ML051330053
| ML051330053 | |
| Person / Time | |
|---|---|
| Site: | Dresden  (DPR-019, DPR-025) |
| Issue date: | 04/25/2005 |
| From: | Dorfman L, Fujikawa K Structural Integrity Associates |
| To: | Office of Nuclear Reactor Regulation |
| References | |
| EXLN-17Q-301, Rev 0 | |
| Download: ML051330053 (11) | |
Text
ENCLOSURE 3 "Dresden Strain Gage Uncertainty Evaluation," SIA File No.: EXLN-17Q-301, Revision 0, dated April 25, 2005
Structural Integrity l CALCULATION File No.: EXLN-17Q-3 Associates, Inc.
' PACKAGE l Project No.: EXLN-17Q PROJECT NAME: Strain Gage Uncertainty for Steam Dryer Load Definition CLIENT: Exclon Generation Co., LLC Contract / P.O. No.: 00083767 PLANT: Dresden Unit 3 CALCULATION TITLE: Dresden Strain Gage Uncertainty El'aluation Project Mgr.
Preparer(s) &
Document Affected Rvso ecito Approval Checker(s)
Revision Ages Revision Description Signature &
Signatures &
Date Date 0
1-8 Initial Issue K. K. Fujikawa L. S. Dorfman App A "I..
4/25/05 4/25/05 K. K. Fujikawa 4/25/05 Page I of 8 SWForm F2001R2
Table of Contents I
INTRODUCTION
.3 2
DRESDEN STRAIN GAGE DATA ACQUISITION 3
2.1 Full Scale Range, Resolution Calculation and Scaling Factor
.3 2.2 Uncertainty Analysis
.5 3
REFERENCES..8 APPENDIX A UNCERTAINTY ANALYSIS SPREADSHEET
.Al List of Figures Figure 1: Wheatstone Bridge and Electrical Schematic
.7 Structural Integrit File No.: EXLN-17Q-301 Revision: 0 Associates, Inc.
Page 2 of 8
1 INTRODUCTION This calculation determines the dynamic pressure resolution and uncertainty for the strain gage measurements taken at Dresden Unit 3.
2 DRESDEN STRAIN GAGE DATA ACQUISITION During the Dresden EPU vibration testing, strain gage measurements were made on the Main Steam piping to determine the internal dynamic pressure. Strain gages were installed at several locations in the pipes' circumferential direction. The hoop strain was then converted to internal dynamic pressure utilizing general strain equations and thick-wall cylinder pressure equations for hoop and axial stress due to internal pressure.
This document reviews the calculations to determine the pressure from the strain measurements and provides the dynamic pressure resolution and uncertainty.
Figure 1 is a diagram of the strain gage circuit including the Wheatstone Bridge and data acquisition system (DAS). The weldable strain gages provided by Hitech Products, Inc. (HPI) for this task were installed in the circumferential direction and connected to the opposite arms of the Wheatstone bridge with completion resistors inserted in the other two arns. The gages and completion resistors wvere assembled and connected in the bridge configuration by HPI.
The four wires, bridge input excitation and output voltage, were then spliced to a 4 conductor, shielded wire leading to the DAS. The DAS consisted of the Yokogawa Bridge Head, Model 701958, Yokogawa Strain Gage signal conditioning module, Model 701271, and the Recorder, Model DL750.
The bridge head provides a location for termination of the strain gage wires, shunt calibration and connection to the signal conditioner. The signal conditioner provides the bridge excitation (10 V), bridge balance, input range (2.5 mV/V), low pass filter (1 kHz), calibration constant (0.000251 mV/V-psi) and analog-to-digital (A/D) conversion (16 bit). The recorder provides the capability to view the data and transfer to disk (2 ksps/ch).
2.1 Full Scale Range, Resolution Calculation and Scaling Factor In this configuration the bridge will add the two arms according to the following equation.
I%=(AR, AR2,AJ~ AR4)
(A) 4 RI R2 R 3 R4 where V.= output voltage of the bridge Vi = bridge excitation voltage AR.
is the change in gage resistance, AR, divided by the gage resistance, R, due to an applied strain, c, for each arm of the bridge.
Structura Integrity lFileNo. EXLN-17Q-301 lRevision: 0 Associates, Inc.
l Page 3 of 8
For this case, R2 and R4 are completion resistors thus AR2 = AR4 = 0 (no resistance change due to strain) and R 3 -?for strain in the same plane along the pipe. Equation A is reduced to (lAR, +AR 3 1
= 4
-)=
-(-)
(B)
The applied strain, c, changes the gage resistance according to the formula AR
= GFc (C)
R where GF is the dimensionless gage factor provided by the gage manufacturer that relates the strain to the change in resistance.
Equation C then becomes vi= 2 GFc or c=
(D) i 2
GF The input range was set to +/-2.5 mVN (%)
thus the full scale strain range calculated from Equation D using a GF of 2.0 (per HPI), is +/-2500 p.w The analog-to-digital, A/D, converter is 16 bits or 216 bits for the full input range of 5000 gE, providing an A/D resolution of (5000/216) = 0.0763 pc.
The relationship between the pipe's internal pressure to the hoop strain was calculated by Dresden (Reference I) to be 0.251 pc/psi from the hoop equations found in Section 2.2 Uncertainty Analysis below.
Using this factor the Full Scale Range = +2500 pc /0.251 pc/psi = +/- 9960psi and the A/D Resolution = 0.0763 pc /0.251 pc/psi = 0.304 psi.
The scaling factor used by Dresden was inserted in the Yokogaxwa recorder to provide the recorded data in psi. This value is based on the input range, A, and strain-to-pressure conversion factor, 0.251 pc/psi through Equation D ll 1, = 2.5 mVN = 2500 pc = 9960 psi Therefore, the system scaling factor is 9960 psi /2.5mVN = 3984 psi/mV/V.
StructuralIntegrity FileNo.: EXLN-17Q-301 Revision: 0 Associates, Inc.
Page 4 of 8
2.2 Uncertainty Analysis The uncertainty analysis combines the uncertainty of the strain-to-pressure calculation and the measurement system. The strain as measured in the circumferential direction is the superposition of the strain in the circumferential and that due to the Poisson effect of the axial strain due to the internal pipe pressure.
The hoop and axial stress are calculated from the equations 2Pd 2 (E) d7
~72-d 1 2
and Pd.
(F) 1=d,2 _ d, The hoop strain is the strain in the circumferential direction minus v times the axial strain as shown in the following equation Cm =
(G)
E Substituting Equations E and F into Equation G yields
-H = (d(2-d)
(H) where the strain per unit pressure is OH di' (2-v) p E(d2-di')
or d,1 (2
)
where CH = Hoop stress due to internal pressure, psi cGL = Axial stress due to internal pressure, psi Hu
= Hoop strain, gin/in p = unit applied internal pressure, psi di= pipe inside diameter, in do= pipe outside diameter, in E
Young's Modulus, psi v Poisson's ratio.
StructuralIntegrity FileNo.: EXLN-17Q-301 Revision: 0 Associates, Inc.
Page 5 of 8
Substituting the strain from Equation D into Equation J results in p= 2 V. -E(d -dd2 )
(K)
GF*d72(2-v)
This equation relates the internal pipe pressure to the measured strain.
The overall uncertainty is determined by a SRSS method used for random errors. The nominal (no error) pressure is calculated first. Then the pressure is calculated again by changing each variable in the equation by the amount of the potential error, one variable at a time. The new pressure calculated for each variable with the error is then subtracted from the nominal pressure and squared. This is done for each case where there is an uncertainty in the parameter of the pressure equation. Each case's squared difference from the nominal is summed and the square root taken of the result.
The nominal values are as follows:
di=l 7.93 in do20 in E= 27.9x10 6 psi v =0.3 GF= 2.0
'i,=2.5 mVN.
The accuracy values are as follows:
di= 2.8%
(ASME Code worst case) do= 0.625%
(ASME Code worst case)
E = 5%
(SI metallurgist, common practice) v 0 (SI, common practice)
GF= 2% per gage, for 2 gages (SRSS) = 2.8% (HP], Reference 2)
Xi = 0.5%
(Yokogawa specification)
The overall uncertainty on the pressure is calculated as described above to be 28.7% (see Attachment A).
The uncertainty due to the measurement of the strain using Equation D and the SRSS method is 2.8%.
Thus most of the uncertainty is due to the uncertainty on the pipe diameters and Elastic Modulus with the pipe diameter uncertainty contributing significantly.
StructuralIntegrit FileNo.: EXLN-17Q-301 Revision: 0 42 Associates, Inc.
Page 6 of 8
g - strain gage, 350ohm cr-completion resistor, 350 ohm 35d Bm II I
I I
I I
I I
I I
L Recorder DL750 with SG 701271 Conditioner Excitation:10 VDC Range: 2.5mvN
-- > DAS Figure 1: Wheatstone Bridge and Electrical Schematic S tructural ntegrity FileNo.: EXLN-17Q-301 Revision: 0 I
Associates, Inc.
Page 7 of 8
3 REFERENCES
- 1. E-mail from Guy DeBoo (Exelon) to K. Fujikawa (SI) and L. Dorfman (SI), dated 2/1/05, "Dresden MS Line Strain Gage Information," SI File No. EXLN-1 7Q-201.
- 2. Y. Dayal, "Exelon Corporation Quad Cities Unit 2 Nuclear Power Plant Dryer Instrumentation Uncertainty", GE-NE-0000-0037-1951-01 Rev 0, February 2005, SI File No. EXLN-1 7Q-202.
FeStructural Integrity File No.: EXLN-1 7Q-301 Revision: 0 4-> Associates, Inc.
Page 8 of 8
APPENDIX A UNCERTAINTY ANALYSIS SPREADSHEET Structural Integrity FileNo.: EXLN-17Q-301 Revision: 0 I
(Associates, Inc.
I Page Al of A2
Dresden Accuracy Accuracy Nominal Nominal Values Plus di 17.93 2.80%
18.43204 do 20 0.63%
20.125 E
2.79E+07 5%
29295000 v
0.3 0
0.3 GF 2
2.8%
2.056 volvi 0.0025 0.50%
0.0025125 I Nominal
+ di
+ do
+ E
+ GF
+ volvi Pressure 110020.466 1 7277.4109 110660.583 1 10521.489 9747.5346 1 10070.568 SRSS I
Theta 97966.236 102418.82
-10020.466 9747.5346 10020.466 Uncert*Theta I 1
2743.0546 J
-640.1176 J
-501.02328 272.93097 1 50.102328 i2874.3913 Pressure =
% Error 10020.466 psi 28.7%
+
2874.3913 psi tructuralIntegrity File No.: EXLN-17Q-301 Revision: 0 Associates, Inc.
Page A2 of A2