2013 1(12)

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   Long abstract



375 - 381






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Abramov A.G., Ivanov N.G., Kovalev G.A., Smirnov E.M.

Saint Petersburg State Polytechnical University (National Research University), Saint-Petersburg, Russia


turbulent convection, heat and mass transfer, film condensation, non-condensable gases, numerical simulation


Nowadays, very significant resources are assigned to improve the operational safety of nuclear power reactors. In new projects, focused on the use of pressurized water reactors (PWR), protective systems based on free-convection mechanism of the decay heat removal from the containment volume in case of accidents are under extensive development. It is assumed that the water vapor produced during Loss of Coolant Accident (LOCA) is removed by condensation on the vertically oriented heat exchangers installed in the under-dome space or on the walls of the containment. Condensation of the steam occurs in the presence of non-condensable gases (hydrogen and air), which reduces significantly the heat transfer rate. Heat exchangers are typically constructed as a row of spaced vertical tubes internally cooled with water. The effectiveness of such the heat removal system, among other factors, is influenced by its structural characteristics (in particular, the distance between the tubes). This question of considerable interest has not been studied in any detail.


The work covers numerical investigation of turbulent convection of steam-air mixture in a confined enclosure under conditions of film condensation of steam on an infinite row of cooled vertical tubes located in the central part of an enclosure. The aim of the computations is to study the influence of the distance between the tubes on the flow structure and heat transfer characteristics.


The problem was formulated for the domain in a form of an infinite rectangular enclosure (4 m high and 0.45 m wide) with an infinite row of vertical cylindrical tubes immersed in the central part of the domain. The tubes characterized by height of 3.5 m and an outer radius R = 0.019 m, were placed at equal distance from each other. Due to the symmetry of the problem, the computations were carried out for the domain containing one quarter of a tube. The analysis was performed for five geometries with different distance between the tubes, which was in the range of 0.5R6R. Two formulations of the problem were considered. In the first, simplified formulation free convection of air in the enclosure heated from below was studied. The second setup was aimed at numerical simulation of steam-air convection under conditions of condensation of steam on the outer surface of the cooled tubes with prescribing a uniform mass flow of hot steam at the bottom of the enclosure. Some geometrical and physical parameters were taken from an experimental work of Dehbi et al. (1991).

The mathematical model describes the low-speed turbulent convective flow of two-component steam-gas mixture, which takes place in the gravity field. The system of governing equations includes balance equations of mass, momentum and energy for the mixture as a whole, as well as the equation of steam transport. A 3D steady-state formulation based on the RANS approach with the SST turbulence model was used. The computations have been carried out using a 3D finite-volume CFD code developed at the Department of Aerodynamics of the St. Petersburg State Polytechnic University. This code (named SINF) has options to solve the problems of free and mixed convection of steam-gas mixture with the surface condensation in the presence of non-condensable gases.


On the base of the computational results obtained, a comprehensive analysis of the structure of the velocity, temperature and concentration fields, as well as the distribution of the heat flux on the surface of the tube was done. In both the setups, intense and qualitatively similar turbulent circulation flow with severe irregularities in the fields is formed in the enclosure under determining action of the buoyancy force. For the space between the tubes, the mixed convection flow is developed. Boundary layers with a prevailing content of the air, which are formed near the surfaces of the tubes, interact with a cocurrent descending external flow of the global circulation. It has been established that the structure of the flow in the vicinity of the tubes and heat flux non-uniformities at the surface of the tubes are very sensitive to the width of the tube space.


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