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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

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