A correlation of rewetting data

Following a loss-of-coolant accident in a water reactor the fuel pins dry out and overheat and it becomes necessary to rewet them to restore normal temperatures. A thermal conduction analysis of rewetting is presented in which it is shown that the heat transfer coefficient associated with rewetting may be taken as an arbitrary function of surface temperature, rather than a constant, without changing the dependency of rewetting velocity on the other variables. An effective heat transfer coefficient then replaces the constant value used in previous expressions for the rewetting velocity. Experiments at atmospheric pressure show that the rewetting rate increases with inlet water subcooling. The available rewetting data at both atmospheric and elevated pressure have been analysed using an existing theoretical model. Taking the effective heat transfer coefficient as proportional to the product of mass flow rate and inlet subcooling a data fit has been achieved to within a factor of two. Expressions are given which predict rewetting rates for a wide range of pressures, wall temperatures, subcoolings, clad materials and geometries.     

Heat conduction analyses on rewetting front propagation during transients beyond anticipated operational occurrences for BWRs

Our previous study investigated the rewetting behavior of dryout fuel surface during transients beyond anticipated operational occurrences for BWRs, which indicated the rewetting velocity was significantly affected by the precursory cooling defined as cooling immediately before rewetting. This study further investigated the previous experiments by conducting additional experimental and numerical heat conduction analyses to characterize the precursory cooling. For the characterization, the precursory cooling was first defined quantitatively based on evaluated heat transfer rates; the rewetting velocity was investigated as a function of the cladding temperature immediately before the onset of the precursory cooling. The results indicated that the propagation velocity appeared to be limited by the maximum heat transfer rate near the rewetting front. This limitation was consistent with results of the heat conduction analysis using heat transfer models for the precursory cooling expressed as a function of distance from the rewetting front, the maximum wetting temperature, and the heat transfer coefficients in the wetted region. This paper also discusses uncertainties in the evaluation of transient heat flux from the measured surface temperature, and technical issues requiring further investigation.     

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.     

Parametric study on rewetting velocities obtained with a two-dimensional heat conduction code

A comprehensive parametric study has been performed to quantify the effect of different variables on the rewetting velocity in a light water reactor following a loss-of-coolant accident. To this purpose, a numerical solution of the general two-dimensional (axial and radial) heat conduction equation in cylindrical geometry has been obtained. The method used is the alternating-direction implicit procedure developed by Peaceman and Rachford. The model accounts for decay heat generation in the fuel, coolant subcooling, different wall temperatures and different heat transfer coefficients across the gap and at the clad surface. The two-dimensional model can be reduced to a one-dimensional model by setting the heat conduction in either the radial or axial direction to zero. Results with the new model agree with previous models and with experimental data.The variables studied were: axial and/or radial heat conduction, clad temperature, quench temperature, coolant temperature, temperature for the onset of nucleate boiling, heat transfer coefficients, stored and decay heats, clad material and clad thickness. The critical thickness (clad thickness for which the calculated rewetting velocity remains constant) was also determined and found to be larger than the clad thickness of light water reactor fuel pins under usual reflood conditions. According to these calculations, the stored and decay heats affect the rewetting velocity significantly.     

Boiling heat transfer during rewetting

An analytical one-dimensional conduction model is developed for the rewetting of a hot surface. The solution scheme is not limited to a specific heat flux profile. Experimental results falling within the range of validity of the one-dimensional solution are correlated using a generalized pool boiling curve. The effect of various heat transfer parameters such as inlet velocity and local subcooling is discussed. A unique relationship is shown to exist between the dimensionless quench front velocity, which is defined here as an eigenvalue of the governing equation, the ratio of the integral of the dimensionless heat flux, and the integral of the surface axial temperature gradient.     

Effect of thermal radiation on rewetting of top spray emergency coolant

A general physical model for top spray rewetting during an emrgency core cooling (ECC) transient is proposed which takes into account thermal radiation in the dry region. The model is employed to study the effect of thermal radiation on rewetting a single rod and a 3 × 3 rod bundle up to 2100°F. The results show that rewetting in a bundle is slower than for an isolated rod, due to reduced thermal radiation heat transfer in the dry region. Also, there is a definite correlation between the decreased radiation heat flux Δq_R and the corresponding decrease in rewetting velocity Δu. Values of Δu are not significant unless Δq_R is larger than 6000 Btu/hr ft², where Δq_R cannot exceed a value of 6000 Btu/hr ft² below a temperature of 1100°F, even in the most adverse conditions. Hence, it is concluded that radiant heat transfer does not significantly affect rewetting velocities up to an initial rod temperature of 1100°F. Beyond this temperature, the rewetting velocities change by more than 1.5% and hence radiation must be included in the model for top spray rewetting.     

Hydrodynamically-controlled rewetting

Transient cooling of a hot tube by a falling liquid film is analysed. Vapor production from the liquid film and the sputtered droplets can produce a countercurrent vapor velocity which exceeds the flooding limit, and rewetting becomes hydrodynamically-controlled rather than heat conduction-controlled. A criterion shows that conduction-controlled rewetting prevails at higher coolant flow rates and flooding conditions at lower flow rates. A solution is obtained for the liquid coolant vaporized during its fall from the sputtering film front. The required thermal radiation properties are also presented. Detailed calculation based on this analysis shows good agreement with experimental results.     

An analysis of rewetting of a nuclear fuel rod in water reactor emergency core cooling

An exact solution of the quasi-steady two-dimensional conduction equation for the rewetting of a nuclear fuel rod in water reactor emergency core cooling is obtained for a cylindrical rod geometry. The analysis adopts the conventional model of two heat transfer regions: zero heat transfer coefficient over the dry surface and a constant heat transfer coefficient over the wetted surface. Both the wet front velocity and the temperature distribution in the rod are computed. The present solution is valid over the whole range of Biot number.     

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.     

Quenching of hot oxidizing surfaces

A one-dimensional time-dependent rewetting model is developed and assessed to describe the interrelated processes of conduction, convective cooling and exothermic steam–metal reactions at the vapor zirconium-cladding interface during quenching of degraded fuel rods. Upstream of the quench front a constant heat transfer coefficient is assumed whereas a heat flux profile of general spatial shape may be prescribed downstream. The quenching velocity history and the temperature profile are computed analytically via a Green's function approach. Numerical results of the present model compare favorably with published 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.     

The effect of precursory cooling on rewetting of a slab

The Dua and Tien (1976) model for the rewetting of a slab with precursory cooling is solved exactly by separation of variables. The solution for the rewetting velocity is found to agree very well with a Wiener Hopf technique solution to this model by the author. Rewetting rates predicted by the approximate solution of Dua and Tien are found to agree with the present solution for small Peclet numbers, while underpredicting them for large Peclet numbers. Theoretical quench front velocities compare favorably with experimental data for copper quenched by liquid nitrogen. Precursory cooling is shown to be able to greatly increase the rewetting velocity, in particular for cases of high flow rates, while neglecting it in modelling may result in much too low quench velocities, as compared to experimental measurements.     

Review and comparison among the different models for rewetting in LWR's

Rewetting of light water reactor fuel rods after a loss of coolant accident corresponds to the re-establishment of water contact with the hot surfaces. A considerable number of analytical and numerical models have been developed in order to solve the heat condition problem in the fuel pin and predict the rewetting velocity. A comparison among the existing models has been performed. Recommendations and suggestions are outlined.     

A general one-dimensional model for conduction-controlled rewetting of a surface

A computer-oriented analytical method for predicting the rewetting rate of a hot dry wall is proposed. The wall, which is modeled as a thin flat plate with internal heat generation, receives a variable heat flux from one side while it is cooled from the other side. The model accounts for the large variations of the heat transfer coefficient near the wet front and for the temperature dependence of the thermal and physical properties of the wall. The one-dimensional heat-conduction equation is solved by dividing the quenching zone into small segments of arbitrary temperature increment and constant properties and heat transfer coefficient. A trial-and-error method is developed to predict the velocity of the wet front, the length of the quenching zone and the temperature profile. The one-dimensional models of other authors can be obtained as particular cases of the present model.     

A method for determining rewetting velocity under generalized boiling conditions

A method is presented for the solution of the quasi-steady state two-dimensional rewetting conduction problem. Using the method of separation of variables, a solution is presented for the case of an arbitrary heat transfer coefficient profile. Numerical results are also presented for the particular case in which a sputting region exists immediately behind the wet front. These results show that value of the heat transfer coefficient in the sputtering region determines the rewetting temperature if the sputtering region length exceeds one quarter of the class thickness. The numerical results in general show that the rewetting phenomenon is very localized with respect to the wet front. Results are compared favorably with experimental data in the low to moderate flow rate range.     

Analysis of Precursory Cooling in Quenching Phenomena

It has been noted that precursory cooling plays an important role in quenching phenomena. In this work, a new model is presented by assuming that the heat transfer in precursory cooling is mainly due to film boiling, which persists in a finite length. Then the quench velocity and temperature profile are obtained based on the three-region model for one- dimensional axial heat conduction in a heated tube. We applied our model to several existing experimental results and obtained a correlation to predict the effective length of precursory cooling region. It turns out that the correlation takes an identical form for both falling-film rewetting and bottom flooding.     

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.     

An experimental study on rewetting phenomena in transient conditions of bwrs

It is known that rod temperature rise after boiling transition (BT) is not excursive and that the peak cladding temperature (PCT) is suppressed by rewetting to return to nucleate boiling, even if BT occurs under severe conditions exceeding abnormal operational transients for a BWR. The purpose of this study is to develop and verify the rewetting correlation. The rewetting correlation was developed based on single rod data, as a function of quality, mass flux, pressure and heat flux. The transient thermal-hydraulic code used in the BWR design analysis (SCAT) with this rewetting correlation was compared with transient rod temperature result after the occurence of BT obtianed by the 8×8 and 4×4 rod bundle. It is concluded that the transient code with the developed rewetting correlation predicts the PCT conservatively, and the rewetting time well.     

The physics of rewetting in water reactor emergency core cooling

Surface rewetting is essential for the re-establishment of normal and safe temperature levels following dryout in rod clusters or boiler tubes, or following postulated loss-of-coolant accidents in water reactors. Rewetting experiments have been performed with tubes and rods with a wide range of materials and experimental conditions (surface temperatures 300–800°C, constant water flows 0.1–30 g s⁻¹). The physical processes involved in the rewetting of high temperature surfaces have been shown to be identical for both falling water films and bottom flooding. The variation of rewetting velocity with mass flow has been determined, and shown to be independent of hydraulic diameter over the range 0.2–6 mm of practical interest. Data have also been obtained on the mass ‘carryover’ fraction. Theoretical solutions for the rewetting velocities have been obtained by analysis of thermal conduction in the surface. At low mass flows, effectively one-dimensional (axial) conduction cools the surface ahead of the rewetting front, and gives agreement with experiment. At higher mass flows the rewetting velocity is substantially independent of surface thickness and conductivity. The present data and the available world data for rewetting are shown to be in agreement with the theory.     

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.