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Rod-drop accident

General description

The "dph/dt" protection system aims at detecting the accidental fall of one or several rods.
The detection condition, already introduced previously, is expressed by the dimensionless condition
(tau s)/(1+tau s)(phc/ph0c) < lim with
tau ≡ tau_au_dphdt,
lim ≡ dphdt_au
are entered in group
&Au_dphdt phc is the average neutron flux, and ph0c a normalizing value (usually the nominal value).

"dphdt" protection system acts as a backup for the other drop detection systems by end-of-stroke detection and by monitoring the radial unbalance of the response 4 fission chambers, appearing in cases of centrally unsymmetrical position of the falling rods.

In the present implementation of the dph/dt protection system, the source signal is the relative flux.
Actually the protection signal is the normalized and inter calibrated response of the 4 fission chambers around the reactor vessel.
The dropping rods configuration is not, in general, centrally symmetric, so that the chamber signals are unbalanced by radial flux tilting and a tilting correction must be applied to each chamber response according its position relative to the dropping group.

In SAFPWR such a correction could easily be simulated by representing each chamber, in turn, as a pseudo hot channel, and calculating ph7ci and omph7ci from the average flux values and pseudo Fxy representing for each configuration, the tilting, factor towards each individual chamber.
Trip occurrence must also account for the trip logics (ex: reactor trip if the threshold lim is reached in 2 out of 3 detectors).

The present application is limited to the detection phase: observation of the trend of the detection variable y2 during the drop.

The choice of the parameters tau and lim results from a compromise: the values should be small enough to detect the lightest reactivity drop group as soon as possible, but still large enough to avoid spurious reactor trip in the course of operational transients.

For given values of tau and lim, the SAFPWR rod drop analysis should aim at identifying the heaviest, non-detected, rod drop configuration, and checking that, in the course of subsequent return to power due to core average temperature regulation, the safety limits (min dnbr, max fuel temp,..) are not jeopardized.

The present rod drop accident application example is solely limited to the detection phase, because the post drop recovery transient analysis requires modeling core power and temp regulation, which are not (yet) implemented in SAFPWR.

Discussion of input data

For detection analysis, a core-only representation is sufficient.
Core data (drop_a_safpwr.dat ) (download) are similar as those used for the loss-of-flow application.
The falling rods are represented by igr=2 falling into an unrodded configuration igr=1.

Rod drop trajectory versus time is represented through the core_config/Zgri_sec/zgri(sec) interpolator.
The emergency trip insertion displacement law dgri(sec) is entered, but not activated here.
Detection parameters are input in core_config/Lstau/&Au list, where an arbitrary high dsec_au is set in order to avoid trip, and in the list &Audphdt where we use typical values for tau (tau_au_dphdt) and lim (dphdt_au).
Detection threshold lim is negative because the system must detect excessive negative flux rate.
In some reactor protection design, the trip relation makes use of absolute formulation as follows:
ABS[(tau s)/(1+tau s)(phc/ph0c)] > lim
with a positive value for lim.
In such a case, the system protects also against excessive positive flux rate, which may provides an early indication for abnormal reactivity insertion.
In namelist core/&Lstc we input as f0c_au_dphdt the reference power used for determining ph0c in the ratio phc/ph0c.
A reference cos distribution is arbitrarily selected for f2ci. The initial power profile is surely a sensitive parameter. The values entered for core/Lstrvg/rog represent a fall of about 1.6% reactivity.

Discussion of results

At execution time, when trip occurs, the following line will appear on the console or on safpwr.lis:
"au_dphdt: sec_au_dphdt, sec_drop, y1_au_dphdt, dphdt_au, y2_au_dphdt 0.936 100.936073 -8.5325E-02 -0.100 -0.126."
sec_au_dphdt is the time at which detection occurs (when y_au_dphdt reaches dphdt_au);
y1_au_dphdt, y2_au_dphdt are bos and eos values of y_au_dphdt for the detection step.

Chart1 pictures y_au_dphdt and core reactivity rc and Chart2 f2c/f0c, q2c/q0c together with falling rod group elevation zgri. At detection time, q2c/q0c is still close to 1 so that the reactivity feedback should be negligible. At sec>3 it is however well apparent: the reactivity decrease is 1.015% while the rog decrease is 1.26%.

Normally, calculation and plotting of y2_au_dphdt is interrupted after detection. In order avoid that, an arbitrary large negative value (here -100) has been set for dphdt_au.

As a matter of test, in chart 1 y_au_dphdt is also calculated from the implicit finite difference discretization approximation
(y1+x2-x1)/(1+dsec/tau) of the operator
(tau s)/(1+tau s).
For the small dsec=.1 selected here, this approximation is very close to the analytical result.

Note: if a flux chamber is simulated as located in a pseudo-hot-channel, its total response (for a long chamber covering the whole active core) the contribution of each configuration to the chamber current will be proportional to the corresponding configuration radial factor fxyg, which amounts supposing that neutrons move horizontally from the core radial boundary to the detector.