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Hot channel

As explained in the introduction, a hot channel model has been attached to the core average channel "c", in order to assess commonly used safety quantities such as max fuel temperature, fuel heat content, max clad temperature, dnb (departure from nucleate boiling ratios,...), used in safety evaluations.

Hot channel representation is activated by the keyword hot_channel which is, normally, called after step_end when the feedback's are stabilized, because the hot channel does not retroact on average core conditions, which are evaluated on the average channel only.

In variables's names, hot channel is pinpointed with a "7" appended to average channel "c"; for example, f2ci for average becomes f2c7i [nuclear power F; at eos 2; in the Core; hot channel 7; Interval].

Input data for hot channel are entered under the data group hot_channel.
Per default, hot-channel fuel rod and channel are assigned the same input data as the average channel (core) , entered under Lstuc.
Hot channel distinctive data can, however be entered under Lstuc7.
For example, a low value of pellet conductivity could be entered under Lstuc7 in order to maximize hot pellet center temperature, whereas it would be taken low for the normal fuel rod in order to minimize power feedback effects.
Additional specific entries for hot channel are:
xwec7 [multiplier X; of floW; at Entry; of Hot 7; Core channel] which makes it possible to underfeed the hot-channel.
xuruc(1:6) is the weighing vector used in calculating the effective pellet temperature.
Here xuruc7 would be specified as xuruc7= 1,0,0,0,0,0 for reaching the center temperature or
0,0,0,0,0,1 for reaching pellet edge temp.

The hot channel is processed exactly like the average channel by (do, core) except that power f27ci in mesh ci is not derived from the local neutron flux but simply scaled from f2ci by means of a radial power form factor fxykn correlated, versus vm, ig, u, h, ehec.
The effect of boron on power peaking is neglected.

Hot channel values calculated by end_step, hot_channel
For each mesh c7i:
f27ci: power deposited in pellet
flu: linear (W/m) power deposited in hot fuel rod.
qlu: linear power heating the water.
qsc7i: heat flux (W/mē) [thermal power Q; per unit surface S; in c7i] in clad-water film.
This thermal flux is used for dnb evaluation.
u2rc7i: [pellet temperature U; Radial distribution; in hot channel cell] on ir=1 for center, 2,3,4,5, for the 4 successive sectors (), 6 for pellet edge,..
At node ck level:
t17ck: water temperature in node
c7k of hot rod.
fluc7: max flu
fqc= fluc7 / fluc, where
fluc is the average of fluc7i
iu27ci: [mesh Index;] where max u27ci is observed
hu2c7: fuel enthalpy (0 J/kg at 0 K) at that location. This property is used in rod-ejection accidents evaluation.

Departure from Nucleate Boiling Ratio

A simplified evaluation of DNB flux qsdnb7ci, [thermal power Q; per unit Surface; at onset of Departure from Nucleate Boiling; in each c7ci] is computed by inserting "dnb" after end_step, hot_channel.
It is the heat flux at onset of boiling crisis from which clad temperature suddenly increases by degradation of film heat-transfer.

This value, calculated by empirical correlations, depends on the local thermal properties and their upstream distribution.

dnbrc7: (Departure from; Nucleate Boiling; Ratio: in c7] is the minimum value of the ratio qs7ci/qsdnb7ci along the fuel channel.
Safety prescription impose a ratio larger than 1 with a margin (of about 30%) accounting for correlation uncertainties.

DNB correlations were established at steady state test conditions and their extension to transient conditions has not, to author's knowledge, been demonstrated.
Although dnb correlations are being developed for each type of fuel, depending on flow mixing grids geometry, the classical Tong correlation has been implemented here (recast in SI units) in order to get a first feeling of the dnbr behavior.

(1:11) reminds the coding of Tong correlation.
(1) is the flow at hot channel inlet
(4:7) cp1 to cp4 are pressure only dependent factors .
(8,9) cx1 and cx2 are function of local x27ci (water quality).
(8) G7 is the flow density;
(10) cd1 depends on hydraulic diameter dhyc

This correlation (2) applies for uniform axial heat flux.

(11) For non-uniform profile, Tong proposes a correcting divisor xtongc7 .
qs7ci: local heat flux
z_ci: elevation of end of ci
z12: boiling length: elevation from nucleate boiing onset position
qs7ci: local heat flux

Nucleate boiling is evaluated, together with film transfer coefficient, by means of the classical Jens-Lotte correlation.

The proposed single, hot channel, representation provides a bounding evaluation of safety margins because:

In case several configurations are present, it implies that the hot channels of the different configurations are aligned.
As the hot channel does not retroact on the transient solution, it is possible to attenuate the over conservatism of the alignment effect by using the configuration fxy 's at state point conditions (at min dnb margin time) and repeat the problem.
In most of the applications, however, most of the enthalpy build up in the hot channel is provided by a single dominant configuration.

The hot channel closure assumption does not allow credit for inter channel gross and local mixing.
This effect could be evaluated by using, if the DNB correlation average channel enthalpy but hot channel heat flux in hot channel.
This model simulates perfect mixing. It is also possible to allow local, partial, enthalpy exchange with the average channel.
These modifications have, however, not been implemented yet.

A simple example

hot_channel_dnb.dat

The application covers only the ini condition (ini, core, hot_channel, dnb);

down_comer/Lsta: required for allocating Lsta
bottom/Lstb: conditions at core inlet
core_config/Lstcfg :
i9gr=1 single config 1present ;
3.65001=core height.
core: actually the neutronic data are not required here for normal and hot channel thermal calculations because power distribution f2ci is imposed at initial condition.
&Lstc
xfuc: .974 of fci power is deposited in the pellet and determines the heat flux in the heat transfer film; the complement is directly deposited in the coolant and contributes to its enthalpy elevation.
Lstuc: thermal data for average channel= default for hot channel
xfruc: internal power distribution in pellet; not relevant of dnb calculation.
xuruc= effective temperature weighting vector: not used for thermal calculations only.
Lstci
f2ci: cos distribution for 3442e6 W total power.
If requested, f2ci can conveniently be scaled by the factor xf0c under &Lstc.
&Lstg: required for defining form factors vs vmg
Lstrvg and Lstsxvg required for structures allocation;
hot_channel/Lstfxyvg/fxyog= 2*1.577: no density effect.
Lstuc7/xuruc7= 1, 5*0: allows to reach center pellet temp; no effect on DNB.
pressu/Lsto/p3= 157.1e5 : only data for pressu.
Results
(chart 1) Min dnbr is reached at idnbrc7=21. Note that nucleate boiling starts already at ci=9, the Tong non-uniform corrector is 1.0999, water is still sub-cooled at min dnbr point.
The results have been benchmarked against COBRA predictions using the same DNB correlation and same closed channel assumption.