Numerical Aspects on the Prediction of Stability Boundaries of Two-Phase Natural Circulation Circuits, Considering Flashing Evaluation

[+] Author and Article Information
P. Zanocco

Centro Atómico Bariloche,  CNEA, Av.a Bustillo Km. 9,500, San Carlos de Bariloche, R8402AGP Río Negro, Argentinazanoccop@cab.cnea.gov.ar

D. Delmastro, M. Giménez

Centro Atómico Bariloche,  CNEA, Av.a Bustillo Km. 9,500, San Carlos de Bariloche, R8402AGP Río Negro, Argentina

J. Appl. Mech 73(6), 911-922 (Dec 29, 2005) (12 pages) doi:10.1115/1.2178835 History: Received May 24, 2005; Revised December 29, 2005

In this work, the stability of a two-phase, natural circulation circuit is analyzed, using a specially developed model. This thermohydraulic model results in a set of coupled, nonlinear, first-order partial differential equations, which are solved by means of the up-wind finite difference method, using combinations of explicit and implicit methods for the numerical integration of the different balance equations. An adaptive nodalization scheme is implemented, minimizing the error of the propagation of small perturbations through the discretized volumes and especially the ones having two-phase flow regime. A linearization method is implemented by means of numerical perturbations. Frequency domain calculations are carried out, allowing a rapid visualization of the stability of the linearized system. Two cases are analyzed: a test case, where the code is compared in a wide range of qualities with an analytical model, and an application case, where the model is used to analyze the stability of an integral reactor cooled by natural circulation. The CAREM prototype is taken as a reference. In both cases, the numerical diffusion and integration errors are analyzed in the stability limit prediction by means of a convergence analysis using different nodalization and numerical integration criteria.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Carem-25 primary system: (a) diagram and (b) used nodalization scheme

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Figure 2

Natural circulation loop used in the test case

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Figure 3

(a) Level diagram obtained with the numerical model, and the stability limit obtained with the analytical model. (b) Frequencies of oscillations, according to the numerical model.

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Figure 4

Eigenvalues of the discretized and linealized system, in the three points analyzed

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Figure 5

Time evolutions for the averaged nondimensionalized flow, according to the linear and nonlinear system, at points (a) stable, (b) neutral, and (c) unstable (points A, B and C). (c) Heater outlet and riser outlet enthalpy, showing propagation.

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Figure 6

Stability map for the application case, without pressure feedback

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Figure 7

Convergence analysis of the numerical model by using the adaptive nodalization: (a) Fully explicit and (b) implicit momentum equation

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Figure 8

Comparison of stability limit prediction using (a) adaptive nodalization and fixed nodalization and (b) Courant limit and lower time step

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Figure 9

Stability map showing the core influence, in the case of constant core inlet coolant temperature

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Figure 10

Amplification factor as a function of QV, using different numbers of intermediate steps (NIT) in the core

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Figure 11

Stability map obtained without intermediate steps in the core

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Figure 12

Convergence analysis for points A, B, and C, using Nr=20, 40, and 80 and NIT=10, 5, and 2, respectively, in order to keep Nc≈const

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Figure 13

Convergence analysis for cases A, B, and C



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