Steam-generator modeling

We retain the same basic modeling ideas as for the primary:
- decomposition of the fluid transformations.
- global pressure approximation:
vmj =vm(hj,p3n) where hj is the local enthalpy and p3n the single, global, pressure attached the whole SG N.
- the contributions of kinetic and gravity energy are converted into thermal energy.

The "core" cn of sg n (n refers to the sg coupled to loop_l; with n=l), contains uniform, fixed volume nodes
nj=1,j9n(n).
Each node j of the secondary side of the sg receives heat power q3nj from an ascending primary node i3 and q4nj from the descending node i4.

The simplified flow sheet describes the successive calculations conducted, for the different parts of the sg, in the course of processing do, steam_gen_n.

Thanks to this internal linearization correction, the heat-exchange process becomes implicit for tli and the qli calculation is stabilized.
Numerical experience indicates that, as long as the nodes are not too large, the linearization correction remedy is only required for the ini phase (see later), but the correction has been maintained, to make sure, for all steps.
The stabilization correction was here feasible because, in each node, the h2li calculation follows that of t1li.
This is, at present, not the case for the Lagrangian balance scheme, without some recoding. However, when Lagrange solution is enabled, the ini process remains eulerian and stable.
Note that the qli and qnj calculations are actually carried out in the course of the do, loop_l processing.

The sg dome region is modelled as an "ideal" representation including an ideal, zero-volume, separator returning saturated water to the annular region an, and releasing saturated vapor to the dome.
Furthermore, the water quantity retained in it is neglected, so that cn is, except in extreme cases, permanently filled with saturated vapor.

The steam dryer is not explicitly represented.
Quality of escaping vapor may also be adjusted at input.

The feed water flow wyan is imposed as input if the sg is free (unregulated) or adjusted by the sg water level regulator described along the an processing.
In case wyan < 0, then hyan=h2an.

At this stage, it will be generally observed that the expanded volume v2an of the an region differs from the value van which should be maintained by water level regulation.
Instead of modeling a real regulator, we have rescourse to an ideal regulator based on the same Newton method as used for heat-exchange stabilization: the whole process is repeated for a unit variation of wyan to obtain the derivative (51).

In spite of its relative simplicity, our "ideal" sg model is believed to be adequate for assessing the effects of sg secondary side behavior on reactor transients.

It is however valid as long as the sg operation remains "normal" ie when cn contains saturated vapor and natural recirculation is active.
In extreme cases (like SLB) some sg may become thermally isolated from the primary, and recirculation will cease because secondary water becomes warmer than that of the primary side.
In such a case, we have rescourse to an elementary "hot water bottle" representation of the whole sg as a single homogeneous volume "n".

It may also happen that the ruptured sg becomes "dry" in the upper part of cn (xnj >1) and the corresponding nodes can then no longer extract heat from primary because their temperature rise rapidly to that of sg tubes.
In order to handle such a situation, we have implemented a tentative model whereby the secondary heat transfer surface is simply nullified in the dry part of the tubes .
In absence of such a remedy, the sg model becomes instable and simulation of the late phase of accident is not possible.
Controlling instability by implicit handling of tnj, as was done for primary side tli could also be contemplated.

ini, steam_gen

Executing the ini procedure necessitates imposing following primary plant data: p3, hsb, q2c, (or f2c), primary pump flows and the contribution of pressu heater and pumps to total primary power.
For each sg: p3n, qgvn (whose sum must balance total primary power), hyan, the recirculation ratio taken as ratio of inputs w2an/wyan and the target value van of v2an. The recirculation ratio is viewed here as a known design characteristic.

Summary of the ini calculation procedure.

Next, the ini process proceeds with updating the t1nj of the under cooled nodes.

A value omqgv>1 must be chosen in order to accelerate the iterations.
This is linked to the fact that the power qli exchanged is under-estimated by calculating it from the node outlet temperature.
xqn corrects also for the finiteness of node volumes and is expected to decrease as the nodalization is finer.
If xqn deviates too much from 1 even with a large number of nodes, it means that the input heat transfer coefficients are unrealistic or that the desired pressure p3n is not feasible.

In some applications, it is acceptable to reduce the representation of the sg secondary side to an uniform distribution t2nj = t1cn.
This is achieved by setting input_t1cn(n) as true and entering t1cn(n) under Lstl.
In such a case, the inclusion of sg in the ini sequence is forbidden.
For an arbitrary t1cn, the execution of the ini sequence ini,bottom, ..., loop_l will result in an enthalpy hsl at l outlet deviating from the imposed hsb and t1cn must therefore be adjusted to eliminates the deviation.