-flux Model Research Articles

Implementation of a Drift Flux Model into SAM with Development of a Verification and Validation Test Suite for Modeling of Noncondensable Gas Mixtures

The advanced thermal-hydraulic system code, System Analysis Module (SAM), was originally developed for the modeling of single-phase flow in advanced reactors. It has since been expanded to include a four-equation drift flux model for the modeling of two-phase flows containing a noncondensable gas. The model was expanded to support the modeling of molten salt reactor (MSR) designs in which the fuel is directly dissolved in the circulating coolant. These designs have shown that circulating gas bubbles can play an important role in the management of fission products and the operational behavior of the reactor. A drift flux model was implemented to more accurately capture the localized behavior of the void in the core and its impact on the mass transfer of fission products. A thorough assessment of the new model was performed by developing a verification and validation test suite. Verification problems were designed to test all major terms in the new governing equations. The new model converged to the correct solution at the expected order of accuracy for all verification cases. The validation cases included a wide range of flow and void conditions in different pipe geometries. Although higher void experiments show a slight underprediction of void by the drift flux model, experiments that aim to reproduce Molten Salt Reactor Experiment (MSRE) experimental conditions show good agreement with the model. The gas transport model was activated for a SAM model of the MSRE to demonstrate that it can be used in a more complex model. This gas transport model will be used along with an interfacial area transport equation being implemented in SAM for the prediction of mass transport behavior in MSR conditions.

Numerical simulation of bubble dynamics in subcooled flow boiling in a channel

In this article, we report bubble dynamics in a subcooled flow boiling in a vertical boiling channel based on numerical simulation using four-equation drift flux model (DFM4). The focus of this work is to validate the bubble phenomena computed by DFM4 in high inlet subcooling, low heat fluxes and low flow rates. The computed bubble parameters such as bubble growth time tg, bubble waiting time tw, bubble departure diameter Dd based on the available correlations were compared with the experimental results obtained from our boiling loop. We also propose an analytical solution for tg and Dd from the asymptotic growth kinetics and the force balance at the time of bubble departure. We have explained some important insights of the axial variation of bubble phenomena under varying heat flux. Unal correlation for bubble departure works extremely well to a highly subcooled boiling in low heat fluxes and low flows.

High-order fully implicit SIMPLE-based model for fully implicit simulation of upward two-phase flow

The drift-flux model has a practical importance in two-phase flow analysis. In this study, a finite volume solution is developed for a transient four-equation drift-flux model through the staggered mesh, leading to the development of a fully implicit discretization method. The main advantage of the fully implicit method is its unconditional stability. Newton’s scheme is a popular method of choice for the solution of a nonlinear system of equations arising from fully implicit discretization of field equations. However, the lack of convergence robustness and the construction of Jacobian matrix have created several difficulties for the researchers. In this paper, a fully implicit model is developed based on the SIMPLE algorithm for two-phase flow simulations. The drawbacks of Newton’s method are avoided in the developed model. Different limiter functions are considered, and the stabilized method is developed under steady and transient conditions. The results obtained by the numerical modeling are in good agreement with the experimental data. As expected, the results prove that the developed model is not restricted by any stability limit.

A numerical investigation on heat transfer dynamics of a periodically forced boiling channel in low amplitudes

In this article, the authors report wall-heat transfer characteristics of a periodically forced vertical boiling channel with the help of numerical simulation based on four-equation drift flux model. The periodic forcing on the boiling channel was initiated by the sinusoidal perturbation of the inlet velocity. The effect of the frequency ω and the amplitude ã of the forcing on the heat transfer enhancement were studied to formulate a mechanism for the enhancement of wall heat flux qw″. qw″ increases with ã in the range of ω less than a critical value ωcrit. The comparison of the numerical solution and the asymptotic solution of a reduced-order model through harmonic balance method (HBM) shows that both the solutions for the amplitude of exit mixture enthalpy decrease with ω consistently and asymptotically, when ω is greater than the characteristic frequency ωc of the channel. The enhancement is also facilitated by chaotic instability (mixing) at higher ã and higher external heat flux.

Numerical studies of a helical coil once-through steam generator

A Thermal Hydraulic analysis code for Helical Coil once-through Steam Generator (TH-HCSG) is developed in the present study in order to predict the heat transfer process and thermal hydraulic characteristics in vertical helical coil steam generators. The numerical model is programmed using a one-dimensional four-equation drift-flux model and evaluated according to the data on HCSG published by the International Reactor Innovative and Secure (IRIS). The results achieved under full load conditions are, then, compared with the RELAP5 codes, with the results of this comparison showing that this model is both correct and reliable and can be used to investigate the instantaneous characteristics of helical coil steam generators. This model is also used to evaluate the influence of the main representative HCSG boundary parameters on HCSG operation characteristics. It was subsequently found that, when there was a ±10% step change in the boundary parameters, the length of the single-phase water region in the secondary side of the HCSG changed considerably, so that the steam flow oscillated obviously, lagging the feedwater flow at an early stage and rapidly reaching a steady state as the water capacity of the secondary side of the HCSG was changed.

Simulation of protected and unprotected loss of flow transients in a WWER-1000 reactor based on the Drift-Flux Model

Abstract In view of the importance of studying coolant transient behavior in a nuclear reactor, this work is devoted to the thermal-hydraulic analysis of protected and unprotected loss of flow transients in a WWER-1000 reactor. A series of corresponding mathematical and physical models based on the four-equation Drift-Flux model has been applied. Based on a multi-channel approach, the core has been divided into different regions. Each region has different characteristics as represented in a single fuel pin with its associated coolant channel. Appropriate initial and boundary conditions have been considered and two situations of tripping four and two primary pumps in a protected core in addition to situation of tripping all four pumps in an unprotected core have been analyzed. For each transient, a full range of thermal-hydraulic parameters has been obtained. For verification of the proposed model, the results have been compared with those of the RELAP5/MOD3 and Bushehr nuclear power plant Final Safety Analysis Report (FSAR). A good agreement between results has been attained for the aforementioned transients.

Simulation and analysis of a WWER-1000 reactor under normal and transient conditions

An accurate analysis of the flow transient is very important in safety evaluation of a nuclear power plant. In this study, analysis of a WWER-1000 reactor is investigated. In order to perform this analysis, a model is developed to simulate the coupled kinetics and thermal-hydraulics of the reactor with a simple and accurate numerical algorithm. For thermal-hydraulic calculations, the four-equation drift-flux model is applied. Based on a multi-channel approach, core is divided into some regions. Each region has different characteristics as represented in a single fuel pin with its associated coolant channel. To obtain the core power distribution, point kinetic equations with different feedback effects are utilized. The appropriate initial and boundary conditions are considered and two situations of decreasing the coolant flow rate in a protected and unprotected core are analyzed. In addition to analysis of normal operation condition, a full range of thermal-hydraulic parameters is obtained for transients too. Finally, the data obtained from the model are compared with the calculations conducted using RELAP5/MOD3 code and Bushehr nuclear power plant data. It is shown that the model can provide accurate predictions for both steady-state and transient conditions.

Numerical implementation, verification and validation of two-phase flow four-equation drift flux model with Jacobian-free Newton–Krylov method

This paper presents a numerical investigation on using the Jacobian-free Newton–Krylov (JFNK) method to solve the two-phase flow four-equation drift flux model with realistic constitutive correlations (‘closure models’). The drift flux model is based on Isshi and his collaborators’ work. Additional constitutive correlations for vertical channel flow, such as two-phase flow pressure drop, flow regime map, wall boiling and interfacial heat transfer models, were taken from the RELAP5-3D Code Manual and included to complete the model. The staggered grid finite volume method and fully implicit backward Euler method was used for the spatial discretization and time integration schemes, respectively. The Jacobian-free Newton–Krylov method shows no difficulty in solving the two-phase flow drift flux model with a discrete flow regime map. In addition to the Jacobian-free approach, the preconditioning matrix is obtained by using the default finite differencing method provided in the PETSc package, and consequently the labor-intensive implementation of complex analytical Jacobian matrix is avoided. Extensive and successful numerical verification and validation have been performed to prove the correct implementation of the models and methods. Code-to-code comparison with RELAP5-3D has further demonstrated the successful implementation of the drift flux model.

Assessment of TAPINS code for application to thermal-hydraulic analysis of an integral reactor, REX-10

The thermal-hydraulic analysis program for integral reactor system (TAPINS) is a thermal-hydraulic system code developed by Seoul National University for transient analysis of an integral reactor, REX-10. Specialized for a fully passive integral pressurized water reactor, TAPINS adopts a one-dimensional four-equation drift-flux model for two-phase flows. It also consists of component models for the core, the helical-coil steam generator, and the steam-gas pressurizer. This paper presents the developmental assessment of TAPINS to validate its applicability to the thermal-hydraulic analysis of REX-10. Assessment problems are determined by taking into account thermal-hydraulic phenomena expected during design basis accidents of REX-10, including the loss-of-feedwater accident and the small-break loss-of-coolant accident. To confirm the predictive capability of TAPINS for these phenomena, the TAPINS model is validated against four sets of separate effects problems, including the pressurizer insurge test, the subcooled boiling experiment, the critical flow test, and the Edwards pipe problem. In addition, the calculation results of TAPINS are compared with the experimental data obtained from a series of integral effects tests using a scaled apparatus of REX-10. From the validation results, it is demonstrated that TAPINS can provide the reasonable prediction on the thermal-hydraulic responses of REX-10 during the transient and accident conditions.

TAPINS: A THERMAL-HYDRAULIC SYSTEM CODE FOR TRANSIENT ANALYSIS OF A FULLY-PASSIVE INTEGRAL PWR

REX-10 is a fully-passive small modular reactor in which the coolant flow is driven by natural circulation, the RCS is pressurized by a steam-gas pressurizer, and the decay heat is removed by the PRHRS. To confirm design decisions and analyze the transient responses of an integral PWR such as REX-10, a thermal-hydraulic system code named TAPINS (Thermal-hydraulic Analysis Program for INtegral reactor System) is developed in this study. Based on a one-dimensional four-equation drift-flux model, TAPINS incorporates mathematical models for the core, the helical-coil steam generator, and the steam-gas pressurizer. The system of difference equations derived from the semi-implicit finite-difference scheme is numerically solved by the Newton Block Gauss Seidel (NBGS) method. TAPINS is characterized by applicability to transients with non-equilibrium effects, better prediction of the transient behavior of a pressurizer containing non-condensable gas, and code assessment by using the experimental data from the autonomous integral effect tests in the RTF (REX-10 Test Facility). Details on the hydrodynamic models as well as a part of validation results that reveal the features of TAPINS are presented in this paper.

Study on the stability behaviour of two-phase natural circulation systems using a four-equation drift flux model

Theoretical investigations were carried out to study the influence of two-phase flow parameters such as friction factor multiplier, drift velocity and void distribution parameter on the stability of boiling two-phase natural circulation systems. The theoretical model considers a four-equation drift flux model which solves the linearised conservation equations of mass, momentum and energy applicable to boiling two-phase natural circulation systems. The model was applied to three boiling natural circulation loops wherein Type I and Type II instabilities were observed over a wide range of operating pressures. The two-phase friction loss was predicted using different friction factor multiplier models available in literature. It was found that these models influence the steady state and threshold powers for stability, especially the Type II instabilities in natural circulation significantly. Since the void fraction depends on the drift velocity and the void distribution parameter in two-phase flow, these parameters were varied and their effects on the natural circulation flow stability were investigated. It was found that an increase in either the drift velocity or the void distribution parameter reduces the unstable regions observed in the Type I or Type II flow instabilities in two-phase natural circulation systems. Further, investigations were carried out to study the effect of loop diameter on the Type I and Type II instabilities in natural circulation. This study is important to reveal the capability of the reduced diameter scaled facilities of the prototype systems to simulate natural circulation instabilities. The results indicate that with increase in the loop diameter, the threshold power of the Type I instability and the Type II instability increases. Moreover, the stability of natural circulation greatly enhances with increase in the diameter of the loop.

A study of forced convective subcooled boiling in heated annular channels

A method is presented for the calculation of inception and subsequent development of forced convective subcooled boiling in heated annular channels at steadystate conditions. Criteria for onset of nucleate boiling and significant net vapor generation are incorporated into the formulation which is a synthesis of single-phase liquid thermal entrance region temperature field calculations and a four-equation drift-flux model representation of the liquid-vapor mixture region. Calculated vapor volume fraction values are compared with new measurements obtained with Refrigerant-113 as the working fluid, and literature data for steam-water.