Page 398 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Multi-scale simulations of liquid 7

metal systems

A. Gerschenfeld, N. Forgione, J. Thomas
DEN-Service de Thermohydraulique et de M ecanique des Fluides (STMF), CEA,
Universit e Paris-Saclay, Gif-sur-Yvette, France

7.1 Introduction and motivation

7.1.1 Modeling scales in reactor thermal-hydraulics
The thermal-hydraulic behavior of complex, large-scale systems such as nuclear reac-
tors is the product of a wide range of fluid-mechanics phenomena. In principle, these
phenomena can be modeled directly (at least for single-phase flows) through the direct
simulation of the Navier-Stokes equations. However, such a “reactor-scale DNS”
approach remains infeasible today, given that such a model would need to span a range
of scales between
l the microscopic scales associated with molecular diffusion (L 10 6 m and t 10 6 s)
6
l and the large scales associated with the behavior of the reactor itself (L 10 m and t 10 s
for long transients).
15
At first glance, a “reactor-scale DNS” model would thus require around 10 –10 18
elements and up to 10 10 transient time steps. While these estimates are probably
off by a few orders of magnitude, it seems likely that reactor-scale direct simulations
will remain unfeasible until the 2050s at the very least.
While this large range of time and space scales remains an obstacle to direct sim-
ulations, it also provides a path to an efficient way to model reactor thermal hydrau-
lics. In almost every case, the phenomena occurring at some small scale, although
complex, only affect the larger scales through their statistical averages (average
and sometimes variance), thanks to statistical self-averaging properties.
When such a “separation of scales” occurs, the overall effect of a given micro-
scopic phenomenon in a large-scale model can be represented, with a satisfactory level
of precision, through a simple model describing its average behavior. Such a model
can in turn be constructed
either by theoretical means, by assuming self-averaging properties of the small-scale equa-
l
tions (such hypotheses underlie the formulation of most turbulence models);
or by performing small-scale simulations of the local phenomenon of interest (in a range of
l
conditions appropriate to the intended application);
or by performing analytic or intermediate-scale experiments, under the relevant scaling laws,
l
to directly formulate a “correlation” for the phenomenon of interest. Such correlations are
widely used to model, at large scales, such commonly encountered effects as pressure drops

Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors. https://doi.org/10.1016/B978-0-08-101980-1.00007-7
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