External coupling

In the external coupling, the whole core is cut out of the ATHLET plant model [Gru95a-c]. The core is completely modelled by DYN3D. The thermal hydraulics is split into two parts: one part describes the thermal hydraulics of the core, the other part models the coolant system. As a consequence of this local cut it is easy to define the interfaces. They are located at the bottom and at the top of the core. The pressures, mass flow rates, enthalpies and concentra- tions of boron acid at these interfaces have to be transferred. It is effectively supported by the GCSM of the ATHLET code. The external coupling uses the GCSM-interface. DYN3D is used within the GCSM formalism as an user defined subroutine. The coupling parameters are defined explicitly as so called GCSM-signals. These data are the above mentioned thermal- hydraulic parameters. The pressures at the bottom and the top of the core and the enthalpy at the bottom of the core are calculated by ATHLET. The interface routine transfers them to DYN3D as boundary conditions for the next DYN3D time step. The ATHLET model includes the special junction „FILL“. It enables the user to simulate a fluid injection or draw off within the ATHLET input data set. The mass flow rate, and in the case of flow injection, additionally the enthalpy of the injected fluid, have to be given to the FILL. These parameters are boundary conditions for the thermal hydraulics of the ATHLET model. The use of this special ATHLET- junction for the coupling leads to the following strategy of interfacial data handling. The pres- sure at the bottom and at the top of the core and the enthalpy at the bottom of the core are cal- culated by ATHLET. The interface routine transfers them to DYN3D as boundary condition for the next DYN3D time step. Having finished the DYN3D calculation for one time step, the interface routine transfers the mass flow rates at the core inlet and core outlet and the enthalpy at the core outlet to ATHLET. These parameters are now boundary conditions for the next ATHLET time step.

The interface routine also coordinates the separate time step control in both parts of the pro- gram. DYN3D calculates as many time steps until the current DYN3D time is greater than the current ATHLET time. Before the data are transferred they are interpolated to the current ATH- LET time. For that reason, the DYN3D time steps can be larger as well as smaller than the ATHLET time steps. Therefore the time step size can be controlled by both codes independent- ly adopted to the needs of the codes.

The splitting of the thermalhydraulics into two independent submodels in external coupling caused stability problems in the coupled calculations. These difficulties were caused by numer-

ical reasons but not by physical compatibility of the models. The coupling of the two thermal- hydraulic parts is done explicitly and very small time steps are necessary for stable calculations. Test calculations showed that the numerical solution was stable for a maximum time step of about 0.01 s. The pressure drop over the core and the core mass flow rates oscillate in a random manner caused by numerical effects. This oscillations can be damped by interconnecting a low pass filter of first order for the pressure drop representing the boundary condition for the DYN3D calculation. This low pass filter does not alter the vector of solution but only the time dependent boundary conditions.

The well known differential equation for a low pass filter of first order is:

where t is the time constant of the filter, x(t) is the input and y(t) is the output. If DP_ATHLET is the pressure drop over the core calculated by ATHLET, DP_old is the pressure drop given as boundary condition to DYN3D at the last ATHLET time step and DP_new is the pressure drop given to DYN3D as boundary condition for the current time step, the equation (11.1) applied to the pressure drops can be written as follows:

That leads to:

The difference between DP_ATHLET and DP_new is split up to the absolute pressures at the bottom and the top of the core:

P_DYN,in = P_ATHLET,in - (DP_ATHLET - DP_new) / 2 (11.3) P_DYN,out = P_ATHLET,out + (DP_ATHLET - DP_new) / 2

In this way it is possible to solve these difficulties and to get stable calculations even for larger time steps. The calculations are numerically stable for all test cases if time constants of the low pass filter of 1 s or larger are choosen.

The low pass filter has practically no influence on the transients that are to be calculated. It only suppresses oscillations of the pressure drop over the core with high frequencies, caused by ran- dom numerical disturbances. There are no distortions even for strong transients, what has been shown by different sample calculations for test cases with fast and large changes of pressure drop over the core (e. g. large break LOCA and ejection of a whole control rod group, both as ATWS) [Gru95a, Gru95b].

y t( ) τ dy t( ) dt

--- ⋅

+ = x t( ) (11.1)

DP_new τ DPnew–DPold DT --- ⋅ + = DP_{ATHLET (11.2a)} DP_new 1 1+τ DT⁄ --- DP⋅ _ATHLET 1 1 1+τ DT⁄ --- – ⎝ ⎠ ⎛ ⎞ _DP old ⋅ + = (11.2b)