The primary and secondary instabilities of the sphere wake are investigated from
the viewpoint of nonlinear dynamical systems theory. For the primary bifurcation,
a theory of axisymmetry breaking by a regular bifurcation is given. The azimuthal
spectral modes are shown to coincide with nonlinear modes of the instability, which
provides a good reason for using the azimuthal expansion as an optimal spectral
method. Thorough numerical testing of the implemented spectral–spectral-element
discretization allows corroboration of existing data concerning the primary and
secondary thresholds and gives their error estimates. The ideal axisymmetry of the
numerical method makes it possible to confirm the theoretical conclusion concerning
the arbitrariness of selection of the symmetry plane that arises. Investigation of
computed azimuthal modes yields a simple explanation of the origin of the so-called
bifid wake and shows at each Reynolds number the coexistence of a simple wake and a
bifid wake zone of the steady non-axisymmetric regime. At the onset of the secondary
instability, basic linear and nonlinear characteristics including the normalized Landau
constant are given. The periodic regime is described as a limit cycle and the power of
the time Fourier expansion is illustrated by reproducing experimental r.m.s. fluctuation
charts of the streamwise velocity with only the fundamental and second harmonic
modes. Each time–azimuthal mode is shown to behave like a propagating wave having
a specific spatial signature. Their asymptotic, far-wake, phase velocities are the same
but the waves keep a fingerprint of their passing through the near-wake region. The
non-dimensionalized asymptotic phase velocity is close to that of an infinite cylinder
wake. A reduced-accuracy discretization is shown to allow qualitatively satisfactory
unsteady simulations at extremely low cost.
The experimental investigation of a prototypical set-up simulating a loss of flow accident in a helium-cooled breeding blanket first wall mock-up under typical heat load conditions is presented. The experimental campaign reproduces the expected DEMO thermal-hydraulics conditions during normal and off-normal situations and aims at providing some insight into the fast transients associated with the loss of flow in the blanket first wall. The experimental set-up and the definition of the experimental matrix are discussed, including pre-test analysis performed in support of these activities. The major experimental results are discussed, and a procedure of using the acquired data for validating and calibrating the RELAP-3D model of the mock-up is introduced. All these activities contributed to the creation of a relevant theoretical and practical experience that can be used in further studies concerning incidental transients in real-plant scenarios in the framework of DEMO plant fusion safety activities.
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