Based on Guderley's self-similar solution, stability of spherical converging shock wave is studied. A rigorous linear perturbation theory is developed, in which the growth rate of perturbation is given as a function of the spherical harmonic number ℓ and the specific heats ratio γ. Numerical calculation reveals the existence of a γ-dependent cut-off mode number ℓc, such that all the eigenmode perturbations for ℓ > ℓc are smeared out as the shock wave converges at the center. The analysis is applied to partially spherical geometries to give significant implication for different ignition schemes of inertial confinement fusion. Two-dimensional hydrodynamic simulations are performed to verify the theory.

Stagnation of a cold plasma streaming to the center or axis of symmetry via an expanding accretion shock wave is ubiquitous in inertial confinement fusion (ICF) and high-energy- (2014)]. Some experimental evidence indicates that stagnation via an expanding shock wave is stable, but its stability has never been studied theoretically. We present such analysis for the stagnation that does not involve a rarefaction wave behind the expanding shock front and is described by the classic ideal-gas Noh solution in spherical and cylindrical geometry. In either case the stagnated flow has been demonstrated to be stable, initial perturbations exhibiting a powerlaw, oscillatory or monotonic, decay with time for all the eigenmodes. This conclusion has been supported by our simulations done both on a Cartesian grid and on a curvilinear grid in spherical coordinates. Dispersion equation determining the eigenvalues of the problem and explicit formulas for the eigenfunction profiles corresponding to these eigenvalues are presented, making it possible to use the theory for hydro code verification in two and three dimensions.

This paper describes the current status of flow-induced vibration evaluation methodology development for primary cooling pipes in the Japan sodium-cooled fast reactor (JSFR), with particular emphasis on recent research and development activities that investigate unsteady elbow pipe flow. Experimental efforts have been made using 1/3-scale and 1/10-scale single-elbow test sections for the hot-leg pipe. The 1/10-scale experiment simulating the hot-leg pipe indicated no effect of pipe scale in comparison with the 1/3-scale experiment under inlet-rectified-flow conditions. The next experiment using the 1/3-scale test section was performed to investigate the effect of swirl flow at the inlet. Although the flow separation region was deflected at the downstream from the elbow, the experiment clarified a less significant effect of swirl flow on pressure fluctuation onto the pipe wall. An additional experiment was intended to study the effect of elbow curvature. The experiments with water revealed no clear flow separation in a larger curvature elbow case than that of the JSFR. Since the interference of multiple elbows should be investigated to understand turbulent flow in the cold-leg pipe geometry, 1/15-scale experiments with double elbows were carried out to clarify that flow in the first elbow influenced a flow separation behavior in the second elbow. Simulation activities include Unsteady Reynolds Averaged Navier Stokes equation (U-RANS) approach with a Reynolds stress model using a commercial computational fluid dynamics (CFD) code and Large Eddy Simulation (LES) approach using an in-house code. A hybrid approach that combined with RANS and LES was also applied using a CFD code. Several numerical results appear in this paper, focusing on its applicability to the hot-leg pipe experiments. These simulations reasonably agreed with the experimental data using the 1/3-scale test section.

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