SAFPWR home page

Loss-of-flow accident

Cause of accident: enforced reactor coolant flow reduction resulting from an accidental drop of electric supply grid frequency.
The assumed primary pump volumic flow coastdown curve is given on chart 01.

Protection is insured by the fall of all rods, supposedly initiated after a time delay core_config/ Lstau/ &Au/ sec_drop= 2 after initiation of flow reduction, occurring at sec=0.

Description of input file

See comments along the lof.dat (download) file.

We remind that the selected input data are "typical" and do not reflect any particular PWR plant data.

S00gvg: SG is represented to allow investigating possible effect of flow reduction on inlet enthalpy hec.
core
Lstci/ f2ci: (chart 6) upwards skewed (dnbr penalizing) profile which could possibly be generated as a result of axial Xe oscillation.
Lstrvg : this simplified set corresponds to a moderator temperature coefficient
d r/d tw= (d r/d vm)(d vm/d h)(d h/d tw)
= (d r/d vm) vmhp htp = -6.4 e-5/K.
The Doppler coefficient:
d r/d tu= roug/2/SQRT(u2c)= -2.8e-4/K,
for u2c=870 K is taken unrealistically hight for maximizing Doppler effect.
hot_channel/Lstfxyvg: for calculating DNBR in hot channel, fxyog would be typical values for unrodded and rodded configurations.
The rodded value is important if the axial slice where the min dnbr is observed is rodded.
Pressu: retain simple typical homogeneous model because only a slight increase of pressure is anticipated.
Lsts: neglecting spray effect enforces pressure increase due to coolant expansion.
loop_1
Lstl1
wvpl(sec) (chart 10) defines the assumed volumic linear flow coastdown law.
Lstli1: simplified loop and steam_gen model tentatively assumed unless a non-negligible increase of hec is observed in the course of the transient.
steam_gen_1: Normally the emergency trip also checks SG vapor release; this is however a long term effect which should normally not impact the dnbr decrease.
Lstn1/qgvn= 9.25e8 = f0c/3 because primary pumps and pressu heater contributions are neglected
Sequences:
S3=
do, call:4 executes the normal enthalpy balances run along the primary loop (S4), with frozen secondary temp field.
redo, call:5 repeats the run, but with core represented as an equivalent heat-gen fed by the heat power q2ck supplied by do, call:4.
Remind that this repetition is provided for controlling the possible instability linked with the non implicit balance of the outlet node when large dsec are used. The redo repetition uses the simplified node enthalpy treatment.
redo, steam_gen_1 updates the sg condition with frozen primary temp field and regulates water level by adjusting wyan.
(do, steam_gen_1 leaves wyan constant)
Once converged eos conditions achieved,
end_step, core is invoked for editing core items, and
hot_channel and dnb are invoked to look at hot channel properties (which do not retro act on the core conditions).
call:6 enables plotting, and
ctrl controls repetition of the looping sequence S3 until secmax is reached.

Discussion of results

Chart 06 illustrates the deformation of axial power distribution in the upper part of hot-channel (in meshes 11 trough 20)
chart 03 exhibits core Δh≡ hsc-hec variation resulting from the conflicting effects of flow decrease caused to pump slow-down and power reduction due by tripping.
Thanks to the combined effects of transport delay of hsc and thermal inertia of sg water, the core inlet hec is barely affected by the accident, at least during the period when the min dnbr is observed.
Chart 04 indicates also that, in the same time period, the primary pressure increase p3 is not worth taking credit for.
Consequently, for the purpose of following dnbr, a simplified model representing the core only, with constant hec and p3, but variable wec is perfectly acceptable.

[lof_core.dat (download)] gives an example of input.dat for such a simplified model.

Note that as the loops are not represented, inlet mass flow must be entered (chart 11) in bottom/Itpsec as wsb(sec) Chart 11 confirms that the effect of hec variation on wec is negligible.
(chart 12) compares the lof_system and lof_core models in terms of dnbr, and confirms that the effect of explicit SG representation is not worthwhile.
chart 01: plots f2c, q2c, together with the relative flow wec/w0ec.
chart 05 shows that, at 2.2 s, when min dnbr is reached, the flow is still at about 85% of its initial value whilst the falling rods bank is still close to top.
chart 06 compares the power f2ci and heat flux qsci (in film) profiles: it is observed that f2ci is directly affected by rod penetration, whilst the film heat flux qsci at sec= 2.2 is barely deformed thanks to the pellet thermal inertia.
chart 08 depicts the same qsci together with the mesh vapor quality in the hot channel: as opposite to qsci, xci is directly affected by the flow reduction; this is actually the main cause of the dnbr decrease.
Stationary verification of safety margins at state-point
The very fact that, at min dnbr time, the heat fluxes is still unchanged, suggests that a fair evaluation of the dnbr effect could also be obtained on a stationary representation of the core, but fed by the flow value observed at min dnbr time.

Lof_core_ini.dat (download) is the input deck for such a problem.

The resulting qsci_ini and xci_ini are plotted on chart 06 and chart 08 for comparison: qsci_ini is indeed still very close to qsci at 2.2 s, whilst x2ci_ini is just above the transient value at sec=2.2 because of the memory effect of flow variation.
This explains why the calculated stationary dnbr is 2.766, slightly below the transient value (chart 07): the stationary evaluation model thus provides a fair, not overly conservative estimation.
If min dnbr would occurs later, as in the application case with sec_drop=4 instead of 2, this conclusion would no longer be valid, because of the not negligible deformation of the qsci distribution at that time.
chart 09 highlights the effect of delaying trip to 4 s.
Curiously, (chart 08)the xci distribution for such a case remains comparable to the initial distribution; consequently, the reduction of dnbr is above all caused by the flow reduction.

The interest of calculating dnbr on stationary representation is to make it possible to apply licensed thermal design methodology, SAFPWR being used to evaluate the min dnbr time and check that the initial distribution of heat flux and vapor quality still apply.