atw - International Journal for Nuclear Power | 04.2019
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<strong>atw</strong> Vol. 64 (2019) | Issue 4 ı April<br />
pressure at the elbow, A 1 and A 2 are<br />
cross sections of the inlet and outlet of<br />
elbow, v 1 and v 2 are the flow velocities<br />
at inlet and outlet of the elbow and Q<br />
is water flow.<br />
| | Fig. 5.<br />
Resulting <strong>for</strong>ces.<br />
The upper load generated by the<br />
change of direction of the flow of water<br />
through one of the elbows is 12217.<br />
2 pounds. The total <strong>for</strong>ce, which is<br />
generated by the couple of elbows of<br />
the “ram head,” is 24434.4 pounds.<br />
The resultant moment was calculated<br />
with SAP 2000 resulting 19496<br />
pound-inch. The resultant <strong>for</strong>ces are<br />
illustrated in the Figure 5.<br />
3.4 Vibration induced<br />
by earthquake<br />
Regarding the dynamic loads that<br />
take place during an earthquake, the<br />
response spectrum <strong>for</strong> a Safe Shutdown<br />
Earthquake (SSE) and the<br />
Operational Basis Earthquake (OBE)<br />
were obtained. The criterion of 1.60<br />
USNRC was followed [13]. In both<br />
cases, the first natural frequencies of<br />
the jet pump arrangement are above<br />
20 Hz. Besides, the peaks of such<br />
response spectrum are in the range<br />
between 2 Hz and 8 Hz. The first five<br />
natural frequencies are close to 33 Hz,<br />
which is the zone of Zero Period<br />
Acceleration (ZPA). There<strong>for</strong>e, the<br />
seismic loads should not affect the<br />
structural integrity of the jet pumps<br />
and these events are not related with<br />
fatigue.<br />
4 Failure analysis<br />
4.1 Determination of the<br />
allowable crack length<br />
on the riser<br />
For this purpose, an initial helical<br />
crack length is postulated as an<br />
envelope to cover horizontal and<br />
vertical cracks (Figure 6). Then, it is<br />
| | Fig. 6.<br />
Determination of the allowable crack length<br />
on the riser.<br />
increased by steps until the maximum<br />
permissible length is reached. The<br />
following considerations apply.<br />
pp<br />
The evaluation of the loads showed<br />
that the hydraulic <strong>for</strong>ces are<br />
relevant to determine the structural<br />
integrity.<br />
pp<br />
As a critical case that helical cracks<br />
are generated at the weld of the<br />
riser brace, arising when the jet<br />
pumps vibrate under a torsional<br />
mode. In order to analyze this sort<br />
of cracks, the Section XI of the<br />
ASME code [14] is applied to evaluate<br />
the crack along the axial and<br />
circumferential projection, as it is<br />
illustrated in the following Figure.<br />
pp<br />
The recirculation system varies the<br />
flow through the core. In this way,<br />
the power density of the reactor<br />
changes. There<strong>for</strong>e, the range of<br />
the variation of the flow of water is<br />
considered to be between 95 % and<br />
107 %.<br />
pp<br />
Fragile and ductile failures should<br />
be evaluated to cover all the aging<br />
steps from ductile <strong>for</strong> the initial<br />
condition <strong>for</strong> stainless steel to<br />
fragile when neutron fluence<br />
produces embrittlement of the<br />
material.<br />
4.1.1 Axial crack<br />
Fracture mechanics analysis (brittle<br />
failure): Initially, the permissible axial<br />
crack length was evaluated. In this<br />
case, equation 1.1, Vol. 2, Pag. 6.1-1<br />
(through wall crack) [15] was considered.<br />
This equation is valid when<br />
is in the range 0 < λ ≤ 5 and<br />
(6)<br />
(7)<br />
(8)<br />
(9)<br />
is the stress intensity factor in mode I.<br />
σ is the circumferential stress and<br />
depends on the mean radius. P and t<br />
are the internal pressure and the<br />
thickness, respectively. The half crack<br />
length is c and the geometrical factor<br />
is F. (Figure 7)<br />
Limit load analysis (ductile failure):<br />
An axial crack through thickness was<br />
considered. Equation 3.1, vol 2, pag<br />
6.3-1 [15] was taken into account.<br />
(10)<br />
This equation is valid when equation<br />
(7) is in the range 0 < λ ≤ 5 and<br />
(11)<br />
P l is the internal pressure plastic collapse<br />
limit. σ f is the flow stress. R and<br />
t are the mean radius and thickness,<br />
respectively. The half crack length is c<br />
and M is a parameter which is in<br />
function of λ.<br />
The maximum length of an axial<br />
crack was evaluated by the equations<br />
mentioned above. The results are<br />
summarized in the following graph.<br />
The range of operation of the reactor<br />
was considered. Two analyses were<br />
carried out. One of them is when only<br />
one header of the Reactor Recirculation<br />
Core System is operating and the<br />
other was when both of them were<br />
operating.<br />
In the same way like the last case:<br />
All the equations mentioned in this<br />
paper were introduced in Matlab<br />
coupled with Excel to per<strong>for</strong>m the<br />
iterations. In this way, the maximum<br />
allowable crack length was determined<br />
in the range of operation<br />
mentioned above. The results are<br />
summarized in the following graph.<br />
These analyses were carried on when<br />
one single loop operation or the two<br />
circuits (normal operation) of the<br />
Reactor Recirculation System in<br />
operation.<br />
The allowable crack length is<br />
constant no matter the core flow of<br />
water, this happens because only the<br />
internal pressure is considered <strong>for</strong> the<br />
calculations. This internal pressure is<br />
the difference of pressure between the<br />
“Annulus” of the reactor and the interior<br />
of the riser (Figure 8).<br />
OPERATION AND NEW BUILD 215<br />
Operation and New Build<br />
Failure Analysis of the Jet Pumps Riser in a Boiling Water Reactor-5<br />
ı Pablo Ruiz-López, Luis Héctor Hernández-Gómez, Juan Cruz-Castro, Gilberto Soto-Mendoza, Juan Alfonso Beltrán-Fernánde and Guillermo Manuel Urriolagoitia-Calderón