An analytical solution to a two-dimensional model of the rewetting of a hot dry rod

The model considers a hot dry rod of infinite length cooled by a film of liquid moving along its surface. The heat transfer coefficient is assumed to be constant on the wet side and zero on the dry side of the rewetting front, and the liquid film is assumed to move at constant speed. We derive an analytical formula relating the temperature difference in the rod, the temperature at the rewetting front, the wet side heat transfer coefficient, and the rewetting speed. The formula is thought to apply to the rewetting of a fuel rod during emergency cooling by flooding.     

Liquid film behavior and heat-transfer mechanism near the rewetting front in a single rod air–water system

ABSTRACT

The rewetting front propagation may occur when the fuel rod is cooled by the liquid film flow after it is dried out under accident conditions for boiling water reactor cores. Our previous study has revealed the importance of precursory cooling, defined as a rapid cooling just before the rewetting, which has a significant effect on the propagation velocity. To understand the mechanism of the precursory cooling, we conducted heat-transfer experiments using a single heater rod contained inside the transparent glass pipe to measure heat-transfer behavior with simultaneous observation using a high-speed camera. The results showed characteristic effects of the wall temperature on the liquid film flow and liquid droplets formation at the rewetting front, i.e. sputtering. Even when the liquid film flows in rivulets under adiabatic condition, horizontally uniformed rewetting front was observed with increasing wall temperature due to enhanced flow resistance by sputtering. This sputtering effect was also confirmed from observations of the liquid film thickness, which increased with approaching the rewetting front. Heat-transfer coefficients were predicted roughly well with a single-phase heat-transfer correlation with entrance effects, suggesting that the thinner thermal boundary layer downstream of the rewetting front may be one of the precursory cooling mechanisms.     

Response to G. Yadigaroglu''s letter

The rewetting or quench temperature is the temperature of a hot solid surface at which a liquid can reestablish contact with the dry surface. An estimation of this temperature is essential in predicting the rate at which the coolant quenches the core of a light-water reactor (LWR) after a loss-of-coolant accident. The present study reviews and evaluates previous work in this area and presents a model relating experiments to theory for the different possible types of reflood in LWRs. It is postulated that, with the exception of those cases of top reflood by a film in a single-rod geometry and bottom reflood with a very low mass flow rate, the quench temperature corresponds to either the minimum film boiling temperature or the Leidenfrost temperature. In cases where there are such exceptions, the quench temperature corresponds to the critical heat flux temperature. New correlations for the rewetting or quench temperature are presented.     

Effects of flow obstacles on film boiling heat transfer

The effect of flow obstacles on film boiling heat transfer in a vertical upward tube is investigated experimentally using R134a as a coolant. The results show that flow obstacles enhance heat transfer downstream of the obstacle and promote rewetting to occur in this region. The rewetting zone is found to increase with a decrease in quality at the obstacle location, and with an increase in mass flux, but the effect of pressure is inconclusive. The rewetting effect is strongest near the obstacle location, and weakens with distance from the obstacle, i.e. at locations axially downstream from the obstacle and circumferentially away from the obstacle. The characteristic time is found to be a good correlating factor to characterize the effect of mass flux. The prediction from the post-dryout look-up table, after applying the appropriate fluid-to-fluid modeling technique, is in reasonable agreement with the experimental results.     

Experimental studies on rewetting of hot vertical annular channel

Studies on the rewetting behaviour of hot vertical annular channels are of interest in the context of emergency core cooling in nuclear reactors following LOCA. Experimental studies were carried out to study the rewetting behaviour of a hot vertical annular channel, with hot inner tube, for bottom flooding and top flow rewetting conditions. The length of the inner tube of the test section was 3030 mm for bottom flooding rewetting experiments and 2630 mm for top flow rewetting experiments. The tube was made of stainless steel. Experiments were conducted for water flow rates in the annulus upto 7 lpm (11.7×10⁻⁵ m³ s⁻¹). The initial surface temperature of the inner tube was varied from 200 to 500°C. The experimental studies show that for a given initial surface temperature of the tube, the rewetting velocity increases with an increase in flow rate of water and it decreases with an increase in the initial surface temperature for a given water flow rate. For a given water flow rate and initial surface temperature, the rewetting velocity is higher in the case of rewetting under bottom flooding conditions as compared to that in the case of rewetting under top flow conditions. These conclusions agree with the conclusions reported in the earlier literature. Using the experimental data of the present work, correlations for bottom flooding and top flow rewetting velocities are developed.     

The quenching of irradiated fuel pins

This paper presents the results of falling film rewetting experiments on two types of irradiated fuel pin and on a complementary range of tubes and heaters. Preliminary measurements of rewetting rate in bottom flooding are presented and a brief comparison is made between falling film and bottom flooding rewetting, including the effects of surface finish. It is demonstrated that fuel pin rewetting behaviour is broadly consistent with that for tubes and heaters and that there are no large systematic effects of irradiation. Surface finish is shown to have an important influence on the falling film rewetting rate and could have influenced the fuel pin behaviour. The preliminary findings for bottom flooding are that there are smaller differences between various heaters than for falling film, and surface finish does not significantly change rewetting behaviour. It is shown that subcooling local to the quench front is an important parameter in rewetting, and can be used as a basis for correlating data. This is in agreement with recent ideas.     

Rewetting front propagation under anticipated operational occurrences for boiling water reactors – development of two-dimensional analytical model

An analytical model to predict a rewetting velocity applicable to high pressure and high flow rate condition during anticipated operational occurrences (AOOs) is developed by applying Wiener–Hopf technique coupled with appropriate kernel substitutions. The model considers the effects of enhanced cooling in the vicinity to liquid film front termed “precursory cooling” and heat input from fuel pellets on back side of wall as boundary conditions of a heat conduction equation. A simplified two-dimensional model neglecting an effect of axial heat conduction is also proposed. It is found through the comparison among the models and experimental data that the contribution of the heat conduction in the wall-depth direction is essential in the prediction of the rewetting velocity at the thermal-hydraulic condition simulating AOOs and the axial heat conduction has little influence when an enhanced heat transfer coefficient in the dried-out region is appropriately given as a function of distance from the liquid film front.     

Investigation of liquid film behavior at the onset of flooding during adiabatic counter-current air–water two-phase flow in an inclined pipe

The liquid film characteristics at the onset of flooding in an inclined pipe (16 mm i.d. and 2.2 m in length) have been investigated experimentally. A constant electric current method and visual observation were utilized to elucidate the flow mechanisms at the onset of flooding. Two mechanisms are clarified to control the flooding in lower flooding and upper flooding, respectively. The lower flooding occurred at lower liquid flow rate and high pipe inclination angle. In this mechanism, the liquid film does not block the pipe cross-section. On the other hand, the upper flooding occurred at higher liquid flow rate and low pipe inclination angle. In this case, blocking of the pipe cross-section by large wave and entrainment plays an important role. The experimental data indicated that there was no reversal motion of liquid film at the onset of flooding during the operation of both lower flooding and upper flooding. The effects of pipe inclination angle on the onset of flooding are also discussed.     

延展表面凝结液膜的动量积分方法

采用动量积分方法分析压水堆发生失水事故时在安全壳的内表面上的液膜凝结、再浸润和蒸发过程。由凝结液膜的质量和动量守恒方程导出了凝结液膜在延展表面的子午线方向平均速度的积分-微分方程。假设液膜以层流的方式流动，把导出的积分-微分方程变成容易进行数值积分的液膜速度的一阶常微分方程，由此求得液膜厚度分布。液膜能量守恒方程的解给出了安全壳内壁面的温度分布。     

Two-phase countercurrent flow in a model of a pressurized water reactor hot leg

The onset of flooding or countercurrent flow limitation (CCFL) determines the maximum rate at which one phase can flow countercurrently to another phase. In the present study, the experimental data of the CCFL for gas and liquid in a horizontal pipe with a bend are investigated. The different mechanisms that lead to flooding and that are dependent on the liquid flow rate are observed. For low and intermediate liquid flow rates, the onset of flooding appears simultaneously with the slugging of unstable waves that are formed at the crest of the hydraulic jump. At low liquid flow rates, slugging appears close to the bend; at higher liquid flow rates, it appears far away from the bend, in the horizontal section. For high liquid flow rates, no hydraulic jump is observed, and flooding occurs as a result of slug formation at the end of the horizontal pipe. The effects of the inclination angle of the bends, the liquid inlet conditions and the length of the horizontal pipes are of significance for the onset of flooding. A mathematical model of Ardron and Banerjee is modified to predict the onset of flooding. Flooding curves calculated by this model are compared with present experimental data and those of other researchers. The predictions of the onset of flooding as a function of the length-to-diameter ratio are in reasonable agreement with the experimental data.     

On the process of rewetting a hot surface by a falling liquid film

A two-dimensional transient heat conduction model for rewetting a hot surface by a falling liquid film predicts that for stainless steel, Inconel or Zircaloy only a wall thickness of some 0.020 in. takes part in the rewetting process in steam at 100–1000 psia. The rewetting rate is nearly independent of heat flux and thermal conductivity, but increases with pressure and decreases with volumetric heat capacity.     

A review of spray-cooling and bottom-flooding work for lwr cores

Rewetting or the re-establishment of water films on the hot, fuel rod surfaces is of fundamental importance following a loss-of-coolant accident in a water cooled reactor. Two techniques are used: rewetting by a falling film of water (top sparay) and rewetting by an upflow of water (bottom flooding). Considerable theoretical and experimental work has been done to investigate the effects of different operating parameters on these techniques, and that work is summarized here.     

An experimental investigation on the quenching of a hot vertical heater by water injection at high flow rate

An experimental investigation on rewetting has been carried out by injecting water from the top of a hot vertical heater. Tests have been performed with varied range of experimental conditions (200-500 °C surface temperatures, constant water flow rates 5.77-30.98 g s⁻¹). Effect of several coolant injection systems on the hydrodynamics of rewetting has been studied. It is observed that for a particular range of flow rate and initial wall temperature (21.58 g s⁻¹, 300 °C) a circumferentially symmetric wet front is observed for the region closer to the coolant injection point even while using sub-cooled water. Rewetting velocity has been calculated from the temperature transients measured during the experiment and was found to vary within 1.0-20.0 cm s⁻¹. Two different rewetting models ( [Sahu et al., 2006] and [Sahu et al., 2008a]) have been used to compare the present experimental data and the comparison is found to be fairly good in both the cases. It has been observed that the flow rate varies linearly with effective Biot number (M) and varies inversely with magnitude of precursory cooling (N) in the present investigation.     

Development of a Transient Boiling Transition Analysis Method Based on a Film Flow Model

A new single-channel, transient boiling transition (BT) prediction method based on a film flow model has been developed for a core thermal-hydraulic code. This method could predict onset and location of dryout and rewetting under transient conditions mechanically based on the dryout criterion and with consideration of the spacer effect. The developed method was applied to analysis of steady-state and transient BT experiments using BWR fuel bundle mockups for verification. Comparisons between calculated results and experimental data showed that the developed method tended to predict occurrence of rewetting earlier, however, onset time of BT and maximum rod surface temperature were well predicted within 0.6 s and 20°C, respectively. Moreover, it was confirmed that consideration of the spacer effect on liquid film flow rate on the rod surface was required to predict dryout phenomena accurately under transient conditions.     

冷却剂丧失条件下钠冷快堆棒束传热的三维蒙特卡罗模拟方法

采用蒙特卡罗方法分析钠冷快堆在假想冷却剂丧失条件下燃料棒束的钠两相流传热问题。以分子运动理论的基本定律为基础，开发出替代宏观经验模型来分析反应堆棒束中的钠蒸发率和冷凝率的微观模型，且采用三维蒙特卡罗方法模拟分子的运动轨迹，分子间的碰撞率以及分子与棒束、分子与棒束组件盒壁的碰撞率。对包壳干涸区的再浸润现象用动力膜模型描述，并计算了通过液膜的液体速度分布和平均液膜速度，对于从冷凝液膜蒸发的钠分子则被重新记为蒙特卡罗计算的源项。用微观和宏观模型相结合的方法数字模拟了德国卡斯鲁尔研究中心的堆外钠沸腾实验。     

Counter-current flow limitations during hot leg injection in pressurized water reactors

A one-dimensional model is presented to predict counter-current flow limitations during hot leg injection in pressurized water reactors. Different from previous models, it may also be applied in case of high Froude numbers of the liquid flow, such as to be expected in the case of emergency coolant injection through the hot leg. The model has been verified with an extensive experimental program performed in the WENKA test facility at the Forschungszentrum Karlsruhe. Typical flow regimes were investigated for a wide range of flow conditions, simulated with air and water at ambient pressure and temperature, in a simplified Pressurized Water Reactor (PWR) hot leg geometry. Depending on the water and air flow rates, flow phenomena such as a hydraulic jump and flow reversal were experimentally observed. The theoretical model shows that not only the nondimensional superficial velocities of liquid and gas, but also the Froude number of the liquid at the injection point and the Reynolds number of the gas play an important role for the prediction of flow reversal. In case of a high liquid inlet Froude number, a flow reversal could only be observed if the liquid flow became locally subcritical, i.e. if a hydraulic jump occurred in the channel. The flow reversal is predicted by the presented model with good accuracy.     

Buoyantly-driven two-phase countercurrent flow in liquid discharge from a vessel with an unvented gas space

This paper details experiments and analyses regarding the phenomenon of liquid discharge into a gaseous atmosphere from the bottom of a vessel with an unvented, upper gas space. The primary goal is the development of a simple model that predicts the rate of liquid discharge under the prevailing unvented condition. A literature survey of previous work on this phenomenon yielded only simple experiments and analyses that were limited in scope. Experiments were subsequently undertaken with an air-water system, using a larger volume and a wide range of drain line diameters. In addition to flowrate data, visual information was acquired regarding the physical mechanism possibly governing the prevalent flow regimes. The governing physical mechanism is identified as the stability of a gas-liquid interface, perturbed by buoyancy, at the drain line entrance. G.I. Taylor's fundamental analysis of interfacial stability lead to the determination of criteria for flow regime transition among the three prevalent flow regimes, corresponding to so-called small, medium, and large diameters. Also, analysis of the growth of interfacial instabilities lead to the application of flooding models for drainage rates within each regime. The models for moderate and large diameters were then compared against data, which confirmed their success in predicting discharge rates under the unvented condition.The motivation for this effort, besides the basic scientific significance of studying such a fundamental phenomenon, was its numerous applications, one of which is commercial nuclear reactor systems. Specifically, the phenomenon prevails in liquid coolant discharge from a PWR pressurizer, with an unvented steam volume, into a steam atmosphere existing in the adjoining hot coolant leg. Such a phenomenon could occur as part of a transient, or severe accident, scenario, entailing saturated conditions and steam production in the normally subcooled primary heat transport loop. The developed model was implemented in the Modular Accident Analysis Program (MAAP), a computer code designed to predict reactor system behavior in response to postulated off-normal conditions, including severe accident scenarios.     

Core Heat Transfer Coefficients Immediately Downstream of the Rewetting Front during Anticipated Operational Occurrences for BWRs

A heat transfer coefficient (HTC) model was developed for the prediction of post-boiling transition (post-BT) behavior that might occur during anticipated operational occurrences (AOOs) for boiling water reactors (BWRs). The model development was based on measurements of heat transfer coefficient, liquid droplet deposition rate, and droplet concentration in our experiments conducted at high pressure. The model focused on the heat transfer near the rewetting front where the cooling by droplet deposition significantly affects the propagation behavior of a liquid film. The correlation by Sugawara was validated for the prediction of the deposition by using the experimental data. The model was also expressed as a function of the distance from the rewetting front to use in analytical models for the rewetting propagation. Both expressions of the present model successfully predicted our experimental data simulating the BWR thermal-hydraulic conditions.     

Wall pressure measurements of flooding in vertical countercurrent annular air-water flow

An experimental study of flooding in countercurrent air-water annular flow in a large diameter vertical tube using wall pressure measurements is described in this paper. Axial pressure profiles along the length of the test section were measured up to and after flooding using fast response pressure transducers for three representative liquid flow rates representing a wide range of liquid Reynolds numbers (Re_L = 4Γ/μ; Γ is the liquid mass flow rate per unit perimeter; μ is the dynamic viscosity) from 3341 to 19,048. The results show that flooding in large diameter tubes cannot be initiated near the air outlet and is only initiated near the air inlet. Fourier analysis of the wall pressure measurements shows that up to the point of flooding, there is no dominant wave frequency but rather a band of frequencies encompassing both the low frequency and the broad band that are responsible for flooding. The data indicates that flooding in large diameter vertical tubes may be caused by the constructive superposition of a plurality of waves rather than the action of a single large-amplitude wave.     

A simple model for vertical annular and horizontal stratified two-phase flows with liquid entrainment and phase transitions: one-dimensional steady state conditions

A simple one-dimensional three-fluid model is presented for the simulation and analyses of vertical annular and stratified horizontal or inclined two-phase flows. The model has been verified for various experimental data: developing annular flow, momentum transfer in an annular flow, plane flow with a hydraulic jump, flooding in a horizontal pipe, and stratified flow with direct steam condensation. Emphasis has been laid upon several mass, momentum and energy interfacial transfer processes. New correlations are proposed for the droplet entrainment intensity in annular flow and for steam direct contact condensation on the liquid film in a stratified flow. The liquid entrainment in the annular flow is correlated with the liquid film thickness. Direct contact condensation is correlated with the turbulent convective heat transfer in the liquid film. It has been shown that the present model is able to predict all dominant processes in both types of flow.