F. B. Cheung

In-Vessel Retention of Molten Corium: Lessons Learned and Outstanding Issues

In-vessel retention (IVR) of core melt is a key severe-accident-management strategy adopted by some operating nuclear power plants and proposed for some advanced light water reactors (LWRs). If there were inadequate cooling during a reactor accident, a significant amount of core material could become molten and relocate to the lower head of the reactor vessel, as happened in the Three Mile Island Unit 2 accident. If it is possible to ensure that the vessel head remains intact so that relocated core materials are retained within the vessel, the enhanced safety associated with these plants can reduce concerns about containment failure and associated risk. For example, the enhanced safety of the advanced 600 MW(electric) pressurized water reactor (AP600) designed by Westinghouse, which relied upon external reactor vessel cooling (ERVC) for IVR, resulted in the U.S. Nuclear Regulatory Commission approving the design without requiring that certain features common to existing LWRs, such as containment sprays, be safety related. Clearly, ERVC offers the potential to reduce the AP600’s construction and operating costs. However, it is not clear that the ERVC proposed for the AP600 could provide sufficient heat removal for higher-power reactors [up to 1500 MW(electric)] without additional enhancements. This paper reviews efforts made and results reported regarding the enhancement of IVR in LWRs. Where appropriate, the paper identifies what additional data or analyses are needed to demonstrate that there is sufficient margin for successful IVR in high-power thermal reactors.

A hydrodynamic critical heat flux model for saturated pool boiling on a downward facing curved heating surface

Abstract A theoretical model is developed to predict the critical heat flux (CHF) limit for saturated pool boiling on the outer surface of a heated hemispherical vessel. The model considers the existence of a microlayer underneath an elongated vapor slug on a downward facing curved heating surface. The micro-layer is treated as a thin liquid film with numerous micro-vapor jets penetrating it. The micro-jets have the characteristic size dictated by Helmholtz instability. Local dryout is considered to occur when the supply of fresh liquid from the two-phase boundary layer to the micro-layer is not sufficient to prevent depletion of the liquid film by boiling. A boundary layer analysis, treating the two-phase motion as an external buoyancy-driven flow, is performed to determine the liquid supply rate and thus the local critical heat flux. The model provides a clear physical explanation for the spatial variation of the CHF observed in experiments and for the weak dependence of the CHF data on the physical size of the vessel.

A model for droplet entrainment in heated annular flow

Abstract The ability to accurately predict droplet entrainment in annular two-phase flow is required to effectively calculate the interfacial mass, momentum, and energy transfer, which characterizes nuclear reactor safety, system design, analysis, and performance. Most annular flow entrainment models in the open literature are formulated in terms of dimensionless groups, which do not directly account for interfacial instabilities. However, many researchers agree that there is a clear presence of interfacial instability phenomena having a direct impact on droplet entrainment. The present study proposes a model for droplet entrainment, based on the underlying physics of droplet entrainment from upward co-current annular film flow that is characteristic to light water reactor safety analysis. The model is developed based on a force balance and stability analysis that can be implemented into a transient three-field (continuous liquid, droplet, and vapor) two-phase heat transfer and fluid flow systems analysis computer code.

Theoretical Modeling of Intumescent Fire-Retardant Materials

A theoretical model is developed to predict the thermochemical be havior of intumescent fire-retardant coatings. The model is based on the assump tion that the intumescent reaction is analogous to the phase change process occurring over a finite temperature range. From the numerical results, it is found that the histories of the substrate temperature can be accurately predicted by choosing adequate pseudo latent heat and temperature range for the intumes cent reaction, and the bending evidence observed in experiments can be success fully predicted by the present intumescence model. Finally, it is shown that the present model can readily be extended to simulate the intumescent process with multi-intumescent zones.

Two-phase gas bubble-liquid boundary layer flow along vertical and inclined surfaces

Abstract The behavior of a two-phase gas bubble-liquid boundary layer along vertical and inclined porous surfaces with uniform gas injection is investigated experimentally and analytically. Using argon gas and water as the working fluids, a photographical study of the two-phase boundary layer flow has been performed for various angles of inclination ranging from 45° to 135° and gas injection rates ranging from 0.01 to 0.1 m/s. An integral method has been employed to solve the system of equations governing the two-phase motion. The effects of the gas injection rate and the angle of inclination on the growth of the boundary layer have been determined. The predicted boundary layer thickness is found to be in good agreement with the experimental results. The calculated axial liquid velocity and the void fraction in the two-phase region are also presented along with the observed flow behavior.

Numerical Study of Transient Thermal Ablation of High-Temperature Insulation Materials

A physical model has been developed to describe the transient ablation phenomena of high-temperature insulation materials for the cases with and without the formation of a melt layer on the material surface. The model takes account of the effects of transient melt-layer formation, variable ablation temperatures, and heat of ablation of the material. Validity of the model has been demonstrated numerically by comparison with available analytical solutions for the special case of a constant ablation temperature. For the general case of variable ablation temperatures, appreciable differences in the predicted ablation rates have been found between the cases with and without melt-layer formation for materials having low heats of ablation and for large imposed external heat fluxes. The present study clearly indicates that the melt-layer effect cannot be neglected at high external heat fluxes, especially for materials such as MXBE-350 that have low heats of ablation.

FINITE-DIFFERENCE ANALYSIS OF GROWTH AND DECAY OF A FREEZE COAT ON A CONTINUOUS MOVING CYLINDER

The process of freeze coating of a polymeric melt on an axially moving continuous cylinder is studied numerically by a finite-difference method, taking into account heat convection from the melt to the freeze coat and spatial variation of the cylinder temperature. The solid-liquid interface location is immobilized in the finite-difference analysis of the problem by transforming the system of equations governing the behavior of the freeze coat and the cylinder temperature into a dimensionless space. Various controlling parameters of the system are identified and their effects on the growth-and-decay behavior of the freeze coat are determined. Also determined are the maximum freeze-coat thickness and the corresponding axial location, based on which criteria for selection of the optimum freeze-coating operation conditions are established. The accuracy of the computational scheme is demonstrated by comparing the numerical results with the similarity solutions that are valid at small dimensionless axial locations.

Limiting factors for external reactor vessel cooling

Abstract The method of external reactor vessel cooling (ERVC) that involves flooding of the reactor cavity during a severe accident has been considered a viable means for in-vessel retention (IVR). For high-power reactors, however, there are some limiting factors that might adversely affect the feasibility of using ERVC as a means for IVR. In this paper, the key limiting factors for ERVC have been identified and critically discussed. These factors include the choking limit for steam venting (CLSV) through the bottleneck of the vessel/insulation structure, the critical heat flux (CHF) for downward-facing boiling on the vessel outer surface, and the two-phase flow instabilities in the natural circulation loop within the flooded cavity. To enhance ERVC, it is necessary to eliminate or relax these limiting factors. Accordingly, methods to enhance ERVC and thus improve margins for IVR have been proposed and demonstrated, using the APR1400 as an example. The strategy is based on using two distinctly different methods to enhance ERVC. One involves the use of an enhanced vessel/insulation design to facilitate steam venting through the bottleneck of the annular channel. The other involves the use of an appropriate vessel coating to promote downward-facing boiling. It is found that the use of an enhanced vessel/insulation design with bottleneck enlargement could greatly facilitate the process of steam venting through the bottleneck region as well as streamline the resulting two-phase motions in the annular channel. By selecting a suitable enhanced vessel/insulation design, not only the CLSV but also the CHF limits could be significantly increased. In addition, the problem associated with two-phase flow instabilities and flow-induced mechanical vibration could be minimized. It is also found that the use of vessel coatings made of microporous metallic layers could greatly facilitate downward-facing boiling on the vessel outer surface. With vessel coatings, the local CHF limits at different angular locations of the vessel outer surface could be enhanced by ~1.2 to 2 times the CHF compared with a plain vessel without coatings. The CHF enhancement could be attributed to the structure of the porous coating itself and the capillary action it induced. The matrix of cavities and voids within the coating effectively trap vapor, which serve as active nucleation sites. These sites in turn are fed with liquid flowing through the interconnected channels. The pores on the surface of the porous coating serve as flow inlets for liquid supply to the heating surface, leading to appreciable enhancement in downward-facing boiling heat transfer and the local CHF limits. Results of the present study suggest that by utilizing an enhanced vessel/insulation design with vessel coating, it is possible to significantly enhance the CLSV and the CHF limits as well as minimize the two-phase flow instability problems, thus substantially increasing the margin for IVR.

Behavior of the Two-Phase Mushy Zone During Freeze Coating on a Continuous Moving Plate

The process of freeze coating of a binary substance on a chilled moving plate is studied theoretically with special emphasis on the behavior of the two-phase mushy zone. The flow and heat transfer in five separate regions of the system, i.e., the moving plate, the freeze coat, the two-phase packing region, the two-phase dispersed region and the molten substance region, are formulated mathematically to describe the freeze-coating process. A supplemental equation derived from a simplified phase diagram and an appropriate viscosity model are employed to complete the mathematical description of the two-phase mushy zone. The system of equations is solved by a combined analytical-numerical technique to determine the spatial variations of the solidus and liquidus fronts. Effects of seven controlling parameters, including the freeze coat-to-wall thermal ratio, the wall subcooling parameter, the molten substance superheating parameter, the Prandtl number, the Stefan number, the equilibrium partition ratio, and the packing limit fraction, on the behavior of the two-phase mushy zone and the freeze-coating process are determined.

Boundary-layer-boiling and critical-heat-flux phenomena on a downward-facing hemispherical surface

A subscale boundary-layer boiling (SBLB) test facility was developed with the aid of a scaling analysis to simulate the phenomena of pool boiling and critical heat flux (CHF) on the external bottom surface of a heated hemispheric vessel. Saturated and subcooled boiling experiments were performed in the SBLB facility to measure the spatial variation of the CHF and observe the underlying mechanisms, including the vapor dynamics and the resulting buoyancy-driven two-phase boundary-layer flow along the downward-facing hemispheric heating surface. Based on the experimental evidence and an advanced hydrodynamic CHF model, a scaling law was established for estimating the local CHF on the vessel outer surface. The scaling law, which compared favorably with the available CHF data obtained for various vessel sizes, was shown to be useful in predicting the local CHF limits on large commercial-size vessels. Additional work, however, is needed to determine the effect of thermal insulation.