atw - International Journal for Nuclear Power | 04.2019

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atw Vol. 64 (2019) | Issue 4 ı April OPERATION AND NEW BUILD 214 significant cracking can be tolerated without loss of essential jet pump safety functions. Therefore, it is important to evaluate the remaining structural integrity when a riser is cracked. 2 Statement of the problem The development of helical cracks at the weld between the riser and the riser brace compromise the structural integrity of the jet pumps. Therefore, it is very important to evaluate the critical size of a crack that could be tolerated, before a complicated reparation has to be introduced. It can be considered that the failure can be in the range of brittle and ductile conditions. So, a methodology which considers both conditions of failure is required. 3 Materials and methods In order to obtain the critical size of the crack, the loads applied on the jet pump arrangement were evaluated. The hydrodynamic loads are included. It has to keep in mind that aging could take place as hours of operation are accumulated. For this purpose, brittle and ductile failures were evaluated with fracture mechanics and net section collapse analysis approaches, respectively. Then, these results were compared against those obtained with Failure Assessment Diagrams. The hydraulic loads considered, were the following: by cross flow, the impulse loading of the pump of the Reactor Recirculation Core (RRC) system and the vibration induced by fluid flow (fatigue). In the last case, the dynamic loads are generated by the bend located at the lower end of the riser, the ram head at the top of the riser and the mixer of the jet pump. The thermohydraulic analysis was carried out with the RELAP/ SCDAPSIM code [7, 8]. Another source of vibration are the dynamic loads from strong earthquakes. However, strong earth quakes are not a source of fatigue because of these events do not happen everyday at the same place. Summarizing, it is important to evaluate the impact of the dynamic loads which will take place on the structural integrity of the jet pumps. 3.1 Cross flow The simplified method, described in the Part N1324.1 “Avoiding Lock-In Synchronization” of Section III of the ASME Code [9], was followed. Initially, the Vortex Shedding frequency is calculated with the following relationship. (1) Where: S is the Strouhal number and it is a function of the Reynolds number, U is the velocity of the cross flow and D is the lower diameter of the assembly of the jet pumps. The calculations show that the Vortex Shedding frequency was 10.7 Hz. In accordance with the criterion of the ASME code mentioned above, 1.3f s must be lower than the first natural frequency (26.3 Hz), in order to avoid “Lock-In Synchronization” with the first mode. So, as a conclusion, cross flow vibration resonance did not take place. 3.2 Impulse loading of the pump of the external Reactor Recirculation Core (RRC) system In accordance with the open literature [10, 11, 12], the centrifugal pump of each circuit of RRC operates at 1,800 RPM. As a result, its frequency is 30 Hz. The impeller of the centrifugal pump has five blades. Therefore, the impulse frequency is 5 (30 Hz) = 150 Hz. If this parameter is compared with the range of the first 5 natural frequencies (26.3 Hz – 67 Hz), it can be concluded that resonance in operation is not induced. 3.3 Flow-Induced Vibration (fatigue) The sources of fatigue on the jet pump arrangement are the dynamic forces and moments generated by the internal flow of water. Forces at the lower elbow of the riser: These forces are generated by the inlet flow of water at the elbow of the riser. They were calculated by the following relationships (Figure 2): (2) (3) ρ is the water density. p 1 and p 2 are the pressures at the inlet and outlet of the bend, respectively. A 1 and A 2 are the cross sections at the inlet and outlet of the bend and θ is the angle of the bend. For a 90° elbow, the forces are resulting. F x = 15,500 lb and F y = 15,500 lb horizontal and vertical respectively. Forces over the mixer nozzles of the jet pumps (Figure 3): This force is | | Fig. 2. Forces on the bend. | | Fig. 3. Forces on the bend. | | Fig. 4. Forces generated by the ram head over the riser. developed by the flow discharge, which comes from the Reactor Recirculation Core System, and is mixed with the suctioned flow of the condensed steam. The vertical force is: (4) ΔP is the differential pressure and A i is the cross section of the nozzle. For the jet pump assembly under study are 186.7 pound/inch 2 and 26.1 inch 2 , respectively. So, the resultant force is 4881 pounds upwards. Forces generated by the ram head over the riser (Figure 4): The vertical loads over the riser, which are generated by both elbows of the ram head, were calculated with the following equation: (5) F y is the vertical force, ρ is the water density, p 1 and p 2 are inlet and outlet 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
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 fatigue. 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. pp The evaluation of the loads showed that the hydraulic forces are relevant to determine the structural integrity. pp 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. pp 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 %. pp 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 material. 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 (6) (7) (8) (9) 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. (10) This equation is valid when equation (7) is in the range 0 < λ ≤ 5 and (11) 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 operating. 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 operation. 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 215 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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