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# Development, Implementation, and Assessment of Specific Closure Laws for Inverted-Annular Film-Boiling in a Two-Fluid Model (NUREG/IA-0133, CAMP004)

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## Publication Information

**Date Published:** October 1996

**Prepared by:** Francois de Cachard

Thermal-Hydraulics Laboratory Paul Scherrer Institute CH-5232 Villigen PSI Switzerland

**Prepared as part of:** The Agreement on Research Participation and Technical Exchange under the International Thermal-Hydraulic Code Assessment and Maintenance Program (CAMP)

Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission Washington, DC 20555-0001

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## Abstract

Inverted-Annular Film-Boiling (IAFB) is one of the post-burnout heat transfer modes taking place, in particular, during the reflooding phase of the loss-of-coolant accident, when the liquid at the quench front is subcooled. Under IAFB conditions, a continuous liquid core is separated from the wall by a superheated vapour film.

The heat transfer rate in IAFB is influenced by the flooding rate, liquid subcooling, pressure, and the wall geometry and temperature. These influences can be accounted by a two-fluid model with physically sound closure laws for mass, momentum and heat transfers between the wall, the vapour film, the vapour-liquid interface, and the liquid core. The applicability of existing IAFB two-fluid models is limited. This is attributed to shortcomings in the description of heat transfer within the liquid core, to the use of certain correlations outside their validity range, and to a limited use of experimental information on IAFB. The usual approach has been to develop models employing generally applicable closure lawsincluding, however, adjustable parameters, and to adjust these using global experimental results. The present approach has been to develop IAFB-specific closure laws in such a form that they could be adjusted separately using detailed, IAFB-relevant, experimental results. Steady-state results, including heat flux, wall temperature and void fraction data have been used for the adjustment.

A key issue in IAFB modeling is to predict how the heat flux reaching the vapour-liquid interface is split into a liquid heating term and a vaporization term. In the model proposed, convective liquid heating is related to the liquid velocity relative to the interface, and not to the absolute liquid velocity, as in previous models. This relative velocity is deduced from the interfacial shear stress, using the liquid-interface friction law. With this modification, the prediction of the experimental trends is greatly improved.

The non-smoothness of the vapour-liquid interface may considerably enhance interfacial transfers. Complex physical processes are involved, such as waves, oscillations of the liquid core, droplet entrainment and redeposition, and turbulence in the vapour film. In the closure laws proposed, these effects are accounted by semi-empirical laws based on simple physical models. The vapour film is divided into a laminar sublayer near the wall which controls heat transfer, and a well-mixed sublayer near the interface. The ratio of the laminar sublayer thickness to the total film thickness has been empirically correlated. Semi-empirical expressions have also been developed for the vapour and liquid friction factors. The main correlating variable used is a non-dimensional film thickness, which is shown to be representative of the degree of irregularity of the interface, and may be easily derived from void fraction measurements. Three possible geometries of the liquid core are considered: flow in a tube, and in square- or triangular-lattice rod bundles. Heat transfer within the liquid core is deduced from momentum transfer using the Chilton-Colburn analogy.

The model is extensively assessed against forced flow, low quality post-dryout data from four independent sources. A total of 52 experiments have been analysed. The quench front velocity, the initial flow parameters just downstream from the quench front, and the wall temperature distribution in the dry region are carefully derived from the measurements and given as inputs to the model. The model then predicts the heat flux and void fraction distributions, which are compared with the experimental values. The overall predictions are good. The model is shown to apply to steady-state as well as to transient (reflooding) conditions, with very different geometries, i.e. tubes and rod bundles with hydraulic diameters ranging from 4 to 14 mm, and for large parameter ranges, i.e. 3 to 50 cm/s in flooding rate, 0 to 30 °C in subcooling, 1 to 4 bar in pressure, and 300 to 1000 °C in wall temperature.

The IAFB-specific closure laws proposed have also intrinsic value, and may be used in other two-fluid models. They should allow to improve the description of post-dryout, low quality heat transfer by the safety codes.

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