Coupled-core Reactor Research Articles

A semi-analytical treatment of xenon oscillations

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.

Evaluation of Eigenvalue Separation by the Monte Carlo Method

A new technique for evaluating an eigenvalue separation by the Monte Carlo method is proposed. This technique uses a fission matrix evaluated by an ordinary Monte Carlo calculation and enables us to evaluate higher order eigenvalues and eigenvectors that have not been able to be determined by Monte Carlo calculation. To validate it, the proposed technique was applied to the analysis of the modeled BWR core and the coupled-core reactor assembled at the C-core tank of KUCA (Kyoto University Critical Assembly). Consequently, it was found that this new technique gave good results regarding eigenvalue separation, although regional division needs to be noted in a system for evaluating a fission matrix.

Evaluation of Eigenvalue Separation by the Monte Carlo Method.

A new technique for evaluating an eigenvalue separation by the Monte Carlo method is proposed. This technique uses a fission matrix evaluated by an ordinary Monte Carlo calculation and enables us to evaluate higher order eigenvalues and eigenvectors that have not been able to be determined by Monte Carlo calculation. To validate it, the proposed technique was applied to the analysis of the modeled BWR core and the coupled-core reactor assembled at the C-core tank of KUCA (Kyoto University Critical Assembly). Consequently, it was found that this new technique gave good results regarding eigenvalue separation, although regional division needs to be noted in a system for evaluating a fission matrix.

Space-Dependent Effect Observed in Subcriticality Measurements for Loosely Coupled-Core System

The results of the subcriticality measurements by various techniques performed for the UTR-KINKI reactor, a light-water-moderated and graphite-reflected coupled-core reactor, are presented. The result of the source-multiplication measurement indicates that the apparent dependence of the subcriticality on the detector position is significantly observed even under a condition 2$ subcritical, and that the location of neutron source remarkably influences the sub- criticality obtained. On the other hand, the spatial dependence in the source-jerk measurement is slight relative to that in the source-multiplication and the rod drop measurements. Furthermore, the result of the Feynman-α measurement suggests that much more samples should be acquired for the reduction of the experimental uncertainty to the same level as that in the above measurements.

Asymptotic stability for delayed differential systems with nonnegative coupling in reactor dynamics

We present in this paper two families, V ±(p ±), of nonquadratic, non positive definite Lyapunov functionals depending on several parameters, that are suited to handle nonlinear stability problems for ordinary or functional (delayed) differential equations. The approach is based on the property of essential positivity of the Jacobian matrix A+B of the nondelayed system, which physically corresponds to nonnegative coupling among state variables, such as powers and precursor populations in a nodal dynamics model of a coupled core reactor. Positive power coefficients in some nodes are compatible with stability provided the remaining ones are sufficiently negative to ensure that A+B is a stable matrix, independently of the magnitude of the delays. In this case the combined use of functionals from the V ±(p ±) families, p ±>1, yields a better estimate H (which of course reduces with increasing the magnitude of the delays) of the domain of attraction of the null solution of the system equations than would be allowed by a single and/or more conventional (e.g. quadratic) functional.

Stability Analysis of a Nonlinear Coupled-Core Reactor Control System

In this paper, stability-equation method is applied to the analysis of a large coupled-core reactor control system having multiple nonlinearities and adjustable parameters. The characteristics of the limit-cycle and the asymptotically stable regions can be easily defined in a parameter plane. A numerical example is given and comparisons with other methods in current literature are made.

On the Generalized Neutron Noise Formulation with Application to a Coupled Core Reactor

This paper describes the formulation of the neutron noise based on a multidimensional, multiregion, multigroup diffusion model. To solve for the flux fluctuations, the model was generalized and clarified using the adjoint function approach, which included checking the reciprocity relation to assure the correctness of the established adjoint function, solving the adjoint function with a finite-volume detector, and increasing the rate of convergence of the series solutions by nonlinear transform. The model was applied to a coupled core reactor to recalculate detector responses to a unidirectional vibration of a neutron absorber. The lack of agreement between the calculated results and the measurements might be partly due to some simplifications and approximations. It is recommended that measurements should be made in cases where the model can be used more feasibly.

Analysis and parameter computation of a delay coupled core nuclear reactor using walsh series expansions

Almost all reactors consist or can be considered to consist of separate cores (regions) each being a subcritical reactor with criticality being achieved through the mutual exchange of neutrons (coupling) among cores. In this paper a class of coupled-core reactors with pure time-delays is considered, and its simulation (analysis) and parameter computation (identification) are studied using Walsh (piece-wise constant) function expansion. The theory was tested with simulated data and provides sufficient accuracy with relatively low computational requirements.

Application of an Exact Model Matching Technique to Coupled-Core Nuclear Reactor Control

In this Note the control problem of linearized coupled-core multivariable nuclear reactors is treated by using a recent exact model matching technique in the frequency domain. The case of state feedback control is first considered and then the results are used where only the output variables of the reactor are available for feedback. A numerical example of a three coupled-core nuclear reactor model with one delayed neutron group for each core and short neutron travel time between cores is included.

Approximate Noninteractive Power Regulation of a Coupled-Core Nuclear Reactor

The present paper describes an application of an approximate decoupling control to the noninteractive power regulation of each core in a coupled-core nuclear reactor model. A method for designing an approximate decoupling controller is presented here. This controller consists of an output feedback compensator and a precompensator which is introduced to diagonalize an open-loop frequency response matrix approximately in the frequency range important to reactor dynamics. A " multipoint diagonalization method " is adopted for the design of the precompensator. This method possesses some superiorities compared with the pseudo-diagonalization method. Digital simulations and graphical studies by the Gershgorin band demonstrate the usefulness of the multipoint diagonalization method as well as the effectiveness of the controller for power regulation.

Approximated Decoupling Control of Coupled-Core Nuclear Reactor

Approximated Decoupling Control of Coupled-Core Nuclear Reactor

Approximated decoupling control of coupled-core nuclear reactor.

An application of approximated decoupling control to a coupled-core nuclear reactor is described, which permits noninteractive regulation of the power level in the individual cores of a reactor that requires to be controlled with account taken of the interference between the cores. The control possesses the advantages of easy design and simple structure of an approximated decoupling controller.The controller is constituted of a precompensator and an output feedback compensator. The control function is ensured with the precompensator playing a key role in approximately diagonalizing an open-loop transfer-function matrix in the frequency range of interest. The precompensator is devised by pseudo-diagonalization, the method being generalized by the authors for application to a wide frequency range.Digital simulations and graphical studies based on the Gershgorin band analysis demonstrate the effectiveness of the approximated decoupling controller as well as the applicability of the generalized pseudo-diagonalization method. Sample results are compared with those obtained by the decoupling theory.

Time-optimal power-change control for coupled-core reactors.

Time-optimal power-change control for coupled-core reactors.

Stability Analysis for Integro-Differential Coupled-Core Reactor Models

Asymptotic stability of a general form of coupled-core reactor models is discussed. The method presented is based on the concept of stability introduced by Driver for integro-differential equations. A Liapunov functional is applied to the investigation of asymptotic stability “in the small.” Next, conditions for global asymptotic stability are established using a modified form of the previously given functional. As an illustration of the general results, an example is discussed in more detail.

Derivation of Pál-Bell equations for two-point reactors, and its application to correlation measurements

For the analysis of noise problems in zero-power coupled-core reactors, one-energy group multipoint Pál-Bell equations are derived and their applications are illustrated. The illustration is made for the neutron correlation experiments of loosely-coupled two-core systems. We first derive a two-point version of the Pál-Bell equations for the neutron detection probability generating functions, and then derive the formulae of Feynman-alpha and Rossi-alpha (Orndoff type) experiments for a coupled-core system, using the factorial moment and cumulant expansions. With these formulae the following coupled-core kinetic parameters can be evaluated from neutron correlation experiments: coupling delay time, coupling coefficient and neutron generation time. The simplicity in the present derivation of Pál-Bell equations is pointed out.

Asymptotic Stability of Coupled-Core Reactors with Arbitrary Reactivity Feedback and No Coupling Time Lag

The question of general asymptotic stability is considered for N-order coupled-core reactors neglecting neutron coupling time lag, but with general nonlinear reactivity functionals. Stability crite...

Irreversible Circulation of Fluctuation in Coupled-Core Nuclear Reactors

Irreversible Circulation of Fluctuation in Coupled-Core Nuclear Reactors

Irreversible circulation of fluctuation in coupled-core nuclear reactors.

The irreversible circulation α of fluctuation a for a coupled-core nuclear reactors is derived. Neutrons in this system are transported from a certain core to another one with a finite time lag and their fluctuations are generally described by a set of non- Markoffian Langevin equations. This system cannot accept Tomita's original theory based on the Markoffian stochastic process. When the system has the exp(-t/τ)-type memory kernel, we can, however, build up an equivalent Markoffian model—points model—by introducing “transit zones”, and we can evaluate the irreversible circulation of fluctuation α. The α for symmetrically coupled-cores takes null-value, while for an asymmetrical case the α becomes finite and turns out to be a new information from which the coupling parameters between the cores can be extracted.

High-frequency structure of space-dependent neutron fluctuation spectra in a coupled-core reactor

The space dependence of neutron fluctuation spectra in a coupled-core reactor is described in terms of propagation phenomena of neutron diffusion waves from one core to two space points of observation. Analytical expressions for the spectra are derived for a reference reactor approximately representative of a coupled-core Argonaut-type reactor. Numerical calculations are carried out to illustrate the effect of the difference of two-slab core loading and ring core loading. The results of coherence function calculations provide good agreement with experimental measurements up to and including the frequency at which the real part of the cross spectra for two observation points vanishes.

Application of stable adaptive schemes to nuclear reactor systems. II. Parameter identification and adaptive control of nonlinear loosely coupled core reactor.

The parameter identification and adaptive control schemes applied in a previous study to a nonlinear point reactor are extended to the case of a loosely-coupled-core reactor with internal feedbacks, constituting a nonlinear overall system. Both schemes are shown to be stable, with the system newly represented on the pattern of the Model Reference Adaptive System (MRAS) with use made of the Lyapunov's method. For either parameter identification or adaptive control of a loosely-coupled-core reactor, there exists no canonical form of multiple input-multiple output system which can be directly applied for deriving the MRAS with the matrix version of the Kalman-Yakubovich lemma as it was in the case of the point reactor. This difficulty is circumvented by the practical assumption that the neutron density can be directly measured on each core as reactivity change is applied as input into the coupled core as a whole. For parameter identification, the model parameters are adaptively adjusted to those of each core...