Page 381 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

344 Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

The advantage of such diversity is that the know-how would be preserved in case
of inability of one partner or of one commercial code. Moreover, it would help to
understand the pros, the cons, or the redundancy of commercial versus open-source
software.

6.2.4.2.2 Gross numbers—order of magnitude analysis
3
From a practical point of view, about 400m of CFD domain have to be modeled.
Let’s make an order-of-magnitude study: keeping in mind the future transient appli-
cations, an upper limit for the number of mesh cells should be around 10 million,
assuming a moderately sized computer cluster. That means that the mean cell (control
3
volume) size is around 40cm giving an equivalent cell length of 3.4cm. To preserve
some margin for the more interesting crucial parts, this base size should be increased
to 5cm in the large bulk regions and reduced to 2cm near the walls and in partic-
ular densely structured regions. Affording 100–200 CPUs, this leads to the ratio of
50,000–100,000 cells per CPU, for which the parallel speed up is still quite good even
for complex simulations.
The well-known CFL condition (or constraint) essentially states that the flow enter-
ing a control volume integrated over a single time step should not exceed too much the
volume of the cell. Allowing ourselves some margin with this constraint and using the a
priori knowledge that the flow speed will approach 2m/s, we can take as a first guess a
typicalvalueof0.02sforthetimestep.Agoodestimationforthecalculationtimeofone
time step is 30–35s corresponding to 2–2.5s of physical time that can be simulated per
hour of simulation. In other words, we can hope to simulate 1min of physical time per
full day. This means that accessible transients of interest should not last for more than a
few minutes of physical time, and only exceptionally for a few tens of minutes.
In practice, during the initial transient, the equilibrium between the principal mass
flows is reached in about 30s for a single-phase model and in about a minute for a
volume-of-fluid (VOF) model, the latter requiring in addition to reach a dynamic equi-
librium of the free surface level. Then, the flow adapts in about 20s to further small to
medium flow perturbations such as adjustments of the pump thrust or some resistance
parameter. Reaching a reasonable steady-state temperature field definitely requires a
much longer time.
The first volumes that can hopefully reach a reasonable steady state are the hot
plenum and the main part of the cold plenum. Pursuing for quite a long time the sim-
ulations, then, the other volumes, of less functional importance, will slowly and pro-
gressively reach a thermal equilibrium. One should be aware that the convergence of
the thermal field could be quite different than the convergence of the momentum field.
One way to alleviate this multitimescale problem is either to perform local time
stepping, which in practice accelerates the local propagation of information mainly
in stagnant regions and in the structures, or to perform a frozen-field simulation, in
which only the temperature field is calculated and updated, thus running much faster.
These techniques are not available in all codes in combination with other models, for