Page 324 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

294 Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

In this chapter, the focus is not only on FSI simulation using URANS of axial flow
in tube bundles as present in nuclear reactor cores but also in heat exchangers and
chemical reactors. In Section 6.2.2.2, the vibration due to large-scale vortices in
the gaps between tubes in a bundle is calculated as an example of an instability-
induced vibration (based on De Ridder et al., 2016b, and De Moerloose, 2016). Sub-
sequently, movement-induced vibration in a bundle with axial flow is analyzed in
Section 6.2.2.3 (based on De Ridder et al., 2015, and De Ridder et al., 2013).

6.2.2.2 Instability-induced vibration: Vortex-induced
vibrations by axial flow in a bundle of tubes

6.2.2.2.1 Introduction
If a dense cluster of tubes is mounted in axial flow, a flow instability similar to a
Kelvin-Helmholtz instability has been observed (M€ oller, 1991). These periodic
large-scale vortices (Meyer and Rehme, 1994) arise from the interaction of the
high-speed flow in the subchannels and the low-speed flow in the gap between tubes.
An overview of the experimental research on large-scale vortices in axial flow is given
by Meyer (2010). As this phenomenon is a large-scale instability, it qualifies of being
computed by URANS, which was successfully done by several authors, for example,
Chang and Tavoularis (2012), Ninokata et al. (2009), and Chandra and Roelofs
(2011). In principle, turbulent scale-resolving simulations such as LES or DNS offer
an increased accuracy, but they also require significantly more computing power as
shown by Ninokata et al. (2009).
This section explains the prediction of vibrations occurring in tightly packed rod
bundles with axial flow. At first, the flow through such geometry with seven tubes
is computed with URANS. Based on those results, two cases are set up in which
one of the tubes is flexible and the resulting vibration is computed by means of
FSI simulations. The cases are constructed in such a way that fluid-elastic instabilities
are avoided and that all vibration results from the flow instability.

6.2.2.2.2 Methodology
The bundle in this study consists of seven tubes as shown in Fig. 6.2.2.1. The geomet-
ric parameters and material properties are given in Table 6.2.2.1. The inlet and outlet
of the domain are periodic, and a pressure gradient of 9810Pa/m is applied. The flow is
computed using URANS simulations with the k-ω SST model (Menter, 1994). The
computational fluid dynamic (CFD) simulations are performed with rigid tubes, while
the fluid-structure interaction is computed by coupling CFD with computational struc-
tural mechanics (CSM) simulations using finite element analysis (FEA). In the FSI
simulations, only one tube is flexible (either tube 0 or 1), and only a part of its length
is flexible. All the equations have been discretized with second-order schemes. The
fluid grid has five radial divisions (from a wall to the middle of the channel), 120 cir-
cumferential divisions per tube, and 480 in streamwise direction. This results in a non-
+
dimensional distance to the wall (y ) value between 2 and 85, using blended wall