atw 2017-07
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<strong>atw</strong> Vol. 62 (<strong>2017</strong>) | Issue 7 ı July<br />
RESEARCH AND INNOVATION 472<br />
| | Fig. 7.<br />
Experimental and calculated temperature of sodium in central subchannel at z=770 mm.<br />
| | Fig. 8.<br />
Experimental and calculated temperature of sodium in peripheral subchannelat z=779 mm.<br />
temperatures in Figures 7 and 8.<br />
Another reason is due to the loop<br />
effects which cause after void formation<br />
and pressure oscillations, the<br />
inlet mass flow rate not to be exactly<br />
according to equation 16 and the real<br />
inlet mass flow rate to be somewhat<br />
lower than what is calculated from 16.<br />
Hence the calculated temperatures in<br />
Figures 7 and 8 drop more rapidly<br />
than experi mental temperatures as<br />
the calculated inlet mass flow rate by<br />
relation 16 is greater than the real<br />
inlet mass flow rate at the moments<br />
when large void fractions there exist<br />
in bundle. Also the effect of the stored<br />
heat in the structures of the bundle<br />
and the facility has not been considered<br />
in the numerical calculations.<br />
Generally the maximum time step<br />
in semi implicit algorithm is the<br />
material courant number. Also the<br />
interfacial drag coefficient has an<br />
important effect on the stability of the<br />
numerical two phase flow calculations<br />
and on the selection of the time step<br />
[15].Various numerical simulations<br />
were performed in this work and<br />
it was found that in numerical<br />
calculations with semi implicit<br />
algorithm and with Wallis correlation<br />
for interfacial drag it was necessary<br />
that the time step to be equal to 5.e -4 s<br />
at most in order to attain numerical<br />
convergence. In numerical calculations<br />
with semi implicit algorithm and<br />
with Atruffe correlation for interfacial<br />
drag it was possible to select the time<br />
step of 10 -3 s which is larger than the<br />
time step when Wallis correlation<br />
is used for interfacial drag as<br />
Autruffe correlation implements<br />
more numerical stability. In full<br />
implicit algorithm for both Wallis and<br />
Autruffe correlations it was possible<br />
to select the time step of 10 -2 s and only<br />
with 3 numerical iterations in each<br />
time step (full implicit method<br />
requires numerical iterations in each<br />
time step as it was discussed in section<br />
2). The total solution times of LOF<br />
experiment with different methods<br />
have been presented in Table 3.<br />
According to Table 3 the simulation<br />
time with full implicit algorithm is<br />
much lower than the simulation time<br />
with semi implicit algorithm. So in<br />
this LOF experiment it was possible<br />
that by selection of low number of<br />
iterations (3 iterations in each time<br />
step) in full implicit algorithm, large<br />
time steps to be selected and consequently<br />
lower total simulation times<br />
to be implemented by full implicit<br />
algorithm.<br />
Full implicit algorithm<br />
(with both Wallis and<br />
Autruffe correlation)<br />
Semi implicit algorithm<br />
(with Wallis<br />
correlation)<br />
| | Tab. 3.<br />
The total solution time of LOF experiment with different numerical methods.<br />
4.2 Numerical results of<br />
sudden flow reduction<br />
In this section a transient which is<br />
sudden reduction of sodium flow in<br />
KNS bundle is simulated. In this<br />
transient sodium inlet velocity reduces<br />
from 3.31 m/s to 0.5 m/s in one<br />
second and the electric power is not<br />
switched off. As this transient has not<br />
been performed on KNS test facility<br />
there are not experimental data for<br />
this transient and it has been considered<br />
only for further investigations<br />
on full implicit and semi implicit algorithms.<br />
Also only Wallis correlation<br />
has been used for interfacial drag<br />
calculations. In this transient boiling<br />
inception is calculated to be 1.3 s after<br />
initiation of the transient. Calculated<br />
void fraction by full implicit and semi<br />
implicit algorithms in the central<br />
subchannel at the height of 775 mm<br />
(z = 775 mm) from start of the heated<br />
section and calculated sodium temperature<br />
in the central subchannel at<br />
the height of 770 mm from start of the<br />
heated section (z = 770 mm) have<br />
been depicted in Figures 9 and 10<br />
respectively.<br />
The results of both algorithms are<br />
the same and thermal hydraulic<br />
parameters reach to the steady values<br />
without numerical stability problem.<br />
In this transient it was necessary to<br />
select the time step of 5.e -4 s at most in<br />
semi implicit algorithm in order to<br />
attain numerical convergence. The<br />
time step in full implicit algorithm<br />
was selected to be 10 -2 s and it was<br />
necessary to select6 numerical iterations<br />
per each time step in order to<br />
attain numerical convergence. The<br />
total simulation time for this transient<br />
with semi implicit and full implicit<br />
algorithms were 253.8 s and 73.5 s<br />
respectively. So similar to the LOF<br />
experiment in section 4.1 it is possible<br />
to attain lower simulation time with<br />
full implicit algorithm relative to semi<br />
implicit algorithm.<br />
5 Conclusion<br />
Sodium boiling in KNS test bundle<br />
has been simulated numerically<br />
by subchannel method with semi<br />
implicit and full implicit algorithms.<br />
According to the results, it is shown<br />
that by the selection of low number<br />
Semi implicit algorithm<br />
(with Autruffe<br />
correlation)<br />
40.4 s 263.4 s 170.9 s<br />
Research and Innovation<br />
Transient Subchannel Simulation of Sodium Boiling in a 37 Rods Bundle with Semi Implicit and Full Implicit Algorithms ı Hamed Moslehi Azad and A.S.Shirani
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