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.     

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 mathematical model for investigation of the rewetting of fuel rods

The computer model ZETHYF simulating the reflood phase after a loss-of-coolant accident with emphasis on the investigation of coolant channel is described. The thermal behaviour of the fuel rod is modeled based on a detailed representation of the heat transfer mechanisms and a moving mesh around the quench front. The flow conditions in the coolant channel are simulated as a one-dimensional transient one- or two-phase flow.     

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.     

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.     

Calculations on the rewetting of hot surfaces

Previous theoretical and experimental work has shown that the rate of advance of a quench front over a hot surface is a function of the initial temperature, the thickness and the physical properties of the hot surface, and the cooling water flow conditions. The heat conduction problem, which determines the quench rate, is solved accurately by an analytic method which requires a computer. The results, based on a constant heat transfer coefficient in the wetted region, can be applied to most conditions of practical interest, and are applied to determining the quenching heat transfer coefficient and the sputtering temperature from previous experimental results at high pressures, with cooling water near its saturation temperature.     

Extended dryout and rewetting of small-particle core debris

Extended dryout of core debris, especially the location, size and temperature distribution of the dry zone and the variation of these parameters with time and power density (down to rewetting) was studied with volume-heated beds. The beds were composed of small, spherical stainless steel particles and water was used as coolant. In addition, transient rewetting was investigated starting with a dry bed of uniform temperature.     

Theoretical spectrum-threshold detector data correlation in EBR-II

An experimental and computer program to further examine the neutron environment in the Experimental Breeder Reactor-II (EBR-II) has been completed. Monte Carlo and S₄ Transport methods were used to determine the neutron spectrum at various positions in the EBR-II core and blanket regions. Response functions for the threshold detectors ⁵⁸Ni (n, p) ⁵⁸Co and ⁵⁴Fe (n, p) ⁵⁴Mn were determined for each position and the corresponding predicted induced activities are compared with experimental results. Based on combinations of calculated neutron spectra, experimental detector responses, and cross section end points an empirical differential cross section was determined for the ⁴⁶Ti (n, p) ⁴⁶Sc threshold reaction. Spectrum averaged cross sections for the three threshold reactions which have been determined at various positions in this facility suggest that significant errors in fast neutron fluences will result if the usual fission spectrum averaged cross sections are used.     

Heat transfer during the rewetting of hot horizontal channels

The heat transfer in the rewetting of hot horizontal channels is investigated. The physical model assumes an inclined rewetting front advancing at a uniform velocity. Precursory cooling in the dry region is considered. Three-dimensional energy equations are solved numerically by a finite difference method. Further, the axial and circumferential temperature distributions are predicted. The influence of various parameters on the rewetting velocity is analyzed, as are the variations of the different heat transfer mechanisms, convection to the fluid and conduction in the three-dimensions, as a function of time.     

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.     

Simulation of the water/freon-113 rewetting process

The paper is concerned with improving our knowledge of the rewetting phenomena which might occur following a loss-of-coolant accident.An analysis on the available steam environment and vapour freon-113 environment rewetting experimental data was performed in order to give a simulation law valid for these two liquids. The simple scaling factor given and also the more general correlation derived extend the freon-113 results to the water range of interest.     

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.     

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.     

Damage function data correlation for the yield stress of iron

The effectiveness of the damage function analysis method of correlating experimental irradiation effects data and predicting material responses in different neutron environments is investigated. Major sources of uncertainty in damage function analysis including the questions of existence, uniqueness and data error propagation are investigated. The semi-empirical damage function and its estimated errors for iron irradiated at about 80°C to fluences of 10¹⁸−10²⁰/n/cm² are analyzed for comparison with other common correlation procedures. The study indicated that damage function analysis can, under certain conditions, be an effective means of establishing both nominal and lower bound fluence for reactor components.     

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.     

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.     

An analytical solution to fuel-and-cladding model of the rewetting of a nuclear fuel rod

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 fuel-and-cladding model. A method of solving non-separable differential equations is presented, which is used in the present analysis. The recently developed theorem of orthogonality of piecewise continuous eigenfunctions is also used to handle the composite rod in the present model. The present analysis reveals that the wet front velocity increases with the increase of the gap resistance between the fuel and the cladding, and approaches a limiting value, which is equal to the wet front velocity of the tube of cladding alone, as the gap resistance becomes infinite. For convenience in practical application, the results of the present analysis are correlated in simple expressions.     

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.     

Experimental investigation of the rewetting process in a freon-113 vapour environment

An experimental facility to simulate two-phase high-pressure flow phenomena using low-pressure Freon-113 has been built, commissioned, and employed to investigate the rewetting process of hot surfaces in a Freon-113 environment at pressures up to 5.43 bar. The experimental results and the correlations derived show good agreement with previous results using water and confirm the feasibility of simulating rewetting phenomena in water by the use of Freon.