A semi-analytical treatment of xenon oscillations. (August 2017)

• Record Type: Journal Article
• Authors: Zarei, M.; Minuchehr, A.; Ghaderi, R.
• Is Part Of: Annals of nuclear energy. Volume 106(2017:Aug.)
• Page Start: 127
• Page End: 135
• Publication Date: 2017-08
• Subjects: Coupled core kinetics -- Xenon oscillations -- Stiffness -- Adiabatic approximation -- Matrix exponential -- Linear time varying system -- Lyapunov exponent; Nuclear energy -- Periodicals; Nuclear engineering -- Periodicals; 621.4805
• DOI: 10.1016/j.anucene.2017.03.043
• Languages: English
• ISSNs: 0306-4549

Abstract

Highlights: A two-group two region kinetic core model is developed employing the eigenvalues separation index. Poison dynamics are investigated within an adiabatic approach. The overall nonlinear reactor model is recast into a linear time varying framework incorporating the matrix exponential numerical scheme. The largest Lyapunov exponent is employed to analytically verify model stability. Abstract: A novel approach is developed to investigate xenon oscillations within a two-group two-region coupled core reactor model incorporating thermal feedback and poison effects. Group-wise neutronic coupling coefficients between the core regions are calculated applying the associated fundamental and first mode eigenvalue separation values. The resultant nonlinear state space representation of the core behavior is quite suitable for evaluation of reactivity induced power transients such as load following operation. The model however comprises a multi-physics coupling of sub-systems with extremely distant relaxation times whose stiffness treatment inquire costly multistep implicit numerical methods. An adiabatic treatment of the sluggish poison dynamics is therefore proposed as a way out. The approach helps further investigate the nonlinear system within a linear time varying (LTV) framework whereby a semi-analytical framework is established. This scheme incorporates a matrix exponential analytical solution of the perturbed system as a quite efficient tool to study load following operation and control purposes. Poison dynamics are updated within larger intervals which exclude the need for specific numerical schemes of stiff systems. Simulation results of the axial offset conducted on a VVER-1000 reactor at the beginning (BOC) and the end of cycle (EOC) display quite acceptable results compared with available benchmarks. The LTV reactor model is further investigated within a stability analysis of the associated time varying systems at these two stages employing the concept of Lyapunov exponent.