# Physical Models

## CATHARE, a system scale thermal-hydraulic software

## A Generic set of Components

The CATHARE code has a modular structure: several modules can be assembled to represent any hydraulic circuit. The three main hydraulic modules are:

- the 1-D module to describe pipes,

- the 0-D module to describe large capacities,

- the 3-D module to describe multidimensional effects in specific components.

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To complete the modelling of the circuits, hydraulic and thermal components can be connected to the main modules:

- multi-layer thermal wall in which radial conduction is calculated,

- heat exchanger between two elements of the same circuit or of two circuits,

- 1-node turbomachinery (pump, blower, compressor, turbine) which can be coupled to each others (in CATHARE 3 a predicitve one-dimensional turbomachinery model is also available),

- valve,

- source, sink and break,

- accumulator,

- fuel pin thermo-mechanics which can predict fuel cladding deformation, creep, rupture, clad oxidation and thermal exchanges,

- point neutronics (a 3-D neutronics code can also be coupled to CATHARE),

- Counter Current Flow Limitation (CCFL) module which may be connected at any junctions, or at any vector node of the 1-D module in order to predict it in complex geometries.

## A Generic set of Equations

All modules use by default the 2-phase model to describe steam-liquid flows and four non condensable gases may be transported. Both thermal and mechanical non-equilibrium of the two phases are described thanks to the 3 balance equations solved for each phase: mass, momentum and energy. All kinds of two-phase flow patterns are modelled. Only two transitions are explicitly written and used in several closure terms of CATHARE: the transition between stratified and no stratified flow and the transition between annular and droplets flows. These two transitions describe the passage from a separate flow to a dispersed flow. Heat transfer with wall structures and with fuel rods are calculated taking into account all heat transfer processes: natural and forced convection in both laminar and turbulent regimes, subcooled and saturated nucleate boiling, critical heat flux, dry-out criterion, rewetting temperature and transition boiling, film boiling for inverted annular, inverted-slug and dispersed flows, film condensation for effects of non-condensable gases, radiation, enhancement model downstream a quench front. CATHARE's closure laws represent 14 terms in the 6 balance equations which involves about 200 corelations deduced from literature and validated on separate effect tests.

## A Generic Numerical Resolution

The numerical method in the CATHARE code uses a first order finite volume - finite difference scheme with a staggered mesh and the donor cell principle. The time discretization varies from the fully implicit discretization used in the 0-D and 1-D modules to the semi-implicit scheme used in the 3-D module. These methods are known for their robustness in a wide range of flow configurations. A hyperbolic system of equations is used to ensure the well posedness of the problem. Mass and energy equations use a conservative form and are discretized in order to keep a very good mass and energy conservation. The phase appearing and disappearing problem is properly solved using some residual volume fractions and an appropriate conditioning of interfacial mass and energy transfers. The wall conduction is implicitly coupled to hydraulic calculations. The non linear system of equations is solved by a Newton-Raphson iterative method following several steps. The solution can be distributed over several processors in order to reduce the CPU time by parallel computing. This will allow real time calculation of reactor transients for the simulator application.

## A Specific Description of Fluids

The CATHARE default fluid is 2-phase water but other possibilities are available for:

- fluid equation of state (thermodynamic and transport properties) for which more than 150 fluids are available in CATHARE 3 by coupling with the REFPROP library,

- fluid closure relationships (mass transfers, wall friction, etc.),

- fluid number of phases (in CATHARE 3 only, it is possible to perform calculations in single-phase flow (gas or liquid), standard 2-phase flow or 3-phase flow (liquid droplets in the continuous gas phase).

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