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Testing ODT protection on a power ramp

The concept odt protection system has been introduced earlier.
The "Group Withdrawal accident at Power" (RGP: Retrait Goupes en Puissance) is the typical accident protected by this system.
The operation of the system will, first of all, be tested by simulating the core as a simple thermal generator delivering a linear power ramp.

Description of input (odt1c_dat) (download)

The system model is similar as for the LOF accident, except that the core is here simulated by heat_gen and steam_gen_1 is solely invoked for initializing the secondary temperature distribution t1nj which, thereafter is kept invariant in the course of the transient.
Indeed, reactor trip usually occurs before significant change of secondary conditions is observed.

The overpower and the two ODT protections are possible tripping candidates if any of the following conditions is satisfied:
f2c > f2c_au, or
dat2_odt > dat2_opdt, or
dat2_otdt > dat2_au_otdt.

At the first (time) step at which one of the conditions is filled, the program computes the trip time at which all the rods (if any) will start dropping as:
sec_drop =
MIN{sec_au_f2c, sec_au_opdt, sec_au_otdt}
+dsec_au
As for the dph/dt protection, when a trip condition is encountered, the corresponding trip items ceases to be calculated for the later steps: on their plot, they keep their level at trip eos.

Trip data are specified under

core_config/Lstau
Lstcfg must not be entered, because there are no configurations in the heat_gen representation.
Entering it would cause execution to halt.
Under &Au, we enter the generic au data, which are the same for all au types.
The odt trip data under &Auopdt and &Auotdt are typical, tentative values.
heat_gen
&Lstc: a single node representation (k9c= 1) is adequate for generating the forced power ramp f2c(sec).
oqc=1 insures that q2c=f2c (no pellet representation).
Itp_sec/f2c(sec): A rather long constant f2c period of 25 s has been allocated for allowing, in case Lagrange representation for the down comer and the loop is selected, a complete transition from Euler initial condition to the Lagrange initial steady system conditions, which are slightly different
Thereafter, a 5 s power ramp to 1.2 nominal is applied.

loop_1
Under Lstl1 list, we set
i9l= 25 nodes and we must specify the hot leg and cold leg nodes
ithl_odt and
itcl_odt where the odt temperatures sensors are connected.
Flow is entered here as the wvpl of a pump located in node ipl.
Data left under comment are specific to Lagrange model to be used later
steam_gen_1
Lstn1: As no power is dissipated by pump and pressu heaters,
qgvn is simply f2c/3.
Entering p3n=52e5, actually imposes the secondary saturation temperature tln(52e5)=539.44.
ini, loop_1 [] determines the tnj temperature field (?), remaining constant later on.
From qgvn and hyan, ini, loop_1 calculates wyan ;
The Ratio of input values wyan and w2an allow setting the initial recirculation ratio, and actual value of wyan.
ini, loop_1 adjusts heat-transfer area so that q2c can be evacuated with the set values of hsb, wvp, p3n, wyan, hyan, and w2an/wyan.
Lstnj1: In addition to the 5 secondary heated nodes we allocate an additional node nj=6 for the riser, although not used for the present application.
read/Plots
Thermal protection related variables are collected in plot0, and plot1.
Odt variables are gathered in plot2.
Analysis of transport effects is accomplished by comparing
tsc vs t2hl_odt and tec vs t2cl_odt.
In terms of odt protection variables the comparison will involve dat2_odt vs datc and t2_odt vs tavc.
The "close" core protection limits datc_opdt and datc_otdt can be used as ideal reference values for assessing the performance of dynamic compensation.
odt items calculation is enabled by end_step, heat_gen.
Last remarks before looking at the results:
dsec_au is supposed to be the same for all au types.
If dsec_au were also used to include the transport delay in the temperature monitoring lines delays, then a au-dependent dsec_au should be used, which is not presently implemented.
Likewise, odt_au is presently provided for loop1 only. If the loops are not balanced, a loop-dependent odt protection could easily be implemented in the program.
Results

Overpower and odt trip results are, first of all, edited at execution time (if trip occurs) on the console or may be redirected to safpwr.lis by means the redirection command
rse safpwr > safpwr.lis.
Excerpt of edited infos:

"gv%epsq,iqgv,dxqgv,zn%xq
9.999E-05 6 -2.244E-04 0.7656":
after 6 iterations, heat-transfer area is scaled with xqn= .7656.
"au_f2c:
sec_au_f2c, sec_drop, f1c, f2c_au, f2c
27.539 29.039 3.094E+09 3.156E+09 3.2088E+09":
au_f2c is reached first, at sec_au_f2c;
rods (if present) start dropping at sec_drop
"au_otdt:
sec_au_otdt, sec_drop, dat2_odt, dat2_otdt
28.8075 29.039 43.322 42.415 ":
au_otdt is second, detected at sec_au_otdt.
sec_drop is not altered
au_opdt:
sec_au_opdt, sec_drop, dat2_odt, dat2_opdt
29.615 29.039 44.343 43.566 :
au_opdt is the last detected.


(chart 1)) plots all odt variables of interest.
The first trip is by au_f2c at sec_au_f2c=27.54 when q2c/q0c reaches 1.102.
Direct core otdt trip (red curves) would be reached at 28 s.
Actual otdt trip (blue curves) is reached at 28.38 (28.81)s, slightly after the "reference" direct trip: the dynamic compensation is therefore satisfactory.
On the contrary, the non-compensated (static) otdt trip would occur much later at 30.4 (32) s (when dat2_odt = dat2s_odt) : the dynamic compensation is indispensable! Static opdt trip occurs still later.
The results may alternatively be presented in the protection plane:(chart 6,7)

Lagrange representation of transport effects

It was explained earlier that the Euler transport scheme suffers from the forward diffusion effect which may alter the odt response.
In order to investigate this effect, the application is repeated with the Lagrange "X" option for the down_comer (xdown_comer) and the loop (xloop_1).

The input set differs from the euler set by adding under Lsta/ davea, the initial element volume.
n99a is the additional max element number which must be provided to account for edge elements splitting.
Similarly, under Lstl1, we enter an element default volume
davel= .5, small enough for monitoring the odt temperatures in nodes 5 and 16.
Note that the initial element volumes is much larger that the vli in the sg tubes: this results, as explained, in a different pattern for initial fields along the loop.
n99l the additional elements splitting allowance. If requested, those allowances could be calculated by the program. Note that the Lagrange related data could be specified for each loop in turn. However, the odt tripping is presently possible for loop_1 only.

Following lines are written on safpwr.lis at execution:

au_f2c:
sec_au_f2c, sec_drop, f1c, f2c_au, f2c
27.539 29.039 3.094E+09 3.156E+09 3.208E+09
au_otdt:
sec_au_otdt, sec_drop, dat2_odt, dat2_otdt
28.93 29.039 44.29 43.939
au_opdt:
sec_au_opdt, sec_drop, dat2_odt, dat2_opdt
29.284 29.039 45.73 44.043
Chart 2 compares Euler and Lagrange solutions for wec: it takes some 25 s to reach the Lagrange initial stationary pattern.
The .5% higher value reached by wec is explained by the slight difference in water density at pump location.
Otherwise, the wec trend is similar, except for an additional wec oscillation after power ramp terminates.
Chart 3 compares the dat (black for Euler, red for Lagrange).
There is no much difference for core dat, which is normal as datc depends only of power.
The Lagrange dat2_odt however is slightly less delayed than the euler one.
This could be explained by the sharper front of the Lagrange temperature.
Same comparisons are repeated on chart 4 for the average values (tavc for core, t2_odt at sg boundaries.
It is of course of importance observing the effect of temperature pattern deviation on the odt responses (chart 5 )
sec_au_f2c is of course not affected.
otdt trip is reached at 29.93 (vs 28.80 for Euler) and slightly after the core otdt trip.
For this application, at least, the otdt detection time is approximately the same for both transport representation.
The opdt detection occurs 1.5 s earlier.