ML061150457

C.D.I. Report No.04-09P, Methodology to Determine Unsteady Pressure Loading on Components in Reactor Steam Domes, Revision 5, Dated January 2005, Non-Proprietary

ML061150457
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Site:	Dresden, Quad Cities
Issue date:	01/31/2005
From:	Continuum Dynamics
To:	Document Control Desk, Office of Nuclear Reactor Regulation
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04-09P, Rev 5
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ATTACHMENT I C.D.I. Report No.04-09P, "Methodology to Determine Unsteady Pressure Loading on Components in Reactor Steam Domes,"

Revision 5, dated January 2005, Non-Proprietary

onUtinM

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3/4 IfOM-13X" C.D.I. Report No. 04-C9P Methodology to Determine Unsteady Pressure Loading on Components in Reactor Steam Domes Revision 5 Prepared by:

Continuum Dynamics, Inc.

34 Lexington Avenue Ewing, NJ 08618 January 2005

-I QtI Ull Dynamics, Inc. Non-Propriet Table of Contents

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

1

2. Observations and Scaling Considerations 2

3. Methodology Formulation 4

4. Component Models 10 4.1 Steam Dome 10 4.2 Main Steam Lines 12 4.3 Steam Dome/Main Steam Line Junction

.14 4.4 Branch Line Junction 15 4.5 Control Valves 16

5. M odel Assembly.............................................................................................. 17

6. EPU Loads for Quad Cities Unit 2 (Example Calculation)

.21 6.1 Dryer Peak Pressures 21 6.2 Dryer Time History 21 6.3 Validation 21 6.4 Model Uncertainty 22

7. Sensitivity Analysis 30

8. Conclusions 32

9. References 33

10. Appendix 34 i

[CMtIuillliumL Dnanih IsJnc..Npn-DI rnplarij

1. Introduction Estimation of the magnitude of the unsteady pressure loads on components inside a reactor steam dome is complicated by the environment in Ihe dlomc itself. It is desirable to develop a loads transfer methodology to infer thc fluctuating prcssurc Field from existing in-plant measurement transducers, provided that it can be demonstrated that the methodology (algorithm) is robust and accurate. This report documents an algorithm that uses well-established analytical methods to compute the unsteady pressure loading in the steam dome using sevcral simultaneous measurements of pressure in tIhC steam supply system. The model is validated with data taken in the Quad Cities Unit 2 plant by comparing predictions of the fluctuating pressure at a location in the B main steam line with inferred data hoop stress pressure measurements.

I

I

Cnis, IUC. Non-Pro)1ictil

2. Observations and Scaling Considerations Previous analysis of main steam line pressure data [1-3] indicates the presence of discrete frequencies, which suggests that deterministic mechanisms are active in the steam delivery system. Furthermore, these mechanisms are power/flowv rate sensitive.

Most flow-induced vibration mechanisms that involve unsteady shear layer oscillations scale with dynamic pressure at constant Macli number. For power uprate in boiling wvter reactor (BWR) plants, system pressures do not change, and increased power is achieved by increasing steam flow velocity in the system. This increase in velocity results in an increase in both the Mach number and dynamic pressure, which scales with the velocity and velocity squared, respectively.

A simple but relevant example illustrates the difficulty in estimating the fluctuating pressures in a complex system. Figure 2-1 illustrates the scaling of the unsteady pressure due to flow over a dead-ended branch line. Data from [4] suggests that the root mean square pressure scales with the dynamic pressure q -1/2 pU2 at constant Mach number (U/a), where U is the flow velocity over the branch line p is the fluid density a is the acoustic speed in the fluid L is the branch line length d is the branch line diameter This scaling can be directly obtained from a scaling analysis. From Figure 2-1, ii is apparent that only when ad/4LU = 0.44 do the pressure fluctuations scale as U2. For sufficiently low and high velocities, pressure fluctuations disappear.

In a system with many junctions and branch lines of various lengths and diameters, it is clear that a simple "back of the envelope" analysis is not achievable to estimate the unsteady loads as a function of reactor power.

For this reason, a methodology is 2

nti namicsine. Non-Proardn-i developcd that uscs measured in-plant data to infcr unstcady loading oil thle dryer (or any intcrnal component) as a function of reactor powcr.

Branch Line Scaling with q U

increasing r/d rF P/q L

nns

^

03 0.35040.0.45 0.50 0.55

- Stmhal No., St (d)

I ad r~~

iI

! 4L p)

Confirms that oscillation pressure scale with q= pU28 U=const.

Figure 2-1 Oscillation in a stagnant branch line.

3

ieis[iIl e

I ictlD3

3. Methodology Formulation 4

Lcwilinuut im kiciuforto 5

a To ine B O.-D24'

Po~v ' Pokv I i A, L-3.18 SRV SRV Figure 3-1 Piping geometry used In the acoustic Circuit Onal)'5i5 for Quad Olls Unit 2 (Q-Z).

6

AWesd IncNin-Pworktan It is desired to develop an analysis wihcerc the pressure field is computed correctly lo the order of the Macli number, which is common for hydrodynaniic analysis.

The hydrodynamic pressure field is typically of the order of Mach number squared. In the steam dome wviherc the Macli number is small, the convective wave equation reduces to the standard wave equation:

I al P_V,P=O a2 at In the steam lines where the flow is essentially one-dimensional, the pressure satisfies the following:

I D2P 2p1 a 2 DI2 O x2

° where D -

-+ U a-, and U is the velocity in the main steam line.

Di Tt ar t

Source region II is well known and exists when a shear flow passes over a dca ended branch line [4, 5]. It is well established that if the velocity over the branch line is U = 0.55da/L, the branch line is excited at the quarter standing acoustic wave in the branch line (also referred to as the first organ pipe mode). Acoustic oscillations exist at a frequency of a/4L and radiate into the flowing system. This mechanism is postulated to occur at the turbine equalizer lines located upstream of the control valves.

i This acoustic excitation mechanism exists in other physical systems, most notably a children's toy consisting of a corrugated tube approximately 3 feet in length and open on both ends. When spun while holding one end, the tube sings" at a fixed tone corresponding to the 1/4 standing wave frequency of the tube.

Tlhe acoustic forcing is supplied by unsteady vortex shedding from the lip of the tube, which periodically perturbs the vena contracta and corresponding head loss of the air entering the tube.

7

t[Cninuun Dvnamics. Inc. NonI-ro rietar.N1 The latter measurement is converted to an internal pressure, which is used for model validation.

In total, cleven independent measuremcnts are available to deduce the pressure fluctuations in the steam dome for this specific example. However, although sources have been assumed at geometric locations, it is not apparent that analyses of test data would show that some of these sources arc in fact negligible.

8

[Conifinuu T~npnuiii, finc. NopijProprieori Main steam line U

Source region 11 Shear layer Instability over branch line Branch line Figure 3-2 Conceptualization of source regions.

9

ICi tilunil Dynamics e,

INDR.1nprdict

4. Component Models In this scetion, models used to reprcsent the dynamics of specific component in the stcam supply system are describcd.

4.1 Steam Dome A cross-section of thc steam domc and steam dryer is shown in Figure 4-1 (a schematic top s'iew of the steam dryer is shown in Figure 6.2).

Dimensions corresponding the QC2 example, as verified in [6], are also indicated. The unsteady pressure field is determined by periodic solution of the vavc equation, since Mach numbers in thc steam dome arc less than 0.1. Assuming harmonic time dependence, the wave equation rcduces to the llelmholtz equation:

VIP+

2 P=0 where P is pressure, co is frequency, and a is acoustic speed. The complex three-dimensional geometry of the steam dome is rendered onto a uniformly-spaced rectangular grid with mesh spacing of three inches. The solution for the pressure P is obtained for each grid point within the steam dome.

The llelmholtz equation is solved for incremental frequencies from 0 to 200 liz, subject to the boundary conditions:

dP 0 dTn normal to all solid surfaces (i.e., the steam dome wall and interior and exterior surfaccE. of the dryer), and:

10

I l

U

)

jaliniCS, [tic, Nonl-llroprtal Tcst canonical problems lhavc rccovcred cxact solutions. A rcprcsentativc solution at 50 Hz is slhown on

]1 R

I I

I I

-1 I 1 1-L_ L_

l J

9 3-Figure 4-1 Cross-sectional description of the steam dome and dryer, with the verified QC2 dimensions of a = 6.0 in, b = 28.5 in, c = 15.5 in, d = 19.0 in, c = 16.25 In, f= 75.0 In, g = 137.0 in, h = 23.0 in, i = 88.5 in, j =

166.63 in, k = 120.0 in, and R = 125.5 in.

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tcolitinu

'nunP I

4.2 Main Steam Lines The Helmholtz solution within the steam dome is coupled to an acoustic circuit solution in the main steam lines. Pressure fluctuations in single-phase compressible medium, where acoustic wavelengths are long compared to characteristic length scales for the internal components and to transverse dimensions (i.e., directions perpendicular to the primary flow directions), can be determined through application of the acoustic 12

omltill uni Dynamiics, Inc. Non-Pftopridtarnl circuit methodology. By restricting the analysis to frequencies below 200 liz, acoustic wavelengths are approximately 8 feet in length, which are sufficiently long compared to most components of interest such as branch junctions, etc.

Acoustic circuit analysis separates the main steam lines into elements that are characterized by length L, cross-sectional area A, mean fluid density p, mean flow velocity U, and mean fluid acoustic speed a + as illustrated in Figure 4-3. Application of acoustic circuit methodology provides solutions for the fluctuating pressure P, 2nd velocity t,, for the nth clement of the form:

[nI

,iX

+ R"A.

e A(no+Ukl,)

1

+ (e L+ U, k2 n) ik2 X]

lIna t[

H A

el

+

+7

)Bnef2A] el where harmonic time dependence of the form e" has been assumed. The wave numb rs Al,, and k2, arc the two complex roots of the equation:

k.2 + if J

_" (W+Unkn )~-2 (w,+U nkn )2 = 0 where f,, is the pipe friction factor for the nth element, Dn is the hydraulic diameter for the nth element, and; -i rl.

The complex constants An and Bn in the expressions for the fluctuating pressure and velocity above are a function of frequency. These constants are determined by satisfying continuity of pressure and mass conservation at the element junctions.

A similar acoustic circuit analysis is used in the instrument lines to transfer the pressure recorded at the transducer to the main steam line. This analysis is summari;zcd in the Appendix.

13

II ll amics, hjc.NimaPr-o 4.3 Steam Dome/Main Steam Line Junction 14

nfiilanuzutyn NOII-nPxuvhrk3i 4.4 Branch Line Junction 15

h Im mnsjncrNo!nroprie 4.5 Control Valves Control valves arc located bceforc the inlets to the steamn turbine and rcprcsent the end of the modelcd system. Control valves, which arc typically open 40%, arc modelcd with the assumption, that downstream acoustic disturbances do not propagate upstream through the valve. This assumption is approximate and becomes more valid as the pressure drop across the valve is increased.

16

CI 1

5. Model Assembly The assembly or the loads transfer methodology is illustrated below in Figure 5-1.

17

[Cuuthiuum D'llanilncs, inc. Noni-Pronridtwri1 In-plant data have bcen obtained as a ftinction of power level. At a given power level, prcssurc time histories are available at thc following locations:

N Il A(t) - at the reactor wall at 450 azimuth N I I B(t) - at thc rcactor wall at 225° azimuth VA(t) - on thc main stcam line at venturi A VB(t) - on thC main steam line at vctituri B VC(t) - on thc main stcam line at venturi C VD(t) - on the main steam line at venturi D TA(t) - on the main steam line at turbine instrument line A TB(t) - on the main steam line at turbine instrument line B TC(t) - on the main steam line at turbine instrument line C TD(t) - on the main steam linc at turbine instrument line D SB(t) - hoop strcss converted to steam line pressure upstream of the line B ERVs In total, eleven independent data sets are available. The model in Figure 5-I has twcdvc unknown sources, which are:

I8

IOIytmI1UsflLD' iluiicita-19

It Dti ya mc',

t icn" r - Ž-ia 20

CI iiiinics, li1C. Non-l' i

I

6. EPU Loads for Quad Cities Unit 2 (Example Calculation)

This section summarizes results from example calculations using the loads transfer methodology. Tlic example uses measured data from the Quad Cities Unit 2 (QC 2) steam supply system during extended powcr uprate (EPU) operation.

6.1 Dryer Peak Pressures Calculations have been performed using measured EPU data Peak pressures and root mean square (RMS) pressure levels are predicted at different dryer locations (node numbers) in Figure 6-1. Physical node locations are shown in Figure 6-2.

6.2 Dryer Time History The differential pressure and associated power spectral density (PSD) across the cover plate is shown in Figure 6-3. In principle, the model can predict the pressure time history at any location in the steam dome to a resolution of approximately three inches.

Examination of the pressure spectrum (PSD) indicates that energy exists at discrete frequencies in the pressure time history.

6.3 Validation As discussed previously, the strain gauge data SB(t) on the B line upstream of the ERVs has not been used in the analysis to provide a separate dataset for model validation.

The estimated pressure in the main steam line from strain gage data is shown in Figure 21

CI

.tin Drnam" 1nX. SN -Pr t

I 6-4 with its associatc(l PSD.

Sevcral calculations werc perforned varying t(iC hulk acoustic specds in thc instrumcnt lincs, and thc results of thcsc calculations arc shown in Figurc 6-S and Figure 6-6, providing predictions of thc prcssurc at this location for bulk instrument line acoustic spceds of 4600 fI/scc and 4700 fl/sec, rcspectively. Refcrring to Figurc 6-7 below, tliesc acoustic spceds correspond to bulk instrument linc water temperatures of 348.3°l and 326.1 TF, rcspectivcly, A comparison of data from Figure 6-4 wvitli model predictions is tabulated belcw.

Comparison or the PSDs shows similar frequency content between measured and predicted pressures.

Peak Pressure (psid)

Prm, (psid)

SB 11.44 2.80 Prediction 4600 f7/sec 11.41 2.80 Prediction 4700 II/sec 11.82 2.79 6.4 Model Uncertainty The loads transfer methodology to deternine the pressure fluctuation magnitudes on the reactor walls or in the main steam lines is undergoing additional validation using a separatc full-scale test program. Once this validation program is complete, the measured pressure data will be subject to uncertainty associated with instrumentation measurement accuracy and thc assumed acoustic speed in the instrument lines.

22

IQiltu D n l

.NI-a$

U q 4

Q CO X C1 2.5 2

1.5 0.5 0

S.

0 20 40 60 80 100 Node Number 120 140 e1-4

'd~

le 0

$-4cn cn 0.6 0.5 0.4 0.3 0.2 0.1 A

1-i f,

x 54 liif i

fI

-!-------i -----5-- ---- ---i--..........................

.4

,j 1.....

0

4. 0.

6 0 100 120 14 I_.

% )

20 40 60 So 100 120 140 Node Number Figure 6-1 EPU loads developed by the current methodology.

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6""juu Dyamc. In. Non-Prnitr~

TOP VIEW:

2,3 Pressure data locations SIDE VIEW:

Pressure data locations Nominal Water Level 2

132 Figure 6-2 Top and side view schematic of pressure node locations on the steam dryer.

24 cO I

kDQnthiiiisii Inc. Nold-Pd pearL EPU Load on the Cover Plate a.)_

I-la.

2....,...j..

3 1i 0 rvA

-L 0.01 0,008 0.006 0.004 0.002 A

5 10 15 20 25 30 Time (see)

EPU Load on the Cover Plate I.3 0

20 40 60 80 100 Frequency (Hz)

Figure 6-3 EPU pressure time history and PSD on the cover plate on the A and B main vent side.

25

CmthuilUumDlnami Is~

En En es%

• 4 uN Strain Gage Data for EPU Conditions 15

-JD 0.14 0.12 0.1 0.08 0.06 0.04 0.02 n

i I,

I.........

)5 10 15 20 25 30 Time (sec)

Strain Gage Data for EPU Conditions

.................. T................

-4......

...... I...........t.........._

.L 0

20 40 60 80 11 Frequency (Hz)

Figure 6-4 EPU pressure time history and PSD derived from strain gage data.

26 1 l0

Ijsui o

Strain Gage Prediction for EPU Conditions I C 10 7'

1 En En 0

-5 1 lllll;!l'}5lllll~lll.5lll1!l lI 1 1 I

l ~l tn I I.

I z I.

I I.

I.

I..

-II) 0 5

10 15 20 Time (sec) 25 30 Strain Gage Prediction for EPU Conditions N

cN-C',

co fAL 0.14 0.12 0.1 0.08 0.06 0.04 0.02 A

_~...._,;.....

7 I

U 0

20 40 60 80 Frequency (Hz)

Figure 6-5 EPU strain gage pressure and PSD predictions with 'the current methodology, for an acoustic speed of 4600 ft/sec. 110 27

lIl l)WnumkU I -

die 15 10 O-N V)

V7 t) 5 Strain Gage Prediction for EPU Conditions 0

-5

-10 0 5

10 15 20 Time (sec) 25 30 Strain Gage Prediction for EPU Conditions

1. 4,

o I%::

cn 0.14 0.12 0.1 0.08 0.06 0.04 0.02 n

.;.:.l.-.

~.

........................ i.. 1,,,...,,,

X 1

QLIDL i u.

0 20 40 60 80 Frequency (Hz)

Figure 6-6 EPU strain gage pressure and PSD predictions with the current methodology, for an acoustic speed of 4700 ft/sec. 100 28

oiiO-tiinnumlynanics, I

-ida 5500 E

5000 4500 4 0 0 0

,x 50_..................................,................

000 100 200 300 400 500 600 Temperature (deg F)

Figure 6-7 Temperature effect on water acoustic speed 171.

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[conthwin yni-

.l n-ouDrictal1

7. Sensitivity Analysis Thle sensitivity of the peakl loads on the dryer to the acoustic spced can be determiricd from thc computed dryer loads at two bulk instrument line acoustic speeds.

This sensitivity (bP/0a ) is shown in Figure 7-1 at an instrument line bulk acoustic speed of 4700 ft/sec.

For the predicted load to have an accuracy of 10%, the bulk acoustic speed must be known to within 500 ft/sec.

The sensitivity to instrument measurement error can also be evaluated.

This evaluation is required since the pressure fluctuations measured on the reference leg transducers arc near the resolution limits of at least one transducer. Calculations w-re run by increasing the water level transducers by 20%. The changes in the predicted peak pressures on the dryer arc shown in Figure 7-2.

It is apparent that the dryer load definition uncertainty benefits from water level measurements with improved accuracy, e--,

L) 0Cn eta

6 Cn 15 d

5 0.0012 0.001 0.0008 0.0006 0.0004 0.0002 0

-0.0002

-0.0004

• J

 ! i.

9

I 4

a 1.:.

I II,,I,,I4I4

,,I,.

0 20 40 60 80 Node Number 100 120 140 Figure 7-1 Sensitivity of the dryer loads to change in acoustic speed.

30

ksontinum ~Dynamics. Inc. Non-Pro rietark 3

~U e_1 to 2.5 2

1.5 1

0.5

---

EPU1-20%v 100 120 140 0

0.7 0

20 40 60 80 Node Number

• t I

r-S n-r

'Cn IUB 0

0.6 0.5 0.4 0.3 0.2 0.1

-V----T T-1 r

VT I--

-~~S EPU EPU+20%

I.

0 0

20 40 60 80 Node Number 100 120 140 Figure 7-2 EPU loads developed by the current methodology, with a 20%

increase in EPU loads for an acoustic speed of 4700 ft/sec.

31

Io1iiiii Dnal~lincsj "IC N n-Pr

8. Conclusions A physically-based, loads transfcr methodology that can predict loads on reactor componcnts from measurcmcnts madc extcrnal to thc reactor steam dome has been developed and validatcd. The model accounts for acoustic sources at locations along tilc steam delivery system that arc known to provide a region where mean flow energy can be transferred in acoustic pressure oscillations. Accuracy of the model-based loads transfer scheme is most likely limited by in-plant pressure measurement accuracy, and thesc errors are therefore quantifiable.

Followving validation of instrumcnt corrccton algorithms, not discussed in this report, the methodology should reliably provide definition of plant-uniquc dryer loads.

32

[ConItinuinnimuuksnIc. Non-ProiirkIlirl

9. References

1. Continuum Dynamics, Inc., "lHydrodynamic Loads on Quad Cities Unit I Steam Drycr," CDI Report No. 03-18, 2003.

2. Continuum Dynamics, Inc, "Ilydrodynamic Loads oil Dresden Unit 2 Steam Dryer,"

CDI Report No. 04-01, 2004.

3. Continuum Dynamics, Inc., "Hydrodynamic Loads on Dresden Unit 3 Steam Dryer,"

CDI Report No. 04-02, 2004.

4. Weaver, D.S. and MacLeod, G.O., "Entrance Port Rounding Effects on Acoustic Resonance in Safety Rclicf Valves," PVP-Vol. 389, Flow-Induced Vibration, 1999 ASME Pressure Vessels and Piping Conference, Boston, MA, August 1999.

5. Ziada, S., "A Flow Visualization Study of Flow-Acoustic Coupling at the Mouth ofa Resonant Sidc-Branch," PVP Vol. 258, Flow-Induced Vibration and Fluid Stncturc Interaction, 1993 Pressure Vessels and Piping Conference, Denver, CO, July 1993.

6. Tu, T., "Verification of Dimensions for Quad Cities 1 & 2 and Dresden 2 & 3 Steam Dome and Steam Dtyer," GE-NE-0000-0026-6917-11, Rev. 1, 2004.

7. McDade, J. C., D. R. Pardue, A. L. Iledrich and F. Vrataric, "Sound Velocity in Water above 212'F," The Journal of the Acoustical Society of America, 31(1')):

1380-1383, 1959.

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I D naillm csjd.

ii

10. Appendix 34

kIofilnum Ibtuaislnc-NonzrnprieraZr 35

0 Dynamics, Inc. Non-Propi 36