On nonlinear dynamics of density wave oscillations in a channel with non-uniform axial heating

“…The mechanism of density wave oscillations for two-phase flow has recently received great attention, remaining as an important issue of scientific and technological interest (e.g., [40,[42][43][44][45][46][47][48]. However, the core stability is due to fluctuations in coolant flow and power generation process coupled via nuclear feedback where the non-linear nature has been a challenge for the development of stability monitors.…”

Section: Discussion and Remarksmentioning

confidence: 99%

Non-Linear Stability Analysis of Real Signals from Nuclear Power Plants (Boiling Water Reactors) Based on Noise Assisted Empirical Mode Decomposition Variants and the Shannon Entropy

Olvera-Guerrero

Prieto‐Guerrero

Espinosa-Paredes

2017

Entropy

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There are currently around 78 nuclear power plants (NPPs) in the world based on Boiling Water Reactors (BWRs). The current parameter to assess BWR instability issues is the linear Decay Ratio (DR). However, it is well known that BWRs are complex non-linear dynamical systems that may even exhibit chaotic dynamics that normally preclude the use of the DR when the BWR is working at a specific operating point during instability. In this work a novel methodology based on an adaptive Shannon Entropy estimator and on Noise Assisted Empirical Mode Decomposition variants is presented. This methodology was developed for real-time implementation of a stability monitor. This methodology was applied to a set of signals stemming from several NPPs reactors (Ringhals-Sweden, Forsmark-Sweden and Laguna Verde-Mexico) under commercial operating conditions, that experienced instabilities events, each one of a different nature.Entropy 2017, 19, 359 2 of 33 operates at a low mass flow and at high nominal power. Another current trend is to increase the size of the core, which causes a weaker special coupling in the neutron field which increases the susceptibility of the reactor to experiencing unstable oscillations. In summary, all current tendencies related to reactor design enhance the regions where the reactor should not be operated (reactor operation at low flow and high power).Also, the DR often jumps discontinuously from the well stable to the far-unstable region [7]. The BWR stability is of primary interest from the point of view of BWR operation, due to the fact, that the stability margin may be strongly reduced during plant maneuvering and transients [8]. According to these issues, the DR might not be a reliable monitoring index after all, under certain operating conditions. Besides, in regular operating conditions, the need for stationary signals might be a handicap for DR estimation. Thus, it is relevant to explore new alternative methodologies and indexes adapted to accommodate for non-stationary and non-linear BWR signal behavior.In [9] a short time Fourier transform based technique was explored to study the time dependence of the natural frequency when the BWR signal is non-stationary. Later, the wavelet theory was applied to explore new alternatives for transient instability analysis [10,11]. However, in general BWR signals are non-stationary and non-linear, thus Fourier-based or wavelet-based approaches might lead to a biased stability analysis. Several methods for non-linear BWR stability analysis have been applied before [12,13], to study BWR signals containing stationary and non-stationary segments. In this work, the Shannon Entropy (SE) was applied, to infer whether it can be used as a novel stability parameter for BWRs. The SE is a concept that was developed by Claude E. Shannon [14] to study a discrete source through the information content of this source. The SE is a statistical index that quantifies the complexity of a signal. In this case, the BWR stability issue is assessed quantifying the complexity of BWR si...

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“…Therefore, nonoscillatory solutions have been observed at the LP boundary. More details of such non-linear phenomena can be found in the literature for different energy systems [15,[47][48][49][50]. Based on the applied external perturbation on the system, growing and constant high amplitude oscillations have been observed near to the unstable side of the stability boundary.…”

Section: Non-linear Analysismentioning

confidence: 99%

“…Recently, flow instability has gained massive attention from researchers since large magnitudes and continuous flow fluctuations can cause mechanical vibrations, disrupt control systems, and cause operational issues. Therefore, flow instabilities are widely studied experimentally [10][11][12][13] as well as numerically [14][15][16][17][18][19]. The discussion reveals that the real dynamics of the above-discussed systems are complex and complicated.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Nodalization Schemes on the Stability Characteristics of a Three Heated Channels under Supercritical Flow Condition

Singh

Berrouk

Saeed³

2022

Energies

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The present analysis is aimed at conducting node sensitivity analysis on the thermal–hydraulic performance of supercritical fluid in a three parallel channel configuration system. The heated channel was divided into different nodes and is examined under wide-ranging operating conditions. Firstly, the heated channel was divided into two nodes, like the two-phase flow system. In the second case, based on the correlation between the fluid properties, the heated channel was divided into three regions: heavy, mixture, and supercritical fluids. Finally, the channel was divided into N-nodes. Post the nodalization analysis, a non-linear analysis of three parallel channels was carried out under varied heat flux conditions. The analytical approximation functions were developed to capture the fluid flow dynamics. These functions were used to capture each node’s density, enthalpy, and velocity profiles under a wide range of operating conditions. The different flow instability (density wave oscillations and static) characteristics were observed at low pseudo- and relatively high subcooling numbers. In the density wave oscillations regime, out-of-phase oscillations and limit cycles are observed. A co-dimension parametric analysis with numerical simulations was carried out to confirm the obtained non-linear characteristics. Such analysis for parallel channel systems under supercritical working fluid flow conditions is missing in the literature which is limited to only linear stability analysis. This analysis can help to improve heat and mass transfer for designing efficient heated channel systems.

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On nonlinear dynamics of density wave oscillations in a channel with non-uniform axial heating

Cited by 12 publications

References 46 publications

Non-Linear Stability Analysis of Real Signals from Nuclear Power Plants (Boiling Water Reactors) based on Noise Assisted Empirical Mode Decomposition Variants and the Shannon Entropy

Non-Linear Stability Analysis of Real Signals from Nuclear Power Plants (Boiling Water Reactors) based on Noise Assisted Empirical Mode Decomposition Variants and the Shannon Entropy

Non-Linear Stability Analysis of Real Signals from Nuclear Power Plants (Boiling Water Reactors) Based on Noise Assisted Empirical Mode Decomposition Variants and the Shannon Entropy

The Effect of Nodalization Schemes on the Stability Characteristics of a Three Heated Channels under Supercritical Flow Condition

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