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Interpretation of PWR transient application 2
Despite of the highly simplified data set and the poor nodalization used for this application, examination of the results will allow gaining a first idea of the system behavior for this unprotected rod withdrawal application case.
The results are collected on the plot files wrt.pl0 to wrt.pl3 written, at execution time, in \SAFPWR directory.
The files are updated at each new application.
(View a excerpt of wrt.pl0.)(003.123)
Chart 1 depicts, versus time
sec on X-axis, the position
zgri(1) of the raising group, plotted on the second Y-axis (as denoted, after the plot legend, by one or several arrows ">" pointing to the right y-axis).
Before initiating the transient, a 10 s period has been allocated for checking the stationarity of the initial state. As the stationarity is well confirmed, this checking period could be skipped.
From transient's inception the nuclear power f2c rises as the result of reactivity injectd by group 1 withdrawal and is only turned back from sec=20 when withdrawal stops.
Reactor thermal power q2c delivered to coolant follows f2c with some time-lag due to fuel thermal inertia and peaks 2 s after the f2c peak.
Thereafter both powers decrease steadily thanks to the sole effect of Doppler and moderator reactivity feedbacks and a new steady state is eventually reached after 100 s of transient time.
Core reactivity
rc is plotted on
chart2.
It peaks at 13 s, thus 7 s before rods withdrawal halts. The peak value is only 33e-5 whilst the potential max reactivity injected by the group rise is
500e-5*1.8/3.658=246e-5 (in point kinetics, reactivity increases linearly with rod displacement).
The rapid attenuation of
rc release is clearly linked to fuel Doppler effect, as demonstrated by the rapid rise of pellet effective temperature
u2ck (
chart 3) and, to a lesser extent, to moderator expansion (
vm2ck).
In case of very slow group withdrawal, the power would steadily transit, without overshoot, to the final stationary power.
Chart 4 shows the average channel enthalpy as compared to the saturated liquid enthalpy
hl0.
Chart 5 shows the primary pressure
p3 increase due to the primary water expansion rate, represented by the flow
wso [floW, Sortie, Outlet] into the pressu expansion line.
Chart 6 depicts the conditions in the hot channel "
7".
Net boiling at channel outlet is observed (
h2c7ck > hl0) .
Chart 7 depicts the trend of
dnbrc7 [Departure from;Nucleate;Boiling;Ratio;in Core;hot channel 7] and
Chart 8 the evolution of center temperature
u2c7k in hottest pellet as compared to effective temperature
u2ck in average pellet.
The transient condition in the SG 1 secondary side is illustated on
chart 9 which depicts the trends of
the total thermal power (q2c+qyp)/3+qyli(ipl) generated in the primary system, for one loop basis,
qyp: pressu heater,
qyli(ipl): power dissipated by primary pump in the node ipl where the pump is located in loop l), together to
power qcn1 [power Q;to Core;of sg N1] transferred by the sg tubes to the secondary coolant, and
net power qn1 delivered by sg n1 to the tertiary side.
It is observed that the increase of primary average water temperature tavc is noticeably larger than that of secondary SG core temperature tnj1 [Temperature; of sg N1;in node J=1].
This is explained by the huge thermal inerty of the secondary water.
For most fast transients the assumption of constant secondary temperature may be retained without overly conservatism.
Chart 10 shows the secondary pressure
p3n evolution resulting from the chocked flow
wydn discharged by the dome
dn through the constant opening nozzle.
Curiously, at transient's onset, the flow
wyan [floW;injected Y;into AN] does not follow the discharged flows
wydn but starts at first to decrease: this is explained by the densification of
cn mixture (caused by pressure increase) which tends to reduce the water elevation
zan in
an, which, in turn, must be counter-balanced by a decrease of
wyan in order of keep
zan constant (cf
chart 11).
Thereafter
wyan catches again the
wydn trend.
This apparently "abnormal" behaviour of
wyan explains why it is not obvious to design a constant level regulator on the sole basis of measuring
zan, wyan and
wzdn.
At last,
chart 11 portrays the
w2an transient, [floW;at eos 2;at the bottom of Annulus;of sg N].
We observe that the relative variation of
w2an is much smaller than that of
wydn. This is a remarkable property of the natural circulation SG's, which helps maintaining good heat-transfer condition on a large spectrum of operational conditions.
The assumption of constant
w2an would no be unreasonable, for most transients, .
The "numerical" level regulator installed in the sg model performs perfectly. The real regulator would tolerate some level error, but it is expected that this would not affect the sg behavior, as far as the primary is concerned.
The unprotected case was presented as first example in order to show how the sole effect of the natural reactivity retroactions is effective in controlling the transient.
Normally, the accidents would be checked by the nuclear overpower (neutron flux) protection trip.
Protected reactor case
An example of a protected case is setup by adding the following data lines to the core_configuration data group:
core_configuration
Lstau
&Au
dsec_au= 1/ !same for all au types
&Auf2c
f2c_au= 3.3e9, which corresponds to a nuclear power trip level of 3.3e9 W, namely at 3.3e9/2.775e9 or 119% of nominal level, with a time delay of 1 s between reaching trip level and drop initiation.
On safpwr.lis additional line will show up:
sec_au_f2c: trip detection time
sec_drop: drop initiation time (dsec_au later)
f2c: power peak
zaugri: withdrawing group elevation at trip time.
The following charts illustrate how some major variables are controlled by the trip.
Chart 12 shows that
f2c peaks slightly above the trip level, but
q2c remains lower.
About 15 s after trip time, the initial power conditions are already recovered.
Chart 13 indicates a small primary pressure
p3 surge and the trend followed by
wso.
The last
chart 14 depicts the conditions in sg where the effects of the event are barely perceived.