Walter Ambrosini

A physically based correlation for drop size in annular flow

Abstract The derivation of a correlation for drop size in annular flow based on a mechanistic model is presented. Optimum values of four constants were obtained by a fit to measured data over a wide range of gas and liquid flow rates, physical properties and pipe diameter.

Statistical characteristics of a water film falling down a flat plate at different inclinations and temperatures

Abstract In this work, the statistical characteristics of the surface of a water film, freely falling down a vertical or inclined flat plate, have been investigated. The study was carried out in the frame of a research on passive cooling of heated surfaces by the evaporation of thin water films. The experiments, performed to confirm and extend previous results by the same authors, involved relatively cold water (ambient temperature or slightly warmer 20–30 °C) and warm water (50 and 70 °C). The range of Reynolds numbers includes the classical threshold for the transition between the laminar-wavy and the turbulent regimes. Two different plate inclinations with respect to the vertical position have been addressed (0° and 45°). Capacitance probes were adopted to collect discrete film thickness time series, which have been processed to extract relevant statistical data. A specific probe configuration including an electrical heating system has been developed in order to overcome the problem of vapour condensation onto the active surfaces of the electrodes in the presence of warm water. Data on mean, minimum and maximum film thickness as well as standard deviation and wave velocity are presented, discussing the trends observed as a function of film flow rate, plate inclination and film temperature, also considering the information coming from previous experimental campaigns.

The effect of truncation error on the numerical prediction of linear stability boundaries in a natural circulation single-phase loop

Abstract This paper discusses the effects of truncation error on the stability of natural circulation in a single-phase loop as predicted by finite difference numerical methods. A short description of the characteristics of the selected problem is firstly given, also showing results obtained by a modal solution. Different numerical schemes are applied and the related effect on predicted stability is shown. The results obtained are then discussed in relation to the applicability of thermal–hydraulic system codes in the analysis of fluid-dynamic instabilities in real systems.

Stability Analysis of Single-Phase Thermosyphon Loops by Finite Difference Numerical Methods

In this paper, examples of the application of finite-difference numerical methods in the analysis of stability of single-phase natural circulation loops are reported. The problem is addressed here for its relevance to thermal-hydraulic system code applications, with the aim to point out the effects of truncation error on stability prediction. The methodology adopted for analyzing in a systematic way the effect of various finite-difference discretization can be considered the numerical analogue of the usual techniques adopted for PDE stability analysis. Three different single-phase loop configurations are considered involving various kinds of boundary conditions. In one of these cases, an original dimensionless form of the governing equations is proposed, adopting the Reynolds number as a flow variable. This allows for an appropriate consideration of transition between laminar and turbulent regimes, which is not possible with other dimensionless forms, thus enlarging the range of validity of model assumptions.

Analysis of Basic Phenomena in Boiling Channel Instabilities With Different Flow Models and Numerical Schemes

The results of a computational study on boiling channel stability are here discussed. The study compares the information obtained by two programs, developed in previous work for the linear and the nonlinear stability analysis of boiling channels basing on a simplified flow model, with the predictions of a well known system code. The phenomena highlighted by the results of the system code, adopted with different flow models and numerical methods, are discussed in a systematic way with the aid of the description obtained by the simplified model, in order to obtain a clearer picture than could be achieved by the mere application of the system code to conditions of interest for boiling water reactor stability. The effects on the obtained results of non-equilibrium, numerical discretization and number of nodes are considered, evaluating their influence on the predicted stability boundaries. Some physical aspects of the density-wave mode of instability are finally discussed basing on the predictions obtained by the different models.Copyright

Prediction of stability of one-dimensional natural circulation with a low diffusion numerical scheme

Abstract This paper presents the results obtained in the analysis of stability of flow in single-phase natural circulation loops by a computer program incorporating two different numerical schemes for the discretisation of the energy balance equation. In particular, in addition to an usual first order upwind scheme, a low diffusion numerical method, devised as an application of a classical second order explicit upwind scheme, has been introduced by simply using an appropriate definition of the “donor cell rule”. Both transient behaviour and linear stability are addressed, the latter obtained by a numerical perturbation technique providing full consistency with the transient algorithm. The behaviour of heat structures is also accounted for both in the non-linear transient program and in its linearised counterpart. After a detailed description of the adopted models, examples of their application are provided in the paper, addressing single-phase natural circulation loop behaviour. The results obtained by the low diffusion scheme are compared with those provided by the first order numerical scheme and with available information from a previous work on experimental loop behaviour, showing a remarkable improvement in the reliability of stability predictions.

Dimensionless Parameters in Stability Analysis of Heated Channels With Fluids at Supercritical Pressures

The paper proposes dimensionless parameters for the analysis of stability in heated channels with supercritical fluids. The parameters are devised basing on the classical phase change and subcooling numbers adopted in the case of boiling channels, proposing a novel formulation making use of fluid properties at the pseudo-critical temperature as a function of pressure. The adopted formulation for dimensionless density of a given fluid provides a unique dependence with respect to dimensionless enthalpy, in a reasonably wide range of system pressures, thus giving generality to the predictions of unstable conditions obtained as a function of dimensionless parameters. It is shown that these parameters allow setting up quantitative stability maps for a single heated channel with imposed overall pressure drop, in analogy with the ones proposed in previous work concerning boiling channels. Similarities with the boiling channel stability phenomena are pointed out, also supporting the conclusions with system code predictions.Copyright

ASSESSMENT OF STABILITY MAPS FOR HEATED CHANNELS WITH SUPERCRITICAL FLUIDS VERSUS THE PREDICTIONS OF A SYSTEM CODE

The present work is aimed at further discussing the effectiveness of dimensionless parameters recently proposed for the analysis of flow stability in heated channels with supercritical fluids. In this purpose, after presenting the main motivations for the introduction of these parameters in place of previously proposed ones, additional information on the theoretical bases and on the consequences of this development is provided. Stability maps, generated by an in-house program adapted from a previous application to boiling channels, are also shown for different combinations of the operating parameters. The maps are obtained as contour plots of an amplification parameter obtained from numerical discretization and subsequent linearization of governing equations; as such, they provide a quantitatively clear perspective of the effect of different boundary conditions on the stability of heated channels with supercritical fluids. In order to assess the validity of the assumptions at the basis of the in-house model, supporting calculations have been performed making use of the RELAP5/MOD3.3 computer code, detecting the values of the dimensionless parameters at the threshold for the occurrence of instability for a heated channel representative of SCWR proposed core configurations. The obtained results show reasonable agreement with the maps, supporting the applicability of the proposed scaling parameters for describing the dynamic behaviour of heated channels with supercritical fluids.

Transient Three-Dimensional Stability Analysis of Supercritical Water Reactor Rod Bundle Subchannels by a Computatonal Fluid Dynamics Code

The paper describes the application of computational fluid dynamics (CFD) in simulating density wave oscillations in triangular and square pitch rod bundles. The FLUENT code is used for this purpose, addressing typical conditions proposed for supercritical water reactor (SCWR) conceptual design. The RELAPS code and an in-house 1D linear stability code are also adopted to compare the results for instability thresholds obtained by different techniques. Transient analyses are performed both by the CFD code and RELAP5, with increasing heating rates and constant pressure drop across the channel, up to the occurrence of unstable behavior. The obtained results confirm that the density wave mechanism is similar in rod bundle and in axisymmetric configurations.

Natural Circulation of Lead-Bismuth in a One-Dimensional Loop: Experiments and Code Predictions

The paper summarizes the results obtained by an experimental and computational study jointly performed by ENEA and University of Pisa. The study is aimed at assessing the capabilities of an available thermal-hydraulic system code in simulating natural circulation in a loop in which the working fluid is the eutectic lead-bismuth alloy as in the Italian proposal for Accelerator Driven System (ADS) reactor concepts. Experiments were performed in the CHEOPE facility installed at the ENEA Brasimone Research Centre and pre- and post-test calculations were run using a version of the RELAP5/Mod.3.2, purposely modified to account for Pb-Bi liquid alloy properties and behavior. The main results obtained by the experimental tests and by the code analyses are presented in the paper providing material to discuss the present predictive capabilities of transient and steady-state behavior in liquid Pb-Bi systems.Copyright