Dynamic analysis of the NPP pressure sensor system

The aim of the work was to develop on-line methods of control and diagnostics of pressure sensors at a NPP. The analysis was carried out along two lines:

1. i) The detection system including the sensor itself was modeled theoretically to obtain and study its transfer function, and to establish correspondence between the spectral characteristics of the pressure signal.

2. ii) The numerical processing of the signal using the AR technique to reconstruct the transfer function and evaluate the system's response, to a step impulse, as well as the spectral analysis. The hydraulic model presented indicate that the spectral lines observed at 10 Hz are due to longitu-dinal oscillations of water in the system branches, while the response time of the detection system is effectively the time of signal retardation in the porous ceramic diaphragms of the δ-cell of the sensor itself.

     

Monte-Carlo calculation of the calibration factors for the interfacial area concentration and the velocity of the bubbles for double sensor conductivity probe

This paper presents a study of the estimation of the correction factors for the interfacial area concentration and the bubble velocity in two phase flow measurements using the double sensor conductivity probe. Monte-Carlo calculations of these correction factors have been performed for different values of the relative distance (ΔS/D) between the tips of the conductivity probe and different values of the relative bubble velocity fluctuation parameter. Also this paper presents the Monte-Carlo calculation of the expected value of the calibration factors for bubbly flow assuming a log-normal distribution of the bubble sizes. We have computed the variation of the expected values of the calibration factors with the relative distance (ΔS/D) between the tips and the velocity fluctuation parameter. Finally, we have performed a sensitivity study of the variation of the average values of the calibration factors for bubbly flow with the geometrical standard deviation of the log-normal distribution of bubble sizes. The results of these calculations show that the total interfacial area correction factor is very close to 2, and depends very weakly on the velocity fluctuation, and the relative distance between tips. For the velocity calibration factor, the Monte-Carlo results show that for moderate values of the relative bubble velocity fluctuation parameter (H_max ≤ 0.3) and values of the relative distance between tips not too small (ΔS/D ≥ 0.2), the correction velocity factor for the bubble sensor conductivity probe is close to unity, ranging from 0.96 to 1.     

Modeling condensation heat transfer on a horizontal finned tube in the presence of noncondensable gases

European designs for the next generation of nuclear reactors incorporate innovative passive systems in their containments to enhance heat removal by condensation under postulated accident conditions. These systems consist of several units of cross-flow finned tube bundles internally cooled with water. So far most of the studies that have been addressed to the issue of heat transfer onto finned surfaces under condensing conditions have involved refrigerants and pure vapor conditions. This study presents a model (HTCFIN) capable of predicting condensation of a cross-flow air–steam mixture onto a single horizontal finned tube. The comparison of HTCFIN predictions to the available databases shows its acceptable accuracy in a wide range of conditions and allows an interpretation of the influence of major variables acting on the scenario. As a consequence, HTCFIN model represents a step forward in the present theoretical capability to estimate heat transfer within containments of next generation of European reactors in the case of a hypothetical accident.     

Influence of subcooled boiling on out-of-phase oscillations in boiling water reactors

In this paper, we develop a reduced order model with modal kinetics for the study of the dynamic behavior of boiling water reactors. This model includes the subcooled boiling in the lower part of the reactor channels. New additional equations have been obtained for the following dynamics magnitudes: the effective inception length for subcooled boiling, the average void fraction in the subcooled boiling region, the average void fraction in the bulk-boiling region, the mass fluxes at the boiling boundary and the channel exit, respectively, and so on. Each channel has three nodes, one of liquid, one with subcooled boiling, and one with bulk boiling. The reduced order model includes also a modal kinetics with the fundamental mode and the first subcritical one, and two channels representing both halves of the reactor core. Also, in this paper, we perform a detailed study of the way to calculate the feedback reactivity parameters. The model displays out-of-phase oscillations when enough feedback gain is provided. The feedback gain that is necessary to self-sustain these oscillations is approximately one-half the gain that is needed when the subcooled boiling node is not included.     

Non-iterative model for condensation heat transfer in presence of non-condensable gases inside passive containment cooling vertical tubes

Some contributions have been stated in order to improve the modeling of concurrent downflow condensation in presence of non-condensables inside vertical tubes. In particular, the influence of non-condensables over the liquid side heat transfer has been considered. The new proposed mechanistic models solve explicitly the real interface temperature by means of a cubic or a fourth order equation. As these models have a non-iterative nature, they can avoid the weakest point of the traditional mechanistic models, which is the slowdown computation if the model had to be implemented in a code. Moreover, as the main non-condensables effects can be accounted for in the heat and mass transfer processes, the new models will be more realistic. The models have been validated with the Vierow experimental data, obtaining a total average relative error, for the fourth order equation method model, of 21% for 268 points.     

Influence of age and environment on antler traits in Spanish red deer (Cervus elaphus hispanicus)

Summary We measured antlers of 484 red deer (Cervus elaphus hispanicus) aged between 1.5 and 13.5 years, from Sierra Morena (Southeast Spain) between 1992 and 1998. We determined the effect of year of birth, season of hunting, age group and farm size on the number of tips, the length, the width and the quality of the antlers. The number of harvested animals, an indicator of population density, was included as a covariable. Highest antler quality is obtained in animals at least seven years old. The lowest quality animals were obtained during the hunting season from October 1995 to February 1996, which coincided with the end of an extended period of drought. The best trophies were harvested during the 1996–1997 season, the period of highest rainfall during the study. Thus environmental conditions have a major influence on antler size. However, animal density had a strong negative effect on certain types of farms, emphasizing the importance of population management.     

Analysis of the suction effect on the mass transfer when using the heat and mass transfer analogy

The transport phenomenon between a fluid in movement and a wall is strongly affected by the permeability of the wall. The application of a correction factor standing for the transpiration effect will be required whenever a heat transfer model is based either on the use of heat, mass or momentum analogies or on the use of empirical correlations for the computation of the heat transfer coefficient.The suction factor commonly used when solving as a function of either mass or molar fractions is called the Bird suction factor. The validity of this factor rests on the hypothesis of the film theory or Couette flow.This paper reviews the Bird suction factor in laminar regime, extending the analysis to turbulent flow conditions and finding thereby that Bird's equation can overestimate the suction factor under turbulent condensation conditions in the gas phase.Finally, an alternative formulation for the suction factor under turbulent condensation conditions has been proposed and compared with Bird's original formulation. In doing this, both data and models developed by other authors and the UW-Madison test facility database have been used.The results show the suitability of the alternative formulation when calculating the condensation rate in turbulent natural circulation scenarios, whereas Bird's formulation seems to be more appropriate for laminar regimes.     

Feynman-α and Rossi-α formulas with spatial and modal effects

Feynman-α and Rossi-α formulas including multiple α-modes are derived for stochastic and continuous neutron sources. The presented formalism is further developed to achieve spatial correction factors for the single α-mode point kinetics representations of the Feynman-α and Rossi-α formulas. As a natural extension of the multiple α-mode formalism, delayed neutrons are included in the Feynman-α formula. The obtained formulas are validated experimentally in a strongly heterogeneous system obeying multiple α-modes, resulting in good agreement with the presented theoretical framework.     

Heat transfer modeling in the vertical tubes of the passive containment cooling system of the simplified boiling water reactor

The long term containment cooling of GE's passive BWR design is based on a new safety system called PCCS (passive containment cooling system). Performance of this system relies on the pressure difference between the drywell and wetwell in case of an accident and on the condensation of steam moving downward inside vertical tubes fully submerged in a water pool initially at room temperature. In this paper a model based on the resolution of momentum equations of both phases, the application of the heat and mass transfer analogy, and the consideration of the presence of a noncondensable gas by diffusion theory in a boundary layer is presented. Assumptions and approximations taken resulted in new methods to estimate film thickness and heat transport from the gas to the interface. Influence of phenomena such as suction, flow development, film waviness, and droplet entrainment has been accounted for. Based on this formulation, a computer programme called HVTNC (heat transfer in vertical tubes with noncondensables) has been built up. HVTNC results have been compared to the experimental data available. Experimental trends have been reproduced. Heat transfer has been found to be severely degraded by the presence of noncondensables whereas high Reynolds numbers of gas flow have been seen to enhance shear stress and therefore, heat transmission. The average error of HVTNC is essentially located at regions where only a residual fraction of heat remains to be transferred, so that minor deviations can be anticipated in the overall heat transfer in the tube. Comparison of HVTNC to other models show a substantial gain of accuracy with respect to earlier models.     

Simulation of bubbly flow in vertical pipes by coupling Lagrangian and Eulerian models with 3D random walks models: Validation with experimental data using multi-sensor conductivity probes and Laser Doppler Anemometry

A set of two phase flow experiments for different conditions ranging from bubbly flow to cap/slug flow have been performed under isothermal concurrent upward air–water flow conditions in a vertical column of 3 m height. Special attention in these experiments was devoted to the transition from bubbly to cap/slug flow. The interfacial velocity of the bubbles and the void fraction distribution was obtained using 2 and 4 sensors conductivity probes.Numerical simulations of these experiments for bubbly flow conditions were performed by coupling a Lagrangian code with an Eulerian one. The first one tracks the 3D motion of the individual bubbles in cylindrical coordinates (r, ?, z) inside the fluid field under the action of the following forces: buoyancy, drag, lift, wall lubrication. Also we have incorporated a 3D stochastic differential equation model to account for the random motion of the individual bubbles in the turbulent velocity field of the carrier liquid. Also we have considered the deformations undergone by the bubbles when they touch the walls of the pipe and are compressed until they rebound.The velocity and turbulence fields of the liquid phase were computed by solving the time dependent conservation equations in its Reynolds Averaged Transport Equation form (RANS). The turbulent kinetic energy k, and the dissipation rate ? transport equations were simultaneously solved using the k, epsilon model in a (r, z) grid by the finite volume method and the SIMPLER algorithm. Both Lagrangian and Eulerian calculations were performed in parallel and an iterative self-consistent method was developed. The turbulence induced by the bubbles is an important issue considered in this paper, in order to obtain good predictions of the void fraction distribution and the interfacial velocity at different gas and liquid flow conditions.