atw - International Journal for Nuclear Power | 04.2019


atw Vol. 64 (2019) | Issue 4 ı April

pressure at the elbow, A 1 and A 2 are

cross sections of the inlet and outlet of

elbow, v 1 and v 2 are the flow velocities

at inlet and outlet of the elbow and Q

is water flow.

| | Fig. 5.

Resulting forces.

The upper load generated by the

change of direction of the flow of water

through one of the elbows is 12217.

2 pounds. The total force, which is

generated by the couple of elbows of

the “ram head,” is 24434.4 pounds.

The resultant moment was calculated

with SAP 2000 resulting 19496

pound-inch. The resultant forces are

illustrated in the Figure 5.

3.4 Vibration induced

by earthquake

Regarding the dynamic loads that

take place during an earthquake, the

response spectrum for a Safe Shutdown

Earthquake (SSE) and the

Operational Basis Earthquake (OBE)

were obtained. The criterion of 1.60

USNRC was followed [13]. In both

cases, the first natural frequencies of

the jet pump arrangement are above

20 Hz. Besides, the peaks of such

response spectrum are in the range

between 2 Hz and 8 Hz. The first five

natural frequencies are close to 33 Hz,

which is the zone of Zero Period

Acceleration (ZPA). Therefore, the

seismic loads should not affect the

structural integrity of the jet pumps

and these events are not related with


4 Failure analysis

4.1 Determination of the

allowable crack length

on the riser

For this purpose, an initial helical

crack length is postulated as an

envelope to cover horizontal and

vertical cracks (Figure 6). Then, it is

| | Fig. 6.

Determination of the allowable crack length

on the riser.

increased by steps until the maximum

permissible length is reached. The

following considerations apply.


The evaluation of the loads showed

that the hydraulic forces are

relevant to determine the structural



As a critical case that helical cracks

are generated at the weld of the

riser brace, arising when the jet

pumps vibrate under a torsional

mode. In order to analyze this sort

of cracks, the Section XI of the

ASME code [14] is applied to evaluate

the crack along the axial and

circumferential projection, as it is

illustrated in the following Figure.


The recirculation system varies the

flow through the core. In this way,

the power density of the reactor

changes. Therefore, the range of

the variation of the flow of water is

considered to be between 95 % and

107 %.


Fragile and ductile failures should

be evaluated to cover all the aging

steps from ductile for the initial

condition for stainless steel to

fragile when neutron fluence

produces embrittlement of the


4.1.1 Axial crack

Fracture mechanics analysis (brittle

failure): Initially, the permissible axial

crack length was evaluated. In this

case, equation 1.1, Vol. 2, Pag. 6.1-1

(through wall crack) [15] was considered.

This equation is valid when

is in the range 0 < λ ≤ 5 and





is the stress intensity factor in mode I.

σ is the circumferential stress and

depends on the mean radius. P and t

are the internal pressure and the

thickness, respectively. The half crack

length is c and the geometrical factor

is F. (Figure 7)

Limit load analysis (ductile failure):

An axial crack through thickness was

considered. Equation 3.1, vol 2, pag

6.3-1 [15] was taken into account.


This equation is valid when equation

(7) is in the range 0 < λ ≤ 5 and


P l is the internal pressure plastic collapse

limit. σ f is the flow stress. R and

t are the mean radius and thickness,

respectively. The half crack length is c

and M is a parameter which is in

function of λ.

The maximum length of an axial

crack was evaluated by the equations

mentioned above. The results are

summarized in the following graph.

The range of operation of the reactor

was considered. Two analyses were

carried out. One of them is when only

one header of the Reactor Recirculation

Core System is operating and the

other was when both of them were


In the same way like the last case:

All the equations mentioned in this

paper were introduced in Matlab

coupled with Excel to perform the

iterations. In this way, the maximum

allowable crack length was determined

in the range of operation

mentioned above. The results are

summarized in the following graph.

These analyses were carried on when

one single loop operation or the two

circuits (normal operation) of the

Reactor Recirculation System in


The allowable crack length is

constant no matter the core flow of

water, this happens because only the

internal pressure is considered for the

calculations. This internal pressure is

the difference of pressure between the

“Annulus” of the reactor and the interior

of the riser (Figure 8).


Operation and New Build

Failure Analysis of the Jet Pumps Riser in a Boiling Water Reactor-5

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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