Reduced Basis Approaches in Time-Dependent Non-Coercive Settings for Modelling the Movement of Nuclear Reactor Control Rods

In this work,two approaches,based on the certified Reduced Basis method,have been developed for simulating the movement of nuclear reactor control rods,in time-dependent non-coercive settings featuring a 3D geometrical framework.In particular,in a first approach,a piece-wise affine transformation based on subdomains division has been implemented for modelling the movement of one control rod.In the second approach,a“staircase”strategy has been adopted for simulating themovement of all the three rods featured by the nuclear reactor chosen as case study.The neutron kinetics has been modelled according to the so-called multi-group neutron diffusion,which,in the present case,is a set of ten coupled parametrized parabolic equations(two energy groups for the neutron flux,and eight for the precursors).Both the reduced order models,developed according to the two approaches,provided a very good accuracy comparedwith high-fidelity results,assumed as“truth”solutions.At the same time,the computational speed-up in the Online phase,with respect to the fine“truth”finite element discretization,achievable by both the proposed approaches is at least of three orders of magnitude,allowing a real-time simulation of the rod movement and control.

PCTRAN Westinghouse AP1000 Power Control of Pressurized Water Reactor Using Simulink of MATLAB

This paper introduces the simulation, and controls using Simulink of MATLAB for PCTRAN (Personal Computer Transient Analysis) of the power control system (PWR) type pressurized water reactor of PWR WESTINGHOUSE AP1000. The power controller model produces mathematical model description in nonlinear relation form in Simulink of MATLAB which is an important and popular program used at most universities for education. The power controller is described by a block diagram in this paper and some details introduce to clearly understand the work function. The results of action control compared with the PCTRAN programme in modes of automatic and manual control.

Vortex-induced vibration response of a circular cylinder surrounded with small rods

In this paper,cross-flow vortex-induced vibration(VIV)responses of a circular cylinder surrounded with different control rods have been investigated in a wind tunnel.The number of rods n is set equal to 3 and 6,and the ratios of diameters d/D(where d is the diameter of small rods,D is the cylinder diameter)are assumed to 0.10,0.16 and 0.20.The spacing ratios of s(s=G/D,where G is the gap distance between the main cylinder surface and the control rod surface)are selected as 0.2,0.4 and 0.6 respectively.The Reynolds number based on the main cylinder is in the region of Re=4000–42000.Results show that the VIV can be significant suppressed if placing the control rods in appropriate arrangement.And the gap between the rod and the main cylinder plays a more important role in the VIV amplitude response.When the spacing ratio between the rod and main cylinder is 0.2,VIV can be best suppressed by 96.7%.However,rods do not always suppress VIV and the responses can be more severe in other spacing ratios(s=0.4,0.6).And typical vortex shedding frequency lock-in phenomenon can be observed.When the spacing ratio is 0.2,other than the natural frequency component,St frequency is also presented in the frequency spectrum of wake velocity.

Optimization of spatial structure designs of control rod using Monte Carlo code RMC

Control rod is the most important approach to control reactivity in reactors,which is currently a cluster of pins filled with boron carbide(B4C).In this case,neutrons are captured in the outer region,and thus the inner absorber is inefficient.Moreover,the lifetime of the control rod is challenged due to the high reactivity worth loss resulted from the excessive degradation of B4C in the high flux area.In this work,some control rod designs are proposed with optimized spatial structures including the spatially mixed rod,radially moderated rod,and composite control rod with small-sized pins.The control rod worth and effective absorption cross section of these designs are computed using the Monte Carlo code RMC.A long-time depletion calculation is conducted to evaluate their burnup stability.For the spatially mixed rod,rare-earth absorbers are combined with B4C in spatial structure.Compared with the homogenous B4C rod,mixed designs ensure more sufficient reactivity worth in the lifetime of the reactor.The minimum reactivity loss at the end of the cycle is only 1.8%from the dysprosium titanate rod,while the loss for pure B4C rod is nearly 12%.For the radially moderated design,a doubled neutronic efficiency is achieved when the volume ratio of moderator equals approximately 0.3,while excessive moderating may lead to the failure of control rods.The control rod with small-sized pins processes an enhanced safety performance and saves the investment in absorbers.The rod worth can be further enhanced by introducing small moderator pins,and the reactivity loss caused by the reduction of absorbers is sustainable.