Two-phase thermal-hydraulics and heat transfer

In general, thermal hydraulic modelling of nuclear reactor systems is based on the onedimensional approach. Thermal hydraulic modelling of the steady state, transient and stability behaviour of two-phase natural circulation systems is no exception to this general approach. System codes have reached a highly developed modelling status and a wide acceptance. They 

Some of the most commonly adopted thermal hydraulic models applicable for the 1-D and multi-dimensional analyses are briefly described below  

These models consider either the thermodynamic or mechanical non-equilibrium between the phases. The number of conservation equations in this case are either four or five. One of the most popular models which considers the mechanical non-equilibrium is the drift flux model. If thermal non-equilibrium between the phases is considered, constitutive laws for interfacial area and evaporation/condensation at the interface must be included. In this case, the number of conservation equations is five, and if thermodynamic equilibrium is assumed the number of equations can be four. Well-assessed models for drift velocity and distribution parameter depending on the flow regimes are required for this model in addition to the heat transfer and pressure drop relationships. The main advantage of the drift flux model is that it simplifies the numerical computation of the momentum equation in comparison to the multi-fluid models. Computer codes based on the four or five equation models are still used for safety and accident analyses in many countries. These models are also found to be useful in the analysis of the stability behaviour of BWRs belonging to both forced and natural circulation type. 

Finally CFD codes have to be used for scaling up detailed results from model experiments to full-scale reactor conditions. They are also more and more used even for designing experiments and their instrumentation arrangement. They can also reliably be used to study in a more qualitative manner the relevance of certain phenomena in flow and heat transfer problems, so far as the governing physics is included in the equations or in the numerical modelling. Thus, they are also used to determine the dominant physical phenomena of nuclear flow problems, so that finally a reliable efficient numerical model configuration (input) can be formulated for a system code. 

For such cases, in which separated phases have to be considered, special numerical tools were developed to keep the interface sharp, like interface capturing, interface tracking, or some approximate numerical methods like surface sharpening. In case of dispersed flows special highly accurate numerical schemes would be required to avoid or at least minimize numerical diffusion, but most codes use standard lower order schemes thus one still has to live with more or less strong numerical diffusion. 

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