Non-linear effects and the use of network analyzer time domain

This paper presents a higher order time domain boundary elements method based on the Rankine sources for the computation of both linear and weakly non-linear effects for both fixed and free floating bodies. The geometry is described based on surfaces in a standard iges file, considering a NURBS (Non Uniform Rational Basis-Spline) description. The potential function, velocity, free-surface elevation and other quantities are defined using b-splines of arbitrary degree and the floating body interaction is solved using the potential acceleration approach on a Runge-Kutta scheme for time evolution. The integral equation is obtained and solved considering several possibilities for the collocation points, leading to an over-determined system. The integration over the panels is performed using a mixed desingularized-numerical method over Gaussian points. The results comparison are performed with WAMIT solution for a floating sphere concerning wave runup, body motions, velocity field, mean drift components in time domain.

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Linear and Nonlinear Stability Analysis of a Self-Pressurized, Natural Circulation, Integral Reactor

12th International Conference on Nuclear Engineering, Volume 1 ◽

10.1115/icone12-49363 ◽

2004 ◽

Cited By ~ 1

Author(s):

Pablo Zanocco ◽

Dari´o Delmastro ◽

Marcelo Gime´nez

Keyword(s):

Time Domain ◽

Amplification Factor ◽

Natural Circulation ◽

The Self ◽

The Core ◽

Non Linear ◽

Pressure Feedback ◽

Linear Effects ◽

The Stability ◽

Integral Reactor

The stability of a self-pressurized, integral reactor cooled by natural circulation is analyzed. CAREM reactor prototype is taken as reference for the present study. Because of the self-pressurization condition, the system is very close to saturation, and some boiling occurs along the hot leg - reactor core and riser -. Possible instabilities caused by this condition are analyzed in this work in the nominal pressure, with special attention to some particular issues of this design. A numerical code is developed to describe the reactor dynamics and it is briefly described. It includes the coolant with a one-dimensional scheme, steam dome and core modelling, considering the flashing phenomena, neutronic and pressure feedbacks. The code numerically solves the whole set of non-linear equations in a time-domain approach; it also includes a linearization method by numerical perturbations, then a classical frequency-domain stability analysis can be also carried out for the linearized system, by means of eigenvalues calculation. The amplification factor for the oscillation is plotted in the core power/steam dome condensation parameter-plane. A parametric study is carried out, to analyze the influence of core dynamic and the pressure feedback due to the self-pressurization. The pressure feedback has a stabilizing effect, increasing stability for smaller steam volumes. The core dynamic has a stabilizing effect when the core power and the steam dome condensation are low, and relatively destabilizing when they are higher. The stability boundary is determined, for several cases. The amplification factor is enlarged in the region where the flashing phenomenon occurs. The dynamic non-linear effects are studied by means of a time-domain approach, for selected conditions in growing and damped oscillations. The limit-cycle for the growing oscillations is determined, and the main non-linear sources are studied: the amplitude is restricted by strong non-linear effects, which appear when the boiling boundary crosses the core-riser limit, and more than one boiling point coexists at the same time, bounding the amplitude of oscillation to values that would remain un-noticed in case of being present in the reactor.

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