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Featured Application: The dimensionless nonlinear model can be modified to the qualitative dynamic analysis of the heated systems with different supercritical fluids under external vertical accelerations. Employing the external force method to regard seismic impact and the three-region methodology to analyze the supercritical heated channel, a non-linear dynamic model was developed to investigate the transient characteristics of single channel or parallel channels under the impacts of vertical sinusoidal and seismic accelerations. The present model was validated against the experimental data, which could suitably estimate the additional pressure drop caused by the vertical vibrations. The influences of parameters on the seismic-induced oscillation conducted in a supercritical heated channel indicated that a longer heated length, uprating operation power and a larger outlet loss coefficient all exhibit unstable effects, while the increase of inlet loss coefficient, a larger tube diameter and a lower inlet fluid temperature would tend to stabilize the system. Moreover, the supercritical fluid would present a high natural frequency in the very small NP-SUB region. The parametric effects on the parallel channel system are related to the inherent stability nature of initial state and the interactions among channels. The more uneven heat flux distribution among channels would cause a larger vibration-induced oscillation. In particular, when it is combined with the resonance effect, the system may exhibit much larger oscillations than in the case of non-resonance. [ABSTRACT FROM AUTHOR]

Highlights • A simple nonlinear model for a supercritical uniformly heated channel is developed. • Parametric effects on the system stability are performed. • Complex nonlinear phenomena could appear in this supercritical heated system. • A route from various periodic oscillations to chaotic oscillations is identified. • unimaginable periodic nonlinear oscillations could occur in the unstable region. Abstract This study develops a simple nonlinear dynamic model of a supercritical uniformly heated channel by dividing the channel into three regions coupled with linear profile approximations between flow enthalpy and flow density. Stability map, nonlinear characteristics and parametric effects of a uniformly heated channel with supercritical water are investigated. The results indicate that the nonlinear oscillations between inlet flow velocity and outlet flow velocity tend to present out-of-phase in the supercritical heated system. The parametric studies on system stability suggest that increasing inlet flow resistance or enlarging the channel diameter would stabilize the system, while increasing outlet flow resistance or lengthening the channel length would destabilize the system. In addition, complex nonlinear phenomena, i.e. supercritical Hopf bifurcations and period-doubled bifurcations, could exist in this supercritical uniformly heated channel system. In the deep unstable region of high pseudo-subcooling number, various periodic oscillations through a series of period-doubled bifurcations would eventually lead to chaotic oscillations. The appearance of period three (P-3) oscillation deduces that unimaginable periodic types of nonlinear oscillations could occur in the limited unstable space of this system. [ABSTRACT FROM AUTHOR]

Highlights • Nonlinear model for parallel supercritical uniformly heated channels is developed. • Three region methodology with polynomial profile approximations is employed. • The present model can explore the stability of parallel uniformly heated channels. • Nonlinear characteristics of the system with supercritical water are investigated. • Parametric effects on the stability of parallel three channel system are discussed. Abstract This study develops a nonlinear dynamic model of parallel supercritical uniformly heated channels based on three-region methodology coupled with polynomial profile approximations between flow density and flow enthalpy. The validation results against the experimental data indicate that the present model has the capability to investigate the stability issues of parallel uniformly heated channels with supercritical water. Nonlinear characteristics, stability maps and parametric effects of three uniformly heated channels with supercritical water are investigated. The results illustrate that channel-to-channel interactions among three channels will drive the system more unstable due to a more asymmetric power distribution. In addition, the hottest channel with the highest steady state flow rate would oscillate with the largest amplitude and out-of-phase with the other less heated channels under constant total inlet flow rate condition. This study also reveals that the nonlinear oscillations between inlet flow velocity and outlet flow velocity in each channel tend to present out-of-phase. It could demonstrate that increasing the pressure drop of heavy fluid region (region 1) would stabilize the system, while increasing the pressure drop of light fluid region (region 3) would destabilize the system. The parametric studies on system stability of three uniformly heated channels suggest that increasing inlet flow resistance or enlarging the channel diameter would stabilize the system, while increasing outlet flow resistance or lengthening the channel length would destabilize the system. [ABSTRACT FROM AUTHOR]

This study employs the nonlinear dynamic model developed previously by the authors to investigate the effect of void-reactivity feedback on the bifurcation phenomena and nonlinear characteristics of a single nuclear-coupled boiling channel in an advanced boiling water reactor. The parametric effects on the system stability are evaluated by nonlinear analyses as well. The effects of void-reactivity feedback and outlet flow resistance will both destabilize the system, while the inlet flow resistance will generate a stable effect on the system. The strength of void-reactivity feedback has a great influence on the bifurcation phenomena and nonlinear dynamics of the single nuclear-coupled boiling channel. The system can evolve from stable state, limit cycle, periodic to chaotic oscillation through supercritical Hopf and period-doubled bifurcations as the increase in the absolute value of void-reactivity coefficient. In addition, the system can experience a series of period-doubled bifurcation to present various types of oscillations, from periodic ones to chaos, in the unstable region as the controlling parameter of steady phase change number or subcooling number under some specific conditions with a relatively strong void-reactivity coefficient of C α = - 0.38 $ / % . The appearance of a periodic cycle of three suggests that there may be immeasurable periodic types of nonlinear oscillations in the limited unstable space of this system. [ABSTRACT FROM AUTHOR]