Page 90 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Rod bundle and pool-type experiments in water serving liquid metal reactors 65

3.1.2.4.5 Flow-induced vibrations

In LMFRs, the low-frequency-induced vibrations (0 50 Hz) are considered as a
potential risk for the fuel assembly integrity and therefore they need to be studied both
experimentally and numerically. When studying the flow-induced vibrations (FIV,
being a specific case of fluid-structure interaction [FSI]) of a rod as part of a bundle
flow experiment, the rod behavior can be described by the fourth-order partial differ-
ential equation given by Chen (1985):

4
2
2
2
2
∂ x 2 ∂ x ∂ x 1 m a U 2 1 ∂ x ∂ x
EI + m a U + C T l z +2m a U
∂z 4 ∂z 2 ∂t 2 2 D 2 ∂z 2 ∂z∂t (3.1.21)
2
1 m a U ∂x ∂x ∂x ∂ x
+ C N U + + C V + m ¼ gðx,tÞ,
2 D ∂z ∂t ∂t ∂t 2
where E is the Young modulus of the rod, I is the moment of inertia of the rod, x is the
rod radial displacement, z is the axial coordinate along the rod, m a is the added mass
that includes the additional force exerted by the fluid as the rod moves, C m is the added
mass coefficient as defined by Pettigrew and Taylor (1994) that includes the confine-
ment effects of the surrounding rods of the bundle, U is the mean axial flow velocity,
C T is the longitudinal viscous force coefficient whose definition is given by Hoerner
(1965), D is the rod diameter, l is the rod length, C N ¼ C T is the normal drag force
coefficient, C V is the viscous damping coefficient (Sinyavskii et al., 1980), and
g(x, t) accounts for random turbulence effects. Eq. (3.1.21) can be solved with the
Galerkin method and the natural frequencies of vibrations plotted against the flow
velocity. Eq. (3.1.21) helps to design the experimental rod bundle with respect to
choices regarding rod geometry and material. A facility for FIV experiments in an
hexagonal rod bundle (SEEDS-1) is under construction at Delft University of Tech-
nology where a part of the central rod is flexible and the vibrations induced by the
presence of gap vortex streets along the rod are to be studied. The length of the flexible
part has to be comparable with the expected size of the coherent structures in order to
expect vibrations of the central rod. The choice of the rod bundle geometry and mate-
rial properties of SEEDS-1 is based both on the solution of Eq. (3.1.21) and on the
CFD study by De Ridder et al. (2016), which shows that the stream-wise length of
the coherent structures is expected to be 7.35 cm. The length of the flexible rod is
set to 10 cm and is composed of silicone.

3.1.3 Fuel bundle experiments

Water-based bundle facilities are well suited to a range of phenomena that take place
in LM reactors. Most of these phenomena are not specific to LM reactors. Therefore, a
large knowledge based on relevant experimental techniques and facilities is available
in the literature. Because temperature fields are impossible to mimic experimentally
due to the much lower Pr number in LM systems, the phenomena described here are
related to the flow field only.