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.     

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.].     

Film boiling heat transfer from a vertical cylinder in forced flow of liquids under saturated and subcooled conditions at pressures

Forced convection film boiling heat transfer on a vertical 3-mm diameter and 180-mm length platinum test cylinder located in the center of the 40-mm inner diameter test channel was measured. Saturated water, and saturated and subcooled R113 were used as the test liquids that flowed upward along the cylinder in the test channel. Flow velocities ranged from 0 to 3 m s⁻¹, pressures from 102 to 490 kPa, and liquid subcoolings for R113 from 0 to 60 K. The heat transfer coefficients for a certain pressure and liquid subcooling are almost independent of flow velocity and of a vertical position on the cylinder for the flow velocities lower than ≈1 m s⁻¹ (the first range), and they become higher for the velocities higher than ≈1 m s⁻¹ (the second range). Slight dependence on a vertical position being nearly proportional to z^−1/4, where z is the height from the leading edge of the test cylinder, exists for the flow velocities in the second range. The heat transfer coefficients at each velocity in the first and second ranges are higher for higher pressure and liquid subcooling. Correlation for the forced convection film boiling heat transfer with radiation contribution on a vertical cylinder was derived by modifying an approximate analytical solution for a two-phase laminar boundary layer model to agree better with the experimental data. It was confirmed that the experimental data of film boiling heat transfer coefficients in water and R113 were described by the correlation within ±20% difference.     

Influence of subcooled boiling on out-of-phase oscillations in boiling water reactors

In this paper, we develop a reduced order model with modal kinetics for the study of the dynamic behavior of boiling water reactors. This model includes the subcooled boiling in the lower part of the reactor channels. New additional equations have been obtained for the following dynamics magnitudes: the effective inception length for subcooled boiling, the average void fraction in the subcooled boiling region, the average void fraction in the bulk-boiling region, the mass fluxes at the boiling boundary and the channel exit, respectively, and so on. Each channel has three nodes, one of liquid, one with subcooled boiling, and one with bulk boiling. The reduced order model includes also a modal kinetics with the fundamental mode and the first subcritical one, and two channels representing both halves of the reactor core. Also, in this paper, we perform a detailed study of the way to calculate the feedback reactivity parameters. The model displays out-of-phase oscillations when enough feedback gain is provided. The feedback gain that is necessary to self-sustain these oscillations is approximately one-half the gain that is needed when the subcooled boiling node is not included.     

Low-quality and subcooled film boiling of water at elevated pressures

Stable film boiling heat transfer data have been obtained in an 8.9 mm ID tube at pressures from 2 to 9 MPa. These data were obtained at low-quality and subcooled conditions, over a mass flux range of 0.11 to 2.75 Mg m⁻² s⁻¹. Excessive film boiling surface temperatures were avoided by using the hot patch technique. Contrary to the high-quality data, the low-quality data showed a decrease in heat transfer coefficient with an increase in quality. The film boiling data were compared with existing film boiling correlations. None of these were found to be satisfactory.     

竖直矩形窄流道内过冷沸腾汽泡生长特性及对换热的影响

在一个大气压下以水为工质研究了竖直矩形窄流道内过冷沸腾的汽泡生长特性。采用Laplace数(La)和时间因子(ξ)无量纲化汽泡半径和汽泡生长时间,得到了不同工况下的无量纲汽泡生长曲线。通过分析质量流速和热流密度变化对无量纲汽泡生长的影响,发现增加质量流速会抑制汽泡生长;增加热流密度则会促进汽泡生长。汽泡的生长行为会严重影响核态沸腾换热系数hNB,从而影响总沸腾两相流动换热系数htp。采用与雷诺数(Re)相关的无量纲时间(t*)的1/3次方模型来预测无量纲汽泡生长,发现此模型能较好地预测本研究中所得到的无量纲汽泡生长数据。     

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.     

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.     

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.     

A mechanistic model of critical heat flux under subcooled flow boiling conditions for application to one- and three-dimensional computer codes

Based on a review of visual observations at or near critical heat flux (CHF) under subcooled flow boiling conditions and consideration of CHF triggering mechanisms, presented in a companion paper [Le Corre, J.M., Yao, S.C., Amon, C.H., 2010. Two-phase flow regimes and mechanisms of critical heat flux under subcooled flow boiling conditions. Nucl. Eng. Des.], a model using a two-dimensional transient thermal analysis of the heater undergoing nucleation was developed to mechanistically predict CHF in the case of a bubbly flow regime. The model simulates the spatial and temporal heater temperature variations during nucleation at the wall, accounting for the stochastic nature of the boiling phenomena. It is postulated that a high local wall superheat occurring underneath a nucleating bubble at the time of bubble departure can prevent wall rewetting at CHF (Leidenfrost effect). The model has also the potential to evaluate the post-DNB heater temperature up to the point of heater melting.Validation of the proposed model was performed using detailed measured wall boiling parameters near CHF, thereby bypassing most needed constitutive relations. It was found that under limiting nucleation conditions; a peak wall temperature at the time of bubble departure can be reached at CHF preventing wall cooling by quenching. The simulations show that the resulting dry patch can survive the surrounding quenching events, preventing further nucleation and leading to a fast heater temperature increase. The model was applied at CHF conditions in simple geometry coupled with one-dimensional and three-dimensional (CFD) codes. It was found that, within the range where CHF occurs under bubbly flow conditions (as defined in Le Corre et al., 2010), the local wall superheat underneath nucleating bubbles is predicted to reach the Leidenfrost temperature. However, a better knowledge of statistical variations in wall boiling parameters would be necessary to correctly capture the CHF trends with mass flux (or Weber number).     

Strain-induced corrosion cracking behaviour of low-alloy steels under boiling water reactor conditions

The strain-induced corrosion cracking (SICC) behaviour of different low-alloy reactor pressure vessel (RPV) and piping steels and of a RPV weld filler/weld heat-affected zone (HAZ) material was characterized under simulated boiling water reactor (BWR)/normal water chemistry (NWC) conditions by slow rising load (SRL) and very low-frequency fatigue tests with pre-cracked fracture mechanics specimens. Under highly oxidizing BWR/NWC conditions (ECP +50 mV_SHE, 0.4 ppm dissolved oxygen), the SICC crack growth rates were comparable for all materials (hardness <350 HV5) and increased (once initiated) with increasing loading rates and with increasing temperature with a possible maximum/plateau at 250 °C. A minimum K_I value of 25 MPa m^1/2 had to be exceeded to initiate SICC in SRL tests. Above this value, the SICC rates increased with increasing loading rate dK_I/dt, but were not dependent on the actual K_I values up to 60 MPa m^1/2. A maximum in SICC initiation susceptibility occurred at intermediate temperatures around 200–250 °C and at slow strain rates in all materials. In contrast to crack growth, the SICC initiation susceptibility was affected by environmental and material parameters within certain limits.     

Phenomenological prediction of CHF under boiling water reactor (BWR) conditions

Critical Heat Flux (CHF) is an important parameter for the thermal design of any heat generating system, most importantly, nuclear reactors. Owing to the complex mechanisms of CHF there has been a large proliferation of the correlations, each having narrow range of validity, which shows that the empirical correlation is not an appropriate approach for the CHF prediction for a wide range of validity. This limitation has led to the development of the phenomenological approach of the CHF prediction. The film dryout mechanism is applicable to the high quality CHF corresponding to the annular flow pattern in which the progressive depletion of the liquid film leads to dryout. The basic concern in the prediction of dryout is the accuracy in the evaluation of the droplet deposition and entrainment. There are various models for the estimation of the entrainment and deposition of droplets. However, most of these models are based on the air-water data at the atmospheric conditions and hence their applicability to the BWR conditions needs to be confirmed. Some of the models are based on the steam-water data which needs to be validated for the dryout prediction under BWR conditions. In this paper, the film dryout modelling has been carried out for the prediction of CHF using appropriate models for entrainment fraction and deposition coefficient. The results have been compared with the CHF data generated to substantiate the appropriateness of the selected models under BWR conditions.     

Experimental investigation of local two-phase flow parameters of a subcooled boiling flow in an annulus

As a series of subcooling boiling flow tests, local two-phase flow parameters were obtained at SUBO (subcooled boiling) test facility under steam–water flow conditions. The test section is a vertical annulus of which the axial length is 4.165 m with a heater rod at the center of a channel. The inner and outer diameters of the test section and the heater rod are 35.5 mm and 9.98 mm, respectively. The test was performed by a two-stage approach. Stage-I for the measurement of local bubble parameters has been already done (Yun et al., 2009). The present work focused on the stage-II test for the measurement of local liquid parameters such as a local liquid velocity and a liquid temperature for a given flow condition of stage-I. A total of six test cases were chosen by following the test matrix of stage-I. The flow conditions are in the range of the heat flux of 370–563 kW/m², mass flux of 1110–2100 kg/(m² s) and inlet subcooling of 19–31 °C at pressure condition of 0.15–0.2 MPa. From the test, local liquid parameters were measured at 6 elevations along the test section and 11 radial locations of each elevation in addition to the previously obtained local void fraction, interfacial area concentration, Sauter mean diameter and bubble velocity. The present subcooled boiling (SUBO) data completes a data set for use as a benchmark, validation and model development of the Computational Fluid Dynamics (CFD) codes or existing safety analysis codes.     

Experimentaland numerical investigation of liquid metal boiling in fuel subassemblies under natural circulation conditions

Boiling of Na-K eutectic alloy (22% Na; 78% K) in parallel channels under the natural circulation condition has been investigated at the AR-1 facility of IPPE. Hydrodynamics and heat transfer data have been obtained at this facility for various experiment set-ups of both single and parallel sections. A thermohydraulic code system based on the subchannel analysis code SABENA-3D has been developed and used to simulate these experiments. Comparisons show that the code system can reproduce the boiling phenomena in the test section with sufficient accuracy, correctly predicting the heat transfer conditions prior to and during the boiling.     

Critical heat flux of forced convection boiling in an oscillating acceleration field — III. Reduction mechanism of CHF in subcooled flow boiling

To investigate the effect of variation in acceleration on the critical heat flux (CHF) in subcooled flow boiling, a photographic study was made. The test section was an internally heated vertical annulus with a glass shroud, in which Freon-113 flowed upwardly. The observation was made at a pressure of 3 bar, a mass flux of 920 kg/m²s, an inlet subcooling 45 K and a slightly lower heat flux level than steady CHF. The vertical acceleration was oscillated with amplitude of 0.3g_e and a period of 6 s.At low apparent gravitational acceleration, bubbles generated on the heated surface moved longer along the surface without detachment and coalesced with other bubbles to form large vapor slugs. This causes early CHF, the mechanism of which is dry-out of the liquid film existing between the heated surface and vapor slugs.     

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.     

Stress corrosion cracking of low-alloy reactor pressure vessel steels under boiling water reactor conditions

The stress corrosion cracking (SCC) behaviour of different reactor pressure vessel (RPV) steels and weld filler/heat-affected zone materials was characterized under simulated boiling water reactor (BWR) normal water (NWC) and hydrogen water chemistry (HWC) conditions by periodical partial unloading, constant and ripple load tests with pre-cracked fracture mechanics specimens. The experiments were performed in oxygenated or hydrogenated high-purity or sulphate/chloride containing water at temperatures from 150 to 288 °C. In good agreement with field experience, these investigations revealed a very low susceptibility to SCC crack growth and small crack growth rates (<0.6 mm/year) under most BWR/NWC and material conditions. Critical water chemistry, loading and material conditions, which can result in sustained and fast SCC well above the ‘BWRVIP-60 SCC disposition lines’ were identified, but many of them generally appeared atypical for current optimized BWR power operation practice or modern RPVs. Application of HWC always resulted in a significant reduction of SCC crack growth rates by more than one order of magnitude under these critical system conditions and growth rates dropped well below the ‘BWRVIP-60 SCC disposition lines’.     

Dependence of bubble behavior in subcooled boiling on surface wettability

This paper presents the results of visualization experiments that were carried out to investigate the dynamics of vapor bubbles generated in water pool boiling. In the experiments, vapor bubbles were generated on a vertical circular surface of a copper block containing nine cartridge heaters, and the contact angle of the heated surface was used as a main experimental parameter. The experiments were performed under subcooled as well as nearly saturated conditions. To enable clear observation of individual bubbles with a high speed camera, the heat flux was kept low enough to eliminate significant overlapping of bubbles. When the contact angle was small, the bubbles were lifted-off the vertical heated surface within a short period of time after the nucleation. On the other hand, when the contact angle was large, they slid up the vertical surface for a long distance. When bubbles were lifted-off the heated surface in subcooled liquid, bubble life-time was significantly shortened since bubbles collapsed rapidly due to condensation. It was shown that this distinct difference in bubble dynamics could be attributed to the effects of surface tension force.