PAUTHENET EDF Septen France,

Division Combustible Nucléaire,

Lyon, France

Abstract

We present in this paper some results obtained with a numerical model of control rod behaviour. Drop time and insertion force are studied by means of a large parametric analysis. Fuel assembly deflection is the main parameter of this study. Several loads are taken into account in control rod displacement calculation: fluid load, gravity and friction force against the guide. Simulations are compared to measurements carried out in a full-scale prototype. The analysis of drop calculation shows that the friction cannot be neglected when fuel assembly is bowed. The main result for insertion force calculation is the important sensitivity to data entry. Determining exact deflection all along assembly with precision is needed. Otherwise, approximated friction force is obtained.

1. INTRODUCTION

In a nuclear pressurized water reactor, control rod clusters are used to control the neutronic activity of the core. Two kinds of experimental tests are used to estimate their behaviour : the drop time measurement test and the insertion strength measurement. Occasionally, longer drop time may be noticed. Reactor start up may be prevented if drop time exceeds a limit value, which is assessed by safety requirements. The measurement of the insertion strength is an indication of the effectiveness of the control rod cluster/guide tube component. It allows to choose the optimal component and can justify the interest of a technical evolution.

In order to simulate both of these experimental tests, a numerical approach is developed. A model of a control rod cluster/guide tube was carried out with Code_Aster (a finite element code). This numerical model is qualified on measurement tests carried out in a full-scale prototype [1].

We present in this paper a methodology including simulations and a parametric analysis (kinetics of drop according to the geometrical, mechanical and fluid characteristics) that can provide general trends. The analysis of those experimental measurements allows to diagnose defective components.

2. NUMERICAL MODEL DESCRIPTION

Control rod is a slim component (13 m high for 0.2 m large). One can observe three principal parts:

drive rod, spider and cluster. Control rod is loosed supported in guide tube to permit the drop. Outer

rod diameter is about 9.7 mm and inner diameter of assembly guide tube is a bit more than 11 mm.

Clearance to diameter varies from 1.6 mm in the upper part to 0.4 mm in the dashpot.

FIG. 1. View of the numerical model

Our numerical model is not a real 3D model with the real geometry of the spider and the twenty-four absorber rods. Calculation would be too heavy to solve because of rods number and long size contact conditions.

The control rod is considered as a single beam with equivalent characteristics for its different parts. This beam is sliding between several plates simulating right and left sides of the four different components of the guide tube (figure n°1).

Mecanisms, guide tube (continuous and discontinuous) and assembly are taken into account with their real height.

Each couple of plates is linked with springs which stiffness is equivalent to the ovalization stiffness of the component.

Each plate is also fixed with an anchor stiffness.

Modal characteristics of control rod and fuel assembly are fitted to reproduce their experimental eigen frequencies.

The bow and S assembly deflections observed in core are considered.

Displacement of control rod is taken at its neutral fibre and is laterally limited in a channel whose size is equal to real clearance between guide tube and rod.

Assembly dashpot induces a reduced channel diameter.

Equivalent component characteristics are principally obtained in respect of stiffness to mass ratio either for absorber rod and assembly. Main eigen frequencies of fuel assembly and control rod are correctly fitted.

3. CALCULATION METHOD

The mechanical model is the same for insertion strength and drop.

For drop time calculation, control rod motion depends on its forces equilibrium: it falls under its weight slowed by Archimede force, viscous and pressure fluid forces and eventually mechanical friction. Fluid forces are calculated at each instant depending on several parameters: control rod position and speed, primary flow, core temperature. Fluid forces calculation has been validated independently on numerical bench mark [2]. Contact and friction forces are evaluated numerically by the contact operator [3]. The result is validated with this study.

A direct in time resolution (by Lagrangian method) is made with contact conditions and “Coulomb”

Anchor

Insertion calculation doesn’t need any fluid forces because the motion is very slow. Netherless, the insertion calculation is more constrained than drop one because of the insertion imposed speed (1 m/min), so calculation time is hardly longer: 40 hours for the insertion and 12 hours for drop with contact and friction.

4. ENTRY AND VALIDATION DATA ORIGIN

Assembly deflection data entries are issued from another FEM approach taking into account all assembly static loadings (mechanics, fluids, temperature…). Static position may also be imposed on the grids. This possibility is interesting because it is the same technique as experimental one, then it permits to furnish equivalent data for simulation and experiment.

Validation of numerical results is realized by measurement tests carried out in a full-scale prototype.

Bow, S and W assembly deflections observed in core may be considered for different deflection values. We chose one bow type and one S type because those deflections are the most frequent. They are also penalizing because of the choice of deflection values.

5. NUMERICAL INSERTION RESULTS AND COMPARISON WITH EXPERIMENTS

Without assembly deflection, insertion force calculation is out of interest. The numerical rod falls straight down without touching the guide tube, when experimentally a light unknown friction force occurs.

Figure n° 2 shows a comparison between calculated and measured forces in a 30 mm bow deflection case. General fitting is good and the evolution is rather well reproduced. Insertion begins on right part of the curve.

0 100 200 300 400 500 600 700 800

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0

Insertion in m

force in N

Calculation Experiment

FIG. 2. Insertion forces. Experiment / calculation comparison for a 30 mm C deflection.

During insertion, strength varies smoothly when passing at each grid level and strongly when entering in dashpot.

For S deflection case (figure n°3), smooth strength variations are different as in bow case, calculation still reproduces them as well.

The main result of the parametrical study is an important sensitivity to data entry. All the geometric details contribute to define contact and friction evolution. Determining exact deflection all along

assembly with precision better than 0.1mm is needed. Otherwise, approximated friction force is obtained. Determining deflection is difficult because of non-linear link between rod, grid and guide tubes. The main error is located in dashpot area where channel is narrower. Figure n° 3 shows the effect of a modification of the drop channel in the grid 2 area (entrance of dash pot).

0 200 400 600 800 1000 1200 1400

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0

insertion in m

force in N

REF2C calc REF0B calc REF7C calc

c

FIG. 3. Effect of a light change on deflection at the entrance of dashpot.

This case is a bit caricatural but it shows clearly strong effect on force insertion of little change in geometry. Fortunatly, this sensitivity occurs after the dashpot has been reached. This shows that data entries must be precise. The important available data bank will permit by reverse method to improve the simulation quality in order to progress in the data entries and calculation knowledge.

6. NUMERICAL DROP RESULTS AND COMPARISON WITH EXPERIMENTS

In this paragraph, figures show the evolution of control rod drop speed with respect to time. In these three cases, hydraulic parameters and Coulomb friction are set and the varying parameter is the assembly deflection type.

Bold curves are the calculated curve while the grey ones are experimental.

In case of figure n°4, assembly is straight. We can see the good global form. Speed is increasing until equilibrium between resistant fluid forces, active weight and a light constant friction force, is reached.

Control rod speed falls down rapidly when rod enters the dashpot. Experimental oscillations are clearly impossible to reproduce. Calculation is chosen to stop at 1.75 s after entering the dashpot.

However speed doesn’t decrease enough. Calculated fluid forces seem not strong enough in the case of this prototype. An increase of experimental friction force is also possible in the dashpot (constant during drop in calculation).

FIG. 5. drop time with 30mm bow deflection.

In case of figure n°5, the assembly is cambered with a 30 mm bow deflection. In comparison with the previous straight case, drop speed is shorter and in consequence drop time is longer.

It shows that the friction force is important enough to modify the drop kinetics in this case. As the experimental speed, the calculated one is almost stable during 1 s before falling down due to presence of the dashpot.

Calculation has been stooped at 2 s.

FIG.6. drop time with S deflection.

In case of figure n°6, assembly is cambered with an S15-12 mm deflection. Drop time is about the same as in the previous case but the speed evolution is clearly different.