Void Drift Research Articles

Proposal of a new type of two-phase interchannel mixing model for application to subchannel analysis of PWR conditions

Prediction accuracy of a subchannel analysis depends strongly on modeling of the interchannel mixing effect. In the present paper, we proposed a new phenomenological two-phase interchannel mixing model in the subchannel code MATRA (Yoo et al., 1999) for application to the bubbly flow regime under PWR pressure level. The three elemental natural interchannel mixing effects (Lahey et al., 1977; Sadatomi et al., 1994), i.e., turbulent mixing (TM), diversion cross flow (DC) and void drift (VD), were separately considered in the proposed interchannel mixing model. The key constitutive relation of the new mixing model is the modeling of void drift, for which the concept of Lahey et al. (1977) that a two-phase flow approaching an equilibrium state was adopted. Based on systematic CFD simulations, correlations were proposed to describe both the void fraction distribution at equilibrium state and the effective mixing velocity due to void drift. In order to investigate the driving force of void drift, detailed examinations of the lift force acting on bubbles were conducted. We found out a close relationship between the lift force and the interchannel mixing effect of void drift. Finally, the new interchannel mixing model along with the proposed void drift model were implemented in MATRA for validation calculation with selected test cases of the ISPRA rod bundle benchmark (Herkenrath et al., 1981).

Anisotropy of electromigration-induced void and island drift

By means of our novel self-learning kinetic Monte Carlo model (Latz et al 2012 J. Phys.: Condens. Matter 24 485005) we study the electromigration-induced drift of monolayer voids and islands on unpassivated surfaces of single crystalline Ag(111) and Ag(001) films at the atomic scale. Regarding the drift velocity, we find a non-monotonic size dependence for small voids. The drift direction is aligned with the electromigration force only along high symmetry directions, while halfway between, the angle enclosed by them is maximal. The magnitude of these directional deviations strongly depends on the system parameter, which are investigated in detail. The simulation results are in accordance with void motion observed in experiments performed on Ag(111).

A new approach to two-phase flow analysis in a rod bundle

This paper deals with the development of a mathematical and numerical technique for the steady-state subchannel analysis. In view of the importance of the drift-flux model (DFM) in two phase flow analysis, the conservation equations are based on this model. The conservation equations are expressed in terms of five field equations: mixture and momentum continuity; liquid energy equations; gas continuity; and radial cross flow equation for the adjacent subchannels. The numerical algorithm of the single-phase subchannel analysis used in the DIYANA code are extended for the present two phase flow subchannel analysis. The transfer of mass, momentum and energy between adjacent subchannels are split into diversion, turbulent mixing and void drift cross-flow components. The transfer of mass by turbulent mixing is assumed to occur in a volume-for-volume scheme reflecting experimental observations. The phenomenon of lateral vapor drift and turbulent mixing enhancement with flow regime are included in the model. In order to validate the prediction, the GE 3×3 rod bundle experiments with both uniform and non-uniform radial power distribution are used. Good agreement has been obtained between the present numerical prediction and the available experimental data. Simulation results showed that the turbulent mixing and void drift phenomena flatten the void fraction and equilibrium vapor quality profile in the rod bundle cross section. The mathematical formulation is considered to be a major step toward a more basic understanding of two-phase flow analysis in fuel rod bundles. Therefore, a fast, efficient and stable numerical technique is presented in this paper for thermal-hydraulic analysis of nuclear reactors.

A mathematical approach to predict dryout in a rod bundle

In this paper, we present the development of a mathematical model to predict dry-out in a rod bundle using film thickness model and subchannel analysis. In two-phase annular flow regime, liquid phase is assumed to divide into liquid film attached to the rod surface and droplets entrained into the gas (vapor) phase existing in the subchannels. Conservation equations in two-phase annular flow regime for each subchannel consist of two mixture equations for the continuity and the momentum, gas phase continuity, liquid film continuity and liquid phase energy. Also, at the interface of adjacent subchannels, radial diversion cross flow equation is considered. It is assumed that dryout occurs when the local film thickness in the annular flow approaches zero. The transfer of mass, momentum and energy between adjacent subchannels are split into diversion cross-flow, turbulent mixing and void drift components. Rod-centered approach which is compatible with the annular flow regime is used for subchannel analysis. It was observed that turbulent mixing and void drift phenomena have significant effect on the prediction of dryout power. The model is verified against several available experimental data and proved viable for prediction of dryout heat flux in rod bundle geometry especially for mass flux greater than 400kg/m2s.

混相流研究の進展 ４ 稠密格子サブチャンネル間のボイドドリフトに及ぼす表面張力低下の影響

Void drift between triangle tight lattice subchannels has been studied experimentally and analytically. In the experiment, a channel having two subchannels simplifying the triangle tight lattice subchannels was used. Experimental data were obtained for both air-water and air-water with a surfactant flows to know the effects of the reduced surface tension on flow and void redistributions due to the void drift. In the analysis, the experimental data were compared with the calculation by a subchannel analysis code based on a one-dimensional two-fluid model in which various constitutive equations of wall and interfacial friction forces were tested. The results of such experiment and test of analysis will be reported.

Effects of Surface Tension on Two-Phase Void Drift Between Triangle Tight Lattice Subchannels

In this study, void drift phenomena, which are one of three components of the intersubchannel fluid transfer, have been investigated experimentally and analytically. In the experiments, data on flow and void redistributions were obtained for hydraulically nonequilibrium flows in a multiple channel consisting of two subchannels simplifying a triangle tight lattice rod bundle. In order to know the effects of the reduced surface tension on the void drift, water and water with a surfactant were used as test liquids. In addition, data on the void diffusion coefficient, D̃, needed in a void drift model, have been obtained from the redistribution data. In the analysis, the flow and the void redistributions were predicted by a subchannel analysis code based on a one-dimensional two-fluid model. From a comparison between the experiment and the code prediction, the present analysis code was found to be valid against the present data if newly developed constitutive equations of wall and interfacial friction were incorporated in to the model to account for the reduced surface tension effects.

Morphological evolution of voids by surface drift diffusion driven by the capillary, electromigration, and thermal-stress gradient induced by the steady state heat flow in passivated metallic thin films and flip-chip solder joints. II. Applications

The void growth and drift motion induced by the combined actions of the phase transformation (evaporation and condensation) and surface drift diffusion driven by the capillary and electromigration forces and thermal-stress gradients are investigated in passivated metallic thin films and flip-chip solder joints via computer simulation using the front-tracking method. As far as the device reliability is concerned, the most critical configuration for solder joint failure occurs even when thermal stresses are low if the void nucleation takes place close to the under bump metallurgy (UBM) where the heat and current flux crowding takes place due to the proximity effect associated with the confinement. The void growth induced by the condensation of excess (athermal) vacancies at the void-matrix dividing surface results in drastic spreading of pre-existing voids along transverse direction of solder joint due to the concurrently occurring heat and current crowding adjacent to the UBM. This accelerated transverse void spreading may eventually cause open-circuit interconnect failure as clearly demonstrated experimentally in literature.

Activation energy and prefactor for surface electromigration and void drift in Cu interconnects

Surface electromigration rates on oxide-free surfaces of unpassivated damascene Cu interconnect segments have been determined through electromigration testing under vacuum. Electromigration-induced voids grew at the cathode end of the segments due to a flux divergence at refractory-metal-lined vias to the lead lines below the test segment. Copper diffusivity on a clean Cu surface was determined by measuring the size of the voids as a function of time and test temperature at a fixed current. An activation energy of 0.45±0.11eV and a prefactor of 3.35×10−12m2∕s were found for the product of the effective charge z* and the surface diffusivity Ds. This result is shown to be consistent with void drift rates measured in passivated interconnects.

Improvement of the Subchannel Flow Mixing Model of the MARS Code

MARS is a best-estimate system analysis code that is based on the RELAP5/MOD3 and COBRA-TF codes. The COBRA-TF code was adapted as a three-dimensional thermal-hydraulic module in MARS. It uses a two-fluid, three-field model for two-phase flows and has a subchannel flow mixing model. The subchannel flow mixing model of the MARS three-dimensional module was assessed by using the ISPRA 16-rod bundle test and the GE 9-rod bundle test data. These tests represent typical pressurized water reactor and boiling water reactor core thermal-hydraulic conditions, respectively. Two interconnected subchannel tests that were performed under atmospheric pressure conditions were also used for the assessment. From the results of the assessments, a simple modification of the subchannel flow mixing model was suggested to take into account the effects of the system pressure on the void drift phenomena.

Kinetics of Void Drift in Copper Interconnects

AbstractWe have observed the real-time behavior of electomigration-induced voids in both passivated and unpassivated copper interconnects in a Scanning Electron Microscope (SEM), and correlated void nucleation, growth, drift and stagnation with post-electromigration crystallographic microanalyses carried out using Electron Back-Scattered Diffraction (EBSD) analysis. Voids that nucleate at various locations along the interconnects often drift toward the cathode, where they grow, coalesce, and eventually cause electrical failure. In-situ SEM observations allowed for the tracking of void shapes and drift rates over long (multi-grain) distances. Changes in the size and the velocity of the voids were observed when the voids passed through different grains. These changes are attributed to the difference in diffusivity for different grain orientations. In passivated lines, voids were often trapped at individual grain boundaries, where they grew to cause failure, or de-trapped to continue to drift toward the cathode. In unpassivated lines, voids did not drift, but instead always nucleated and grew and grain boundaries. Locations at which voids grew in unpassivated lines, or at which voids were trapped and grew in passivated lines, were correlated with the crystallographic orientations of “upwind” and “downwind” grains. From these analyses, we find that the average electromigration interface diffusivities (z*D) as a function of grain orientation are ordered according to {100} > {111} > {110}. Quantitative analysis of void dynamics, correlated with crystallographic microanalyses, provides important data for modeling of electromigration-induced failure, and for process-optimization for improved reliability.

Modelisation d’écoulement diphasique dans l’analyse du sous-canal de grappe d’assemblages

In order to practice a design-by-analysis of thermohydraulics design of BWR fuel rod bundles, the subchannel analysis would play a major role. There, the immediate concern is improvement in its predictive capability of CHF due in particular to the film dryout (boiling transition phenomena: BT) on the fuel rod surface. Constitutive equations in the subchannel analysis formulation are responsible for the quality of calculated results. The constitutive equations are a result of integration of the local and instantaneous description of two-phase flows over the subchannel control volume. In general, they are expressed in terms of subchannel-control-volume- as well as area-averaged two-phase flow state variables. In principle the information on local and instantaneous physical phenomena taking place inside subchannels must be counted for in the algebraic form of the equations on the basis of a more mechanistic modeling approach. They should include also influences of the multi-dimensional subchannel geometry and fluid material properties. Thermohydraulics phenomena of interests in this deed are: 1) vapor-liquid re-distribution by inter-subchannel exchanges due to the diversion cross flow, turbulent mixing and void drift, 2) liquid film behaviors, 3) transition of two-phase flow regimes, 4) droplet entrainment and deposition and 5) spacer-droplet interactions. These are considered to be five key factors in understanding the BT in BWR fuel rod bundles. In Japan, a university-industry consortium has been formed under the sponsorship of the Ministry of Economics, Trade and Industry. This paper describes an outline of the on-going project and, first, an outline of the current efforts is presented in developing a new two-fluid three field subchannel code NASCA being aimed at predicting onset of BT, and post BT phenomena in advanced BWR fuel rod bundles including those of the tight lattice configuration for a higher conversion. Then the current methodology adopted to improve the NASCA code capabilities for BT is described. There a combination of experimental and computational fluid dynamics approaches is undertaken to construct a two-phase fluid dynamics database. The experimental approach consists of 1) high-resolution airwater tests performed under the room-temperature and atmospheric pressure conditions for the intersubchannel exchanges, three-dimensional behaviors of liquid films, and spacer effects; and 2) integral steam-water tests performed at high-temperature and at higher pressure. In the integral tests, state-of the- arts of multi-phase flow measurement technologies are applied in order to obtain local and instantaneous data that reveal underlying detailed physical processes including high resolution void distributions inside a 4x4 bundle, liquid film thickness and two-phase flow regime. The analytical approach consists of computational multi-phase fluid dynamics (CMFD) applicable to two-phase flows. A physical interpretation of the equilibrium two-phase flow redistribution inside a rod bundle is discussed that is considered to closely be related to the void drift phenomena. Identification of interactions among dominant factors is a main objective of the integral test and acquired data will be utilized in verifying the improved subchannel code. Construction of a complete set of two-phase fluid dynamics database will be made by supplementing missing data regions with the aid of numerical analyses. Dependency on important state variables is extracted from the database and prototype constitutive equations are going to be proposed in the final stage of the project.

Two-Phase Void Drift Phenomena in a 2 × 3 Rod Bundle: Flow Redistribution Data and Their Analysis

To improve a void drift model used in a subchannel analysis, new experimental data are obtained for air-water two-phase flows in a vertical 2 × 3 rod channel consisting of six subchannels simulating a square array boiling water reactor fuel rod bundle. The data include the axial redistributions of flow rates of both phases and void fraction in the respective subchannels. By fitting the above data with the Lahey and Moody void settling model, we have determined a void diffusion coefficient in their model. It is found that the void diffusion coefficient for slug, churn, and annular flows could be well correlated in terms of a turbulent Peclet number developed in our previous study. Furthermore, a subchannel analysis code based on a two-fluid model proposed in our previous study is examined against the present data. In the code, the void settling model is incorporated with usual conservation equations of mass and momentum. From the examination, it is found that the subchannel analysis code can predict well the data on subchannel flow and void fraction for the 2 × 3 rod channel if appropriate correlations are adopted to evaluate wall and interfacial friction forces needed in the two-fluid model.

A modified equilibrium void distribution model applicable to subchannel-scale vapor–liquid cross flow model for conventional square and tight lattice BWR fuel bundles

As a part of the advanced subchannel code development project sponsored by Ministry of Economy, Trade and Industry, Japan, this paper describes improvement of the equilibrium void distribution model that is a main part of the vapor–liquid cross flow model. The three-component cross flow (TCCF) model is defined as the present framework that separates contributions of diversion, turbulent mixing and void drift. The Lahey's void settling model is introduced to express the latter two components. Based on the high-resolution air–water database and other published data of steam-water tests, general trends of vapor–liquid cross flow processes are examined. It can be assumed that subchannel void distributions are dominated by the three major effects, i.e. the fluid dynamic effect, the geometrical effect and the narrow gap effect. The equilibrium void distribution model is modified to include the above-mentioned three effects. Three characteristic parameters are assigned for each of the three effects and they are identified experimentally as functions of the void fraction. Multi-dimensional lattice geometries are incorporated based on the two-dimensional flow network model. The network equation is constructed by mapping the equilibrium void balance problem into the force-deflection problem. The resultant models are verified based on equilibrium void distribution data obtained by Sadatomi and Kawahara.

Multi-dimensional analysis of two-phase flow inside subchannels of nuclear fuel assembly

In subchannel analysis, the conservation equations are solved for each channel in a complex fuel bundle, where the effects of fluid exchange between each subchannel are considered. The fluid exchange is commonly referred to as that caused by cross flow. Void drift is considered to be phenomenon resulting from attaining a hydrodynamic equilibrium state. Its mechanism has not been clarified, and the transport due to void drift is therefore estimated through empirical models in conventional subchannel analyses. Therefore, mechanistic model for the void drift phenomenon is required to apply the subchannel analysis to a variety of fuel bundle geometry. In this study, multi-dimensional analysis using two-fluid model was applied to two-phase flow inside a geometry simulating fuel bundle subchannels, for the purpose of clarifying the void drift mechanism. The comparison between the results of the numerical analysis and the experiment confirmed that the reliability of the numerical method used in this study. In this paper, a mechanistic model based on the Stanton number, which expresses the void diffusion coefficient based on the Lahey's proposal, was proposed.

Single- and two-phase turbulent mixing rate between adjacent subchannels in a vertical 2 × 3 rod array channel

To complete a subchannel analysis code for prediction of thermal–hydraulic behavior of a coolant in BWR fuel rod bundle, an accurate estimation of fluid transfer between subchannels is essential. Under two-phase gas–liquid flow conditions, the fluid transfer is usually subdivided into turbulent mixing, void drift and diversion cross-flow. We focused on the turbulent mixing in this study. Until now, experimental data on two-phase turbulent mixing rate have been obtained exclusively for simpler channels with two subchannels alone, and prediction methods of the mixing rates have been proposed based on such data. In order to obtain data necessary to validate the prediction methods, we newly constructed a vertical test channel simulating a BWR fuel rod bundle, which contained six rods in a rectangular array and two kinds of six subchannels. Using this channel, flow distributions and turbulent mixing rates of both gas and liquid phases were measured for single-phase water and two-phase air–water flows under a hydrodynamic equilibrium flow condition at ambient pressure. In this paper, the experimental data on turbulent mixing rates in comparison with the data for two-subchannel system at 0.34 MPa obtained by others are presented and discussed.

次世代稠密格子サブチャンネルにおけるボイドドリフトによる二相流量再配分の調査(流体工学(混相流II))

次世代稠密格子サブチャンネルにおけるボイドドリフトによる二相流量再配分の調査(流体工学(混相流II))

BWR模擬2×1ロッド流路のボイドドリフトによる流量再配分の実験と解析(流体工学(混相流II))

BWR模擬2×1ロッド流路のボイドドリフトによる流量再配分の実験と解析(流体工学(混相流II))

C202 稠密14本バンドル内沸騰二相流の可視化

Visualization of 3D and instantaneous void fraction distribution of boiling flow in a tight-lattice 14-rod bundle is conducted by using neutron tomography and high-frame-rate neutron radiography void fraction measurement techniques. The purpose of the experiment is to understand vapor bubbles/water behavior ranging from the onset of boiling to the high void fraction region based on (3D+2D+Time) void fraction data, and to obtain the fine-mesh database for verification of advanced analysis codes. Following phenomena are made clear from the present experiment: Vapor accumulates in the channel center; High void fraction spots appear between adjacent heater rods, that is, in narrow space at the inlet; Void fraction in the triangular space among three rods becomes high by void drift phenomenon, and 'vapor chimney' is formed; Flow is intermittent, and vapor bubble clusters are formed periodically; Onset points of net vapor generation are scattered not only in the center but in the peripheral.

Two-phase turbulent mixing and buoyancy drift in rod bundles

This paper describes the development of generalized relationships for single- and two-phase intersubchannel turbulent mixing in vertical and horizontal flows, and lateral buoyancy drift in horizontal flows. The relationships for turbulent mixing, together with a recommended one for void drift, have been implemented in a subchannel thermalhydraulics code, and assessed using a range of data on enthalpy migration in vertical steam–water flows under BWR and PWR diabatic conditions. The intent of this assessment was to optimize these relationships to give the best agreement with the enthalpy migration data for vertical flows. The optimized turbulent mixing relationships were then used as a basis to benchmark a proposed buoyancy drift model to give the best predictions of void and enthalpy migration data in horizontal flows typical of PHWR CANDU 1 CANDU=CANada Deuterium Uranium, registered trademark of Atomic Energy of Canada Ltd. 1 reactor operation under normal and off-normal conditions. Overall, the optimized turbulent mixing and buoyancy drift relationships have been found to predict the available data quite well, and generally better and more consistently than currently used models. This is expected to result in more accurate calculations of subchannel distributions of phasic flows, and hence, in improved predictions of critical heat flux (CHF).

2116 2x3 ロッドバンドル流路におけるボイドドリフト(二流体モデルによる流量再配分計算)

The purpose of this study is to describe analytically two-phase void drift phenomena in a 2×3 rod bundle channel simulating BWR fuel rod bundle. For that, a subchannel analysis code, which was developed by the present authors and based on a two-fluid model, was used, and prediction of gas and liquid flow redistribution due to void drift between subchannels in the 2×3 rod bundle channel was conducted. In the code, a void settling model for evaluating the void drift effect was incorporated with usual conservation equations of mass and momentum. From a comparison, it was found that the subchannel analysis code can predict well the data on subchannel flow and void fraction variations in the 2×3 rod channel if an appropriate correlation was employed to evaluate wall and interfacial friction forces.