ML15023A031

Computation of Cumulative Usage Factor for the 115% CLTP Power Level at Nine Mile Point Unit 2 with the Inboard RCIC Valve Closed, C.D.I. Technical Note No. 14-04NP, Revision 0, Non-proprietary Version

ML15023A031
Person / Time
Site:	Nine Mile Point
Issue date:	04/30/2014
From:	Teske M Continuum Dynamics
To:	Office of Nuclear Reactor Regulation
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ML15023A070	List: ML15022A661 ML15022A662 ML15022A663 ML15023A030 ML15023A031
References
NMP2L 2566 14-04NP
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ATTACHMENT 1 NONPROPRIETARY VERSION OF CDI REPORT NO.14-04P I

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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information C.D.I. Technical Note No. 14-04NP Computation of Cumulative Usage Factor for the 115% CLTP Power Level at Nine Mile Point Unit 2 with the Inboard RCIC Valve Closed Revision 0 Prepared by Continuum Dynamics, Inc.

34 Lexington Avenue Ewing, NJ 08618 Prepared under Purchase Order No. 7736902 for Constellation Energy Nine Mile Point Nuclear Station, LLC.

P.O. Box 63 Lycoming, NY 13093 Approved by Alan J. Bilanin Prepared by Milton E. Teske April 2014

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table of Contents Section Page T able of C ontents.....................................................................

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1. Introduction............................................................................

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2. A pproach...............................................................................

2 3.

R esu lts..................................................................................

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4. C onclusions...........................................................................

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5. R eferences.............................................................................

6 Appendix A: Computation of Stress Intensity...................................

7 Appendix B: Description of the Rainflow Counting Algorithm...............

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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information

1. Introduction A recent re-analysis of the Nine Mile Point Nuclear Station Unit 2 (NMP2) steam dryer at 115% Current Licensed Thermal Power (CLTP) examined dryer stresses that resulted from closure of the inboard Reactor Core Isolation Cooling (RCIC) valve [1]. This re-analysis was based on a conservative load definition that incorporated the larger total uncertainties between ACM Rev. 4.1 and 4.1R [2], along with the inclusion of a stiffener channel to correct the (initially) low alternating stress ratio at what was identified as Location 2 [1]. The calculations found nine locations on the steam dryer where the alternating stress ratios were below 2.0. The stress ratios reported at these locations are summarized in Table 1.

The RCIC line is positioned on main steam line B. The inboard RCIC valve (inside containment) is closed on an infrequent basis and, when closed, results in acoustic pressure signals in the main steam line and dryer pressure loads that result in stress levels (at the dryer structural model node locations summarized in Table 1). Documentation from NMP2 confirms that the RCIC valve cannot be closed for longer than fourteen days without shutting down the plant.

The infrequency of valve closure suggests that the impact of fatigue loading on the steam dryer could be approached by stress intensity cycle counting and the computation of the cumulative usage factor. This report summarizes the cycle counting approach and the reinterpretation of dryer stresses at these limiting locations.

Table 1: Alternating stress ratios, SR-a, below 2.0, on welds at 115% CLTP conditions with frequency shifts, for closure of the inboard RCIC valve [1].

Location Node x

y z

SR-a Freq (Hz)

Tie Bar 137575 17.6 59.8 88.0 1.5 89.3 Outer End Plate/Outer Hood 94509 101.9

-63.3 24.6 1.5 89.3 Side Plate/Top Plate 103080 49.6

-108.6 88.0 1.7 89.3 Side Plate/Top Plate 91055 81.1

-85.2 88.0 1.7 89.3 Thick Vane Bank Plate/Thin Vane Bank 90786 87.0

-85.2 11.6 1.8 89.3 Plate/Side Plate/Side Plate Ext/Outer End Plate Outer End Plate/Outer Hood 94514 100.8

-64.9 36.8 1.8 89.3 Thin Vane Bank Plate/Inner Base Plate 99635 15.6 114.4 0.0 1.8 89.3 Side Plate/Top Plate 101600

-17.6

-119.0 88.0 1.9 89.3 Middle Base Plate/Inner Backing Bar Out/Inner 85631 39.9 108.6 0.0 1.9 89.3 Backing Bar/Inner Hood I

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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information

2. Approach Cycle counting is an accepted procedure employed in fatigue analysis [3], and, while several approaches are available [4], it appears from the available literature that the rainflow counting algorithm is preferred [5].

Application of this technique to the RCIC dataset in question (specifically at node 94509, the "outer end plate / outer hood" location identified in Table 1) will be examined by example using the stress results computed by an ANSYS model of the NMP2 steam dryer [6]. All other nodes in Table 1 are handled in the same manner and reported in Section 3 of the report.

The first step in the analysis is to generate a time history of the stress components at node 94509. This process involves the three normal stress components and the three shear stress components computed by the ANSYS model at this location (node).

Solution of a cubic equation recovers the three principal stresses, 01, 02, and G3, ordered such that a, -> 02 Ž 03, and used to compute stress intensity, oa = maximum of Iol -

G21, IoI - G31, and 0o2 - 031. The solution approach is discussed in Appendix A. A portion of the time history is plotted in Figure 1.

It should be noted that the nine locations subject to cycle counting are all on welds, requiring that the stress intensities be multiplied by a weld factor of 1.8. The stress intensities are also multiplied by a factor of 1.1 to correct for temperature effects. Plastic effects are not in play. ((

(3)))

Node 94509 ci) 4 3

2 1

0

-1

-2

-3 55 55.05 55.1 55.15 55.2 55.25 Time (sec) 55.3 Figure 1: Maximum stress component at node 94509 on the NMP2 steam dryer, shown between 55.0 and 55.3 seconds (95.694 sec total time signal).

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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information It may be seen from Figure 1 that the stress time history displays maximum and minimum values at 180 Hz (twice the approximate 90 Hz loading).

Cycle counting involves three steps:

1. Determine the peaks (local maximum values) and valleys (local minimum values) in the stress time history.

2. Count the cycles between peaks and valleys by the rainflow algorithm (summarized in Appendix B), placing the alternating stress intensity results into a histogram.

3. For each histogram interval, determine the fatigue limit stress intensity from the design fatigue curves [7], plotted in Figure 2, and compute the usage factor for this stress interval. Repeat the process for each of the histogram intervals to find the cumulative usage factor at the node examined.

1000 ASME Design Fatigue Curve

~i2 100 10 105 107 Number of Cycles 10"1 Figure 2: The ASME design fatigue curve for austenitic steels, nickel-chromium-iron alloy, nickel-iron-chromium alloy, and nickel-copper alloy for temperatures not exceeding 8000F, including Curve C [7]. Linear interpolation between data points (identified by the open circles) is permissible on the log-log axes.

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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 3: Histogram results for node 94509.

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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information

3. Results Cumulative damage is assessed by summing the usage factors from each histogram interval:

k CU E

=

H Ni where CUF is the cumulative usage factor, k is the number of histogram intervals, ni are the individual counts within each interval (for one day), and Ni are the limiting number of counts for a, in each interval. This equation is known as Miner's Rule [8], with the regulatory stipulation that CUF must be less than 1.0 to avoid damage [4].

Table 2 summarizes the CUF values determined at the nine nodes at which the alternating stress intensities were less than 2.0. ((

(3)))

Table 2: Cumulative usage factors for the locations where SR-a < 2.0 at 115% CLTP conditions with frequency shifts, for closure of the inboard RCIC valve.

(3)))

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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information

4. Conclusions A recent stress analysis of the Nine Mile Point Nuclear Station Unit 2 (NMP2) steam dryer at 115% Current Licensed Thermal Power (CLTP), for closure of the inboard Reactor Core Isolation Cooling (RCIC) valve, found nine locations on the steam dryer where the alternating stress ratios were below 2.0. These locations were re-examined by counting peaks and valleys in the stress intensity computed from stress components predicted by ANSYS at these locations (nodes). The counted cycles were then summed in stress intensity intervals in a histogram, and the cumulative usage factor was computed at each node.

(3) 6

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information

5. References

1. Continuum Dynamics, Inc. 2014. Compilation of Alternating Stress Ratios for Nine Mile Point Unit 2 at 115% CLTP Conditions (Rev. 1). C.D.I. Technical Note No. 14-06 (Proprietary).

2. Continuum Dynamics, Inc. 2014. Acoustic and Low Frequency Hydrodynamic Loads at 115% CLTP Target Power Level on Nine Mile Point Unit 2 Steam Dryer to 250 Hz Using ACM Rev. 4.1R (Rev. 0). C.D.I. Report No. 14-09 (Proprietary).

3. ASME. 2007. ASME Boiler and Pressure Vessel Code: III Division 1 - Subsection NG, Core Support Structures Rules for Construction of Nuclear Facility Components. NG-3200.

4. ASTM. 2011. Standard Practices for Cycle Counting in Fatigue Analysis. ASTM Document E1049-85.

5. EPRI. 2011. Stress-Based Fatigue Monitoring: Methodology for Fatigue Monitoring of Class 1 Nuclear Components in a Reactor Water Environment. Technical Report No. 1022876.

6. ANSYS 10.0.

7. ASME. 2007. ASME Boiler and Pressure Vessel Code: III Division 1 - Appendices, Rules for Construction of Nuclear Facility Components. Tables 1-9.1 and 1-9.2.2.

8. Miner, M. A. 1945. Cumulative Damage in Fatigue. Journal of Applied Mechanics 12(3):

159-164.

9. Press, W. H., S. A. Teukolsky, W. T. Vetterling and B. P. Flannery. 1992. Numerical Recipes in Fortran: The Art of Scientific Computing (Second Edition). Cambridge University Press.

10. Matsuishi, M. and T. Endo. 1968. Fatigue of Metals Subjected to Varying Stress. Presented to the Japan Society of Mechanical Engineers. Fukuoka, Japan.

11. Downing, S. D. and D. F. Socie. 1982. Simple Rainflow Counting Algorithms. International Journal of Fatigue 4(1): 31-40.

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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Appendix A: Computation of Stress Intensity At each node on the steam dryer, the stress tensor (computed by ANSYS [6]) has six unique components, the three normal stresses (a,, fy, az), one in each coordinate direction (x, y, z), and the three shear stress values (axy,,,

ayz az), perpendicular to the normal stresses. The coordinate system can be rotated to an orthogonal set of axes, with stresses identified by the subscripts 1, 2, or 3, and called principal axes. With respect to these principal axes, the shear stress components are all zero.

The principal stresses (a,, a2, a3) are the roots (eigenvalues) of a cubic equation calculated from the stress components:

fx -- G0 Gxy Txz fxz Gyz f

GO fo or:

f3--(fx +ay +

fz)X;2 2

2 _G 2 0

+(fxfy

+ fy

+/-az xaf

-afxy -aY -ayz

.X 2

2 2

-- (fx X ay X z + 2 x axy x

,yz x fxz -

Tx x ayz - ay x Txz -a f

x y) 0 where a0 are the three principal stresses, computed from the solution to the above cubic equation

[9] with the substitutions:

a =-(ax +Wy +

WY) 2 2

2 a-a a

a~ -a

-a

-- fxz) b =( rx x cry + f y X Cfz +

CFx X CYz O'x C FX yz 2

2 2

c=-(aYx X ay X az + 2 x (YXy X fyz X*xz -a x X yz-ay xz -a z

Xxy) a2 -3xb Q-

>0 9

R 2xa 3 -9xaxb+27xc 54 0 = arccos for Q 0; otherwise 0 = 0 Q3/2 ) f 8

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information The three roots (the three principal stresses) are:

a, =-2xQQ2 X 0+2St-a o2=2x" 2 cost C O+7 a

(03 )3 a3 =-2xQ/2 xcos 3O 2n The principal stresses are reordered from highest to lowest, such that:

G 1 2 02 Ž G3 The stress intensity 01 is then:

cy = maximum of Ioi - G21, Ioi - 031, and 0O2 - 031 The calculation is repeated at each time increment so as to generate a time history of the stress intensity.

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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Appendix B: Description of the Rainflow Counting Algorithm After identification of the stress time windows, stress intensities are paired to create stress cycles. Cycle-pairing is performed using the rainflow counting algorithm, developed in [10],

popularized in [11], and explained in [4]. The rules for the approach are illustrated in Figure 4 and summarized in Table 3, based upon examining an artificial stress intensity time signal.

0.)

0.)

--- -----------........1........................

---

iiiil i i i i i i i i i i i i i i i i i i i......-

ii Time Figure 4: Schematic of the rainflow counting algorithm for a stress intensity signal from a valley to a peak and back to a valley.

Table 3: Interpretive directions for applying the rainflow counting algorithm (adapted from [4 ]).

Step Action 0

Let X denote the interval under consideration, where Y is the previous interval and S is the initial starting point.

I Read the next peak or valley. If at the end of the time signal, go to Step 6 2

If there are fewer than three points in the time signal, go to Step 1. Otherwise, form the absolute stress intensities Ys, and Xs1 (as shown in Figure 4), using the three most recent peaks and valleys that have not been discarded.

3 Compare stress intensities Xs1 and Ys5 : if Xsl Ysl, go to Step 1, otherwise, go to Step 4.

4 If Ys, contains the starting point S, go to Step 5; otherwise, count Ys1 as one cycle, increasing the cycle count in the histogram stress intensity interval that includes Ysl, discard the peak and valley of Ysr, and go to Step 2.

5 Count Ys, as one-half cycle, increasing the cycle count in the histogram stress intensity interval that includes YsI, discard the first point in Ys1, move the starting point S to the second point in Ys1, and go to Step 2.

6 Count each time interval that has not been previously counted as one-half cycle and increase the cycle count in each corresponding histogram stress intensity interval.

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