Page 385 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

348 Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

pursued in parallel in OpenFOAM, strengthening the redundancy and diversification
strategy.
The aim in OpenFOAM was to develop a solver, MyrrhaFoam, using the open-
source simulation platform OpenFOAM, in such a way not to be restricted by license
costs and to be able to use the available computational capacity. In this framework, a
simplified model was considered, and the primary aim was to simulate the operating
condition of the reactor. Some aspects of the physical modeling will be discussed in
the following.

6.2.4.2.5 Buoyancy treatment
An essential difference between the two models relates to the way buoyancy is taken
into account. In the STAR-CCM+ model, the LBE density depends on temperature,
and buoyancy arises naturally from applying the gravity force, while the OpenFOAM
model is based on the Boussinesq approximation.
In the Boussinesq approximation, buoyancy is introduced only through a forcing
term in the momentum equation dependent on temperature, gravity, and the LBE ther-
mal expansion coefficient. The LBE density is kept constant, and the flow remains
divergence-free, allowing to take profit from all the methodologies and algorithms
requiring this property. The approximation is valid in the measure of small density
variations that, in our case, can reach about 1% for the main flows, up to 2% in
the core, and slightly more but very locally during some incidental transients. Another
advantage of this approximation is that the mass and the volumes are conserved
together. In a pool-loop configuration, this is particularly relevant as the pool can
safely be hydraulically closed and separated from the external world.
On the other hand, allowing the density to vary with temperature, at fixed LBE
inventory, its volume can change. We recall that the cover gas is set at constant den-
sity. Thus, during thermal transients, the extra volume produced must be expelled
from the numerical domain. In case of volume contraction, some additional volume
must be put in. The evacuation can be done through a pressure outlet, typically
arranged at the top of the numerical domain. The insertion can be done with a similar
stagnation inlet. Historically, an outlet boundary was not compatible with an inflow
condition (even locally) and could result in divergence of the simulation, idem for an
outlet flow condition in a stagnation pressure inlet. Close to steady state, we can
expect to have locally both slight inflow and outflow condition together at the same
boundary. To avoid possible instabilities, a simple trick consists in coupling the ded-
icated boundary with a local volumetric source in the relevant equation (the cover gas
volume fraction in STAR-CCM+) if the boundary is set as outlet or with a sink if it is
taken as inlet. The source/sink must be dimensioned so as to ensure the right natural
condition at the boundary during all the time of the simulation. A corresponding
source/sink must, obviously, be implemented in the energy equation.

6.2.4.2.6 Global control

As already mentioned, the STAR-CCM+ model is based on the VOF framework and
cannot afford steady-state simulations. Only physical transients are allowed. Bringing
the numerical model close to a steady-state nominal condition requires a long physical