René Girard

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Nuclear Engineering


Dr. J.-S. Chang


Reflux condensation in vertical inverted U-tube steam generators forms an important heat removal mechanism for nuclear reactors in certain accidents. Reflux condensation phenomena in single vertical tubes were studied for two well defined boundary conditions to develop an improved understanding of the mechanisms governing heat removal and liquid holdup. A correspondence between an imposed boundary condition and its resulting flow regime has been made where total reflux condensation occurs for an imposed drop across the tube and fill and dump cycling occurs for an imposed steam flow rate at the tube inlet.

Total reflux condensation is characterized by a flow pattern made by a single-phase region oscillating over a two-phase region. This flow region can be maintained indefinitely while the average single-phase and two-phase region lengths remain constant. It is also characterized by the complete condensation of the injected steam with all the condensate flowing back to the tube inlet.

Fill and dump cycling is characterized by a cyclical operation where, during one cycle, the length of the single-phase region increases at the expense of the two-phase region until a point where the system becomes unstable and the single-phase region is ejected from the top of the tube. All the injected steam is condensed and contrary to total reflux condensation, not all the condensate flows back to the tube inlet. Instead, part of the condensate is carried over the condensation length to form the single-phase region. This flow regime could be qualified as dynamic as opposed to quasi-static for total reflux condensation.

Experimental measurements were made in three single vertical tubes with a cooling jacket. These data show fill and dump cycling to be more efficient than total reflux condensation in condensing steam and to allow the condensate not to be trapped in the tube as in total reflux condensation. In addition, the experimental data suggest that total reflux condensation could be well the limiting flow regime for fill and dump cycling as the cycle period becomes very long and consequently it could define conservative lower bounds for the values of total heat removal.

An analysis of counter-current film-wise condensation was conducted to model total reflux condensation, central to this model is an extended Nusselt's model of film-wise condensation, a linearized stability analysis of the condensate film flow and the use of three concepts: critical layer, maximum mechanical energy and transfer and film instability. The agreement between the experimental data and the prediction of total heat removal (via condensation rates) and liquid holdup is satisfactory. Both the present model and the experimental data show that flooding occurs at the tube inlet and plays a key role in defining the heat removal and the distribution of condensate in the tube. In particular, it is shown that for a given inlet cooling water temperature, the flooding flow rates, in terms of the Kutateladze variable, are nearly independent of the tube size and system pressure. In general, for a given tube size and system pressure, the inlet cooling water temperature has a notable influence on the value of the flooding flow rates, except for the smaller tube size, and it does not affect the amount of condensate holdup in the tube.

The results of the present work could be used in small-break LOCA analyses were the present model could estimate the heat removal capabilities of steam generators and the amount of coolant (condensate holdup) trapped in the steam-generator tubes that would be available for core cooling.

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