Modeling of low-pressure subcooled boiling flow of water via the homogeneous MUSIG approach

Applying a three-dimensional two-fluid model coupled with homogeneous multiple size group (MUSIG) approach, numerical simulations of upward subcooled boiling flow of water at low pressure were performed on the computational fluid dynamics (CFD) code CFX-10 with user defined FORTRAN program. A modified bubble departure diameter correlation based on the Unal's semi-mechanistic model and the empirical correlation of Tolubinski and Kostanchuk was developed. The water boiling flow experiments at low pressure in a vertical concentric annulus from reference were used to validate the models. Moreover, the influences of the non-drag force on the radial void fraction distribution were investigated, including lift force, turbulent dispersion force and wall lubrication force. Good quantitative agreement with the experimental data is obtained, including the local distribution of bubble diameter, void fraction, and axial liquid velocity. The results indicate that the local bubble diameter first increases and then decreases due to the effect of bubble breakup and coalescence, and has the maximum bubble diameter along the radial direction. Especially, the peak void fraction phenomenon in the vicinity of the heated wall is predicted at low pressure, which is developed from the wall repulsive force between vapor bubbles and heated wall. Nevertheless, there is a high discrepancy for the prediction of the local axial vapor velocity.     

Improvement of the subcooled boiling model for low-pressure conditions in thermal-hydraulic codes

The functioning of the subcooled boiling model adopted in a thermal-hydraulic computer program has been investigated in detail, for low-pressure conditions, and necessary refinements have been incorporated into the code. The investigation has been carried out in two stages; in the first stage, the performance of the interfacial heat transfer/condensation is studied. Necessary refinements to the vertical flow map for the transition from bubbly to slug flow regimes and the interpolation with the ‘umbrella’ limitation that bounded the interfacial heat transfer values are carried out. Simulations of low-pressure subcooled boiling experiments were performed with the refined code version and a reasonable agreement with the experimental void fraction data was obtained. In addition, a high-pressure experiment was also simulated with the refined code version to check if these revisions do not affect the code performance at high pressures. No significant adverse effects were observed. In the second stage of the study, the performance of the wall heat flux partitioning model adapted in the code was investigated. In particular, the effectiveness of the ‘pumping factor’ formulation in the above model and its functioning at low-pressure conditions was investigated. Different ‘pumping factor’ formulations available in the literature were implemented into the code. Simulations of low-pressure subcooled boiling experiments were performed with the refined code version and the appropriate ‘pumping factors’ to be used for low-pressure conditions were determined.     

Interfacial area measurements in subcooled flow boiling

The purpose of the present study was to measure two-phase parameters in subcooled flow boiling. These parameters include void fraction distribution, interfacial area concentration distribution, Sauter mean diameter, and the interfacial velocity. A literature review was conducted and the results show that only three researchers have made local measurements in the subcooled boiling region. None of the previous have included results for interfacial area concentration distribution. To make these measurements an experimental facility was constructed that allows insertion of advanced local two-phase flow instrumentation. Experiments were performed for a number of conditions at atmospheric pressure.     

Vapour void fraction in subcooled flow boiling

Experimental data on steam void fraction and axial temperature distribution in an annular boiling channel for low mass-flux forced and natural circulation flow of water with inlet subcooling have been obtained. The ranges of variables covered are: mass flux = 1.4 × 10⁴−1.0 × 10⁵ kg/hr m²; heat flux = 4.5 × 10³−7.5 × 10⁴ kcal/hr m²; and inlet subcooling = 10–70°C. The present and literature data match well with the theoretical void predictions using a four-step method similar to that suggested by Zuber and co-workers.     

Analysis of the Peach Bottom flow stability test number 3 using the coupled RELAP5/PARCS code

Nowadays, the coupled codes technique, which consists in incorporating three-dimensional (3D) neutron modeling of the reactor core into system codes, is extensively used for carrying out best estimate (BE) simulation of complex transient in nuclear power plants (NPP). This technique is particularly suitable for transients that involve core spatial asymmetric phenomena and strong feedback effects between core neutronics and reactor loop thermal-hydraulics. Such complex interactions are encountered under normal and abnormal operating conditions of a boiling water reactors (BWR). In such reactors Oscillations may take place owing to the dynamic behavior of the liquid-steam mixture used for removing the thermal power. Therefore, it is necessary to be able to detect in a reliable way these oscillations. The purpose of this work is to characterize one aspect of these unstable behaviors using the coupled codes technique. The evaluation is performed against Peach Bottom-2 low-flow stability tests number 3 using the coupled RELAP5/PARCS code. In this transient dynamically complex neutron kinetics coupling with thermal-hydraulics events take place in response to a core pressure perturbation. The calculated coupled code results are herein assessed and compared against the available experimental data.     

Prediction of the onset of flow instability in transient subcooled flow boiling

A new model to predict the onset of flow instability (OFI) in transient subcooled flow boiling has been developed. The model is based upon the influence on vapor bubble departure of the single-phase temperature profile. The steady-state result of the present model was compared to the experimental data of Whittle and Forgan [1] and Dougherty et al. [2], showing an excellent agreement. The model was then employed in a transient analysis of OFI for vertical downwards turbulent flow to predict whether OFI takes place. The condition for OFI to occur in transient flow situations was also predicted by this model. Two modes for pressure gradient change inside the channel are considered in the present study: step change and ramp change. The calculations were made for various combinations of the flow operating condition and the mode of pressure drop change.     

Experimental study of onset of subcooled annular flow boiling

An experimental study on the onset of nucleate boiling (ONB) is performed for water annular flow to provide a systematic database for low pressure and velocity conditions. A parametric study has been conducted to investigate the effect of pressure, inlet subcooling, heat and mass flux on flow boiling. The test section includes a Pyrex tube with 21 mm inner diameter and a stainless steel (SS-304) rod with outer diameter of 6 mm. Pressure, heat and mass flux are in the range of 1.73 < P < 3.82 bar, 40 < q < 450 kW/m² and 70 < G < 620 kg/m² s, respectively. The results illustrate that inception heat flux is extremely dependent on pressure, inlet subcooling temperature and mass flux; for example in pressure, velocity and inlet subcooling as 3.27 bar, 230 kg/m² s and 41.3 °C; consequently q_w,ONB is 177.3 kW/m². In other case with higher inlet temperature of 71.5 °C and with P, 3.13 bar and G, 232 kg/m² s the inception heat flux reached to 101.6 kW/m². The data of ONB heat flux are over estimated from the existing correlation, and maximum deviation of wall superheat (ΔT_w,ONB) from correlations is 30%. Experimental data of inception heat flux are within 22% of that predicted from the correlation.     

Void fraction distribution in low flow rate subcooled boiling

Experimental data are presented for the void fraction distribution in low flow rate forced convection subcooled boiling of water in a heated vertical tube at steady-state conditions. The measurements are based on gamma attenuation and X-ray radiography techniques. The measured local equilibrium quality at the point of net vapor generation and the void fraction profiles are compared with theoretical and empirical models of subcooled boiling. A close fit to the experimental results is obtained by the Levy model and by the Saha and Zuber correlation.     

Vapour bubble growth and recondensation in subcooled boiling flow

A physical model for the dynamics of vapour bubbles is presented, which is applicable to bubbles generated at the heated wall of channels with boiling flow. By comparing the theory with experimental data from various sources, it is shown that simultaneous agreement can be obtained with regard to bubble size, bubble lifetime and recondensation rate within the error band of experimental data by the proper choice of one fitting parameter only. The proposed model is then compared with some previously published approaches. Correlations for the dependence of bubble lifetime and bubble size on local fluid conditions are derived which are suitable for the prediction of vapour contents in heated channels with subcooled inlet flow.     

Multi-component diffusion analysis and assessment of GAMMA code and improved RELAP5 code

A loss-of-coolant accident (LOCA) has been considered a critical event for very high temperature gas-cooled reactor (VHTR). Following helium depressurization, it is anticipated that unless countermeasures are taken, air will enter the core through the break by molecular diffusion and ultimately by natural convection leading to oxidation of the in-core graphite structure. Thus, without any mitigating features, a LOCA will lead to an air ingress event, which will lead to exothermic chemical reactions of graphite with oxygen, potentially resulting in significant increases of the core temperature.New and safer nuclear reactors (Generation IV) are now in the early planning stages in many countries throughout the world. One of the reactor concepts being seriously considered is the VHTR. To achieve public acceptance, these reactor concepts must show an increased level of inherent safety over current reactor designs (i.e., a system must be designed to eliminate any concerns of large radiological releases outside the site boundary).A computer code developed from this study, gas multi-component mixture analysis (GAMMA) code, was assessed using a two-bulb experiment and in addition the molecular diffusion behavior in the prismatic-core gas-cooled reactor was investigated following the guillotine break of the main pipe between the reactor vessel and the power conversion unit. The RELAP5 code was improved for the VHTR air ingress analysis and was assessed using inverse U-tube and NACOK natural circulation data.     

Semi 2D modeling of the horizontal steam generator PGV-1000 using the RELAP5 code

Developing a reliable thermal-hydraulic model of the steam generator is an essential process in the steady state and transient analysis for the Pressurized Water Reactor type of the Nuclear Power Plants. This paper provides a semi two dimensional thermal-hydraulic model of the PGV-1000 horizontal steam generator using the RELAP5 code. Applying the qualified nodalization and the cross-flow effects are some of the advantages in the present model. The obtained results from the RELAP5 steady state analysis showed a reasonable agreement with the Bushehr NPP Final Safety Analysis Reports (FSAR).     

Analysis of the VVER1000 coolant trip benchmark using the coupled RELAP5/PARCS code

Incorporation of full three-dimensional models of the reactor core into system thermal–hydraulic transient codes allows better estimation of interactions between the core behavior and plant dynamics. Considerable efforts have been made in various countries and organizations to verify and validate the capability of the so-called coupled codes technique. For these purposes appropriate Light Water Reactor (LWR) transient benchmarks based upon programmed transients performed in Nuclear Power Plants (NPP) were recently developed on a higher ‘best-estimate’ level. The reference problem considered in the current framework is a Main Coolant Pump (MCP) switching-on transient in a VVER1000 NPP. This event is characterized by a positive reactivity addition as consequence of the increase of the core flow. In the current study the coupled RELAP5/PARCS code is used to reproduce the considered test. Results of calculation were assessed against experimental data and also through the code-to-code comparison.     

Thermal hydraulic analysis of Syrian MNSR research reactor using RELAP5/Mod3.2 code

This paper presents the development and validation of a MNSR-RELAP5 model. MNSR is a 30 kW, light-water moderated and cooled, beryllium-reflected, tank in pool type research reactor. A RELAP5 model was set up to simulate the entire MNSR system. The model represents all reactor components of primary and secondary loops with the corresponding neutronic and thermal hydraulic characteristics. Under the MNSR operation conditions of natural circulation, normal operation, step reactivity transients and reactivity insertion accidents are simulated.     

Analysis of the hot gas flow in the outlet plenum of the very high temperature reactor using coupled RELAP5-3D system code and a CFD code

The very high temperature reactor (VHTR) system behavior should be predicted during normal operating conditions and postulated accident conditions. The plant accident scenario and the passive safety behavior should be accurately predicted. Uncertainties in passive safety behavior could have large effects on the resulting system characteristics. Due to these performance issues in the VHTR, there is a need for development, testing and validation of design tools to demonstrate the feasibility of the design concepts and guide the improvement of the plant components. One of the identified design issues for the gas-cooled reactor is the thermal mixing of the coolant exiting the core into the outlet plenum. Incomplete thermal mixing may give rise to thermal stresses in the downstream components. To provide flow details, the analysis presented in this paper was performed by coupling a VHTR model generated in a thermal hydraulic systems code to a computational fluid dynamics (CFD) outlet plenum model. The outlet conditions obtained from the systems code VHTR model provide the inlet boundary conditions to the CFD outlet plenum model. By coupling the two codes in this manner, the important three-dimensional flow effects in the outlet plenum are well modeled while avoiding modeling the entire reactor with a computationally expensive CFD code. The values of pressure, mass flow rate and temperature across the coupled boundary showed differences of less than 5% in every location except for one channel. The coupling auxiliary program used in this analysis can be applied to many different cases requiring detailed three-dimensional modeling in a small portion of the domain.     

Two-phase flow regimes and mechanisms of critical heat flux under subcooled flow boiling conditions

A literature review of critical heat flux (CHF) experimental visualizations under subcooled flow boiling conditions was performed and systematically analyzed. Three major types of CHF flow regimes were identified (bubbly, vapor clot and slug flow regime) and a CHF flow regime map was developed, based on a dimensional analysis of the phenomena and available experimental information. It was found that for similar geometric characteristics and pressure, a Weber number (We)/thermodynamic quality (x) map can be used to predict the CHF flow regime.Based on the experimental observations and the review of the available CHF mechanistic models under subcooled flow boiling conditions, hypothetical CHF mechanisms were selected for each CHF flow regime, all based on a concept of wall dry spot overheating, rewetting prevention and subsequent dry spot spreading. Even though the selected concept has not received much attention (in term or theoretical developments and applications) as compared to other more popular DNB models, its basis have often been cited by experimental investigators and is considered by the authors as the “most-likely” mechanism based on the literature review and analysis performed in this work. The selected modeling concept has the potential to span the CHF conditions from highly subcooled bubbly flow to early stage of annular flow and has been numerically implemented and validated in bubbly flow and coupled with one- and three-dimensional (CFD) two-phase flow codes, in a companion paper. [Le Corre, J.M., Yao, S.C., Amon, C.H., in this issue. A mechanistic model of critical heat flux under subcooled flow boiling conditions for application to one and three-dimensional computer codes. Nucl. Eng. Des.].     

Numerical simulation of bubble behaviors in subcooled flow boiling under swing motion

A numerical investigation of bubble behaviors in subcooled flow boiling of water under the effect of additional inertial forces has been performed considering energy and mass transfer during phase change based on the VOF (volume-of-fluid) method. The pressure ranges from 0.1 to 1.0 MPa, and heat flux from 200 to 500 kW/m². The mass flow rate and inlet subcooling are specified at 320 kg/m² s and 10 K, respectively. The liquid-vapor interface is captured using the piecewise linearity interpolation calculation (PLIC) geometry restructuring method. The simulations are carried out on upward water flow in a vertical, rectangular duct with single side heating surface. The pressure, velocity vector and temperature distribution around two isolated bubbles are studied firstly. The behaviors of bubble coalescence, sliding, detachment from the heated wall, and the bubble shape variation during lifetime are further examined. The bubble behaviors in the different pressure and heat flux are investigated. The simulated results of bubble growth rate and wall temperature are agreed well with the correlations in the literatures. The additional inertial forces caused by swing are negligible, but the fluctuation of mass flow rate caused by swing motion influences the forces acting on bubble significantly. Compared with the motionless condition, the pressure drop is increased and the fluctuation becomes acute as heat flux increases under the swing condition.