ML20062D578
| ML20062D578 | |
| Person / Time | |
|---|---|
| Site: | Fermi  |
| Issue date: | 08/02/1982 |
| From: | Tauber H DETROIT EDISON CO. |
| To: | Youngblood B Office of Nuclear Reactor Regulation |
| References | |
| EF2-58-955, NUDOCS 8208060148 | |
| Download: ML20062D578 (60) | |
Text
v Harry Tcut>st
' krw m Cmstructon Deirolf Edison FEE 5 August 2, 1982 EF2 - 58,955 Mr. B.
J. Youngblood, Chief Licensing Branch No. 1 Division of Licensing U. S.
Nuclear Regulatory Commission Washington, D. C. 20555
Dear Mr. Youngblood:
Re ference :
Enrico Fermi Atomic Power Plant, Unit 2 NRC Docket No. 50-341
Subject:
Mark I Containment Request For Additional Information Attached please find our response to your June 29, 1982 request for additional information on the Fermi 2 Plant Unique Analysis Report (PUAR).
Due to the time constraint, the response is submitted in the question / response format.
After you have reviewed and accepted our response, we will incorporate the attachment into the PUAR, revising PUAR pages if applicable.
If you have any questions regarding the above, please contact Mr. Larry E. Schuerman, (313) 649-7562.
Sincerely, eb/A 0or 9
/
Attachment cc:
Mr. L. L. Kintner Mr. J. Ranlet (Brookhaven National Laboratories)
Mr. W. Seagraves (Franklin Research Institute) 8208060148 820802 PDR ADOCK 050003gg A
Question 1 Published acceleration drag volumes were used to determine the drag loads on sharp cornered submerged structures instead of the equivalent cylinder procedure specified in the acceptance criteria.
Provide a list of structures which were treated in this manner.
For the ring beam, provide specific dimensions of the structure, as well as the local acceleration and velocity for the post-chug loading condition.
A copy of K.
T.
Patton's MS thesis from the University of Rhode Island (1965) would be useful in resolving this issue if it is available.
Response to Question 1 1.
The alternate method for calculating acceleration drag volumes was used for the following structures:
Ring beam T-quencher support beam T-quencher support pedestal T-quencher support gusset plates The ring beam was divided into the segments shown in PUAR Table 2-2.2-9 for analysis of post-chug submerged structure loads.
Dimensions of the ring beam sections are:
Sections 1 through 6 Sections 7 through 10 and 11 through 16 16"
=
=
U 16" a
a v
- 1. 5 "
i i
a
^
3.4'
- 1. 5 "
2.292' p
u d
a 1.5"
- 1. 5 1.5"
- 1. 5 "
Post-chug submerged structure loads on the ring beam were calculated
. on the basis of the two nearest downcomers chugging at the maximum source strength with the downcomer phasing selected to maximize the local acceleration.
Segment 7 of the ring beam experiences the highest loads as shown in PUAR Table 2-2.2-9.
Forces are calculated for the 50 frequencies and corresponding source strengths listed in PUAR Table 1-4.1-15.
As an example, the velocities and accelerations on Segment 7 for the frequency of 26 Hz and the maximum source strength of 3
2 377.83 ft /sec are:
Velocity (ft/sec)
Acceleration (ft/sec )
Vx = -0.010 Ax = -1.753 Vy = -0.010 Ay = -1.742 Vz = -0.017 Az = -2.747 To obtain the total loading on Segment 7 the velocities and accelera-tions corresponding to the remaining 49 frequency regimes would have to be considered.
The right-hand coordinate system is:
TORUS CROSS SECTION TO RPV q l
hY x
_ _ _ E ~_
l K.
T.
Patton's Master's thesis is not available from either the University of Rhode Island or the author.
Both the author and the University were contacted.
4
~
Question 2 A statistical basis was used to account for random phasing of the loading harmonics for condensation oscillation and chugging loadings.
The random phasing approach consists of multiplying the absolute sum of the responses (i. e., the AC accepted approach) by a scale factor determined from the FSTF data.
Provide more detailed docu-mentation for the justification of the 0.65 value of the scale factor and comment on the remaining conservatism after application of this factor for both the condensation oscillation and chugging loading.
List all loads (such as C.O., post chug, etc.) and all structures (such as torus shell, ring beam, etc.) for which the scale factor is used.
In addition provide the basis for the statement that alternate 4 leads to a 20% increase in the loads and verify the numbers given in Table 1-4.'l-4 on page 1-4.48.
In particular, check the consistency of these numbers with those given in the FSTF letter report MI-LR-81-01.
Response to Question 2 The loads for which the random phasing methods were used to combine harmonic responses are:
a.
DBA Condensation Oscillation Loads on the Torus Shell b.
DBA Condensation Oscillation Loads on Submerged Structures c.
Post-Chug Loads on the Torus Shell d.
Post-Chug Loads on Submerged Structures The components of the torus and vent system affected by the above loads are identified in Fermi-2 PUAR Tables 2-2.2-1 and 3-2.2-1.
The components of the SRV piping and T-quenchers affected include the submerged portion of the SRV piping, the T-quenchers, and their supports.
F6r combining harmonic responses, NEDE-24840 recommends use of a 50% non-exceedance probability (NEP) value based on random phasing cumulative distribution function (CDF) curves as a means of providing
an appropriate level of conservatism for the combined response.
The approach used in the Fermi-2 plant unique analysis (PUA) con-sists of multiplying the absolute, sum of the harmonic responses by a scale factor of 0.65, determined from the data contained in NEDE-24840.
The method estimates the response at 84% NEP with a 90% con-fidence level as described in'Section 1-4.1.7.1 of the PUAR.
This method of combining harmonic responses is more conservative than that recommended in NEDE-24840.
The scale factor of 0.65 was derived from the 14 response quan-tities given in Tables 6-1 through 6-3 of NEDE-24840.
Ratios of the absolute sum and 84% NEP response values from these tables were calculated as shown in the attached Table 2-1.
The mean (p) and standard deviation (c) values were calculated for the ratios of these 14' responses.
Using a Gaussian (normal) distribution, the tolerance limit (Ra, y ) is then calculated as:
i Ra,y = p - g o Where a = Confidence level 1
i l
y = Non-exceedance probability (NEP)
K = Tolerance factor for normal distribution; l
depends on a,y and the sample size Using the values in Table 2-1, a tolerance limit (Ra,y) with an 84%
NEP and 90% confidence level is determined to be 1.53.
Thus an 84%
NEP response with a 90% confidence level can be calculated using a scale factor of 0.65 (reciprocal of 1.53) applied to the absolute sum response.
l l
A comparison of FSTF responses. calculated using the Fermi-2 methodology with the maximum measured FSTF responses in various tests is provided in PUAR Table 1-4.1-4.
A copy of this table is attached with two minor revisions which will be included in the next PUAR revision.
The comparison provides an assessment of the conservatism which results when applying the Fermi-2 methodology.
The values for maximum measured FSTF response listed in PUAR Table 1-4.1-4 were obtained using the same methods as for NEDE-24840.
The FSTF letter report MI-LR-81-01 may have used preliminary test results, or slightly different data reduction or analysis techniques.
The differences between the PUAR and MI-LR-81-01 are very slight, and do not affect the conclusions of the comparison of the analysis to the data.
The analysis techniques used in the Fermi-2 PUA are conservative and result in predictions that bound the maximum measured FSTF response by a wide margin.
Measured' pressure amplitudes from FSTF test M12 were used in the Fermi-2 PUA as a fourth alternate in calculating the response due to the condensation oscillation load.
It has been observed that FSTF test M12 condensation oscillation torus shell pressures at certain frequencies are higher than the pressures for the three alternates specified in the LDR.
A comparison of the torus re-sponses for Fermi-2 due to application of FSTP test M12 amplitudes and amplitudes for the three LDR alternates shows that the addi-tional conservatism in the response due to M12 is location depe-ndent.
At some locations, the response is as much as 27% greater than that due to the LDR alternates, as shown in the attached
Table 2-2.
It is estimated that the fourth-alternate (M12) has added about 10 to 30% of additional conservatism to the Fermi'-2 condensation oscillation response.
4 0
4
i Table 2-1 Torus Response Ratios from Tables 6-1 through 6-3 of NEDE-24840 Response Ratio Response Quantity (Abs. sum / 84% NEP) 1 1.53 2
1.55 j
3 1.69 j
4 1 70-5 1.72 l
l 6
1.74 l
7 1.78 8
1.80 9
1.86 10 1.88 11 1.94 12 2.01 13 2.01 14 2.02 1
I Mean (p) value 1.80 Standard Deviation (c) 0.16 i
}
i l
}
1
PUAR Table 1-4.1-4 FSTF RESPONSE TO CONDENSATION OSCILLATION MAXIMUM MEASURED CALCULAT ED FSTF RESPONSE RESPONSE QUANTITY FSTF RESPONSE AT 84% NEP(l)
M8 MllB M12 BOTTOM DEAD CENTER 3.0 2.3 1.6 2.7 AXIAL STRESS (ksi)
BOTTOM DEAD CENTER HOOP STRESS (ksi) 3.7 2.6 1.4 2.9 BOTTOM DEAD CENTER 0.17 0.11 0.08 0.14 DISPLACEMENT (in.)
INSIDE COLUMN 184 93
((H 109 FORCE (kips) 68 OUTSIDE COLUMN 208 110 46-141 FORCE (kips) 81
')
NOTE:
(1) USING CO LOAD ALTERNATES 1, 2 AND 3.
)
DET-04-028-1
[](jf{}f}
Revision 0 1-4.48
Table 2-2 Comparison of Fermi-2 Torus Response Due to Condensation Oscillation Load Alternate 4 (M12) and the Three LDR Alternates Maximum Response Conservatism due Response Quantity to Alternate 4 Alternate 4 Alternates 1,2, (percent)
(M-12) and 3 from LDR Inside Column downward Force (kips) 206.76 182.58 13.2 Outside Column downward Force (kips) 225.44 200.31,
12.5 Inside Saddle downward Force (kips) 289.48 261.38 10.8 Outside Saddle downward Force (kips) 350.23 309.98 13.0 Memb. Stress Intensity at Bottom Dead Center near mid bay (ksi) 6.57 5.81 13.1 Memb. Stress intensity at about 60 below equator at miter on outside 8.8 7.81 12.7 Memb. stress intensity at 30 above equator near miter 6.44 5.07 27.0
Question 3 The downcomer dynamic load methodology derived from the supplemental FSTF tests was for tied downcomers.
Justify the use of the method-ology for the untied downcomers as shown in the PUAR.
Response to Question 3 Section 4.4.3.1 of the LDR, Revision 2, states that the load defi-nition for condensation oscillation downcomer loads is applicable to downcomer pairs which are tied by lateral bracing, or where the downcomer-to-vent-header intersection is stiffened with' gussets or other means.
The Fermi-2 downcomer pairs are stiffened at each intersection by a crotch plate and by outer stiffener plates shown in PUAR Figure 3-2.1-12.
A frequency analysis of Fermi-2 downcomers shows that the predominant fundamental mode of vibration is the sway mode,.i.e., both downcomers in a pair simultaneously deflect-ing in the same direction.
This results in the Fermi-2 downcomers responding as if they were tied by lateral bracing at the ends of the downcomers.
This behavior is identical to that of the FSTF tied downcomer pairs.
6
Question 4 The acceptance criteria specified that for multiple downcomer chugging the force per downcomer shall be based on an exceedance probability of 10-4 per LOCA.
A correlation between load mag-nitude and probability level derived from a statistical analysis of FSTF data was utilized in the PUA.
Provide the details of the derivation and justification for the use of the correlation.
Response to Question 4 The multiple downcomer chugging load probability of exceedance specified in NUREG-0661 was based on the premise that the down-comer load magnitudes observed in FSTF would not excedd the design load more than once per LOCA.
The 10-4 value discussed in Section 4.5.3.3 of the LDR corresponds to a plant with 120 downcomers in which all downcomers are assumed to be loaded in the same direction at the same time.
For plants with fewer downcomers such as Fermi-2, or in cases where fewer-than all of the plant's downcomers are assumed to be loaded, the probability of exceedance required to ensure the downcomer load magnitude will not be ex'ceeded more than once per LOCA is greater than 10-4 The methodology used to compute the probabilities of exceedance for the Fermi-2 multiple downcomer chugging loads is illustrated in Table 3-2.2-15 of the PUAR.
The total number of chugs in a LOCA for a given number of downcomers for Fermi-2 was calculated using a bounding chugging duration of 900 seconds for Fermi-2, together with the chugging duration, number of downcomers, and number of chugs measured at FSTF.
The e'xceedance probability for the number of Fermi-2 downcomers assumed to be loaded was then taken as the reciprocal of the total number of chugs.
This approach ensured that the lateral load magnitude would not be exceeded more than
once per LOCA.
The downcomer lateral'1 cad magnitudes are determined, using the resulting exceedance probabilities in Figure.3.9-3 of NUREG-0661.
The downcomer lateral loads determined from Figure 3.9-3 are con-i verted to resultant static equivalent loads (RSEL's). for Fermi-2, using the conversion factor in Table 3-2.2-14 of the PUAR.
The resulting load magnitudes as a function of the number of down-comers loade'd are shown in Table 3-2.2-15 of the PUAR.
1 e-e k
,---_r w -.
y e-
i Question 5 (a) On page 1-4.113, it is stated that the peak positive bubble pressure and maximum bubble pressure differential from the Monticello T-Quencher test data are 9.9 psid and 18.1 psid, respectively.
Our information (Table 3-3, Page 3-10, NEDE-21878-P) indicates that these values are 9.3 psid and 17.4 psid.
Provide information to permit clarification of this discrepancy.
(b) We require additional information to determine whether modi-fication of the bubble pressure bounding factor from the LDR value of 2.5 to the proposed value of 1.75 is justified.
Specifically, the peak positive and negative bubble pressure predicted by the SRV bubble pressure methodology when the 1.75 multiplier is employed should be reported.
The initial conditions for this calculation are to correspond to the CP, NWL, SVA case as listed in Table 3-2 of NEDE-21878-P.
Response to Question 5 (a) The peak positive bubble pressure and maximum bubble pressure differential from the Monticello test data are 9.3 psid and 17.4 psid, respectively.
The statement in the PUAR regarding the values of 9.9 psid and 18.1 psid refers to the calculated values of peak positive and maximum bubble pressure differen-tial using the bubble pressure bounding factor of 1.75.
(b) The predicted values using the 1.75 factor for the CP, NWL, SVA case listed in Table 3-2 of NEDE-21878-P are:
Peak positive bubble pressure = 9.9 psid Peak negative bubble pressure = 8.2 psid l
a Question 6 The post-chug submerged structure loads, as specified in the accept-ance criteria, were to be computed on the basis of the two nearest downcomers chugging at the maximum source strength with phasing between the downcomers that maximizes the local acceleration.
On PUAR page 2-2.39 it is stated that the loads were developed using the average source strength.
Please clarify the situation by docu-menting the calculation in detail for the ring beam giving the source strengths used and their locations.
Response to Question 6 The statement on PUAR page 2-2.39 which says that the post-chug loads were developed using the average source strength is incorrect.
The maximum source strengths calculated using the LDR methods were used in the Fermi-2 analyses.
The source strengths as a function of frequency used for the Fermi-2 post-chug submerged structure load analyses are listed in Table 1-4.1-15.
These post-chug sub-merged structure loads were computed on the basis of the two nearest dcwncomers chugging at the maximum source strengths, with phasing between the downcomers that maximizes the local acceleration as required in Appendix A of NUREG-0661.
The Response to Question 2 provides additional details on the calculation of post-chug loads on the ring beam.
The correction on PUAR page 2-2.39 will be included in the next PUAR revision.
_e
+
Question 7 Provide a more detailed discussion of the method used to account for FSI' effects on condensation oscillation and chugging submerged struc-ture loads.
Include an explanation of how the local pool fluid ac-celerations are determined.
Response to Question 7 A detailed discussion of the method used to account for FSI effects on condensation oscillation and chugging submerged structure loads is provided in the attached Continuum Dynamics, Inc. Tech Note No.
82-15, Revision 0, " Mark I Methodology for FSI Induced Submerged Structure Fluid Acceleration Drag Loads".
t l
4 h
i
~
-.__.m
TECH NOTE NO. 82-15 MARK I METHODOLOGY FOR FSI INDUCED SUBMERGED STRUCTURE FLUID ACCELERATION DRAG LOADS Revision 0 PREPARED FOR THE GENERAL ELECTRIC COMPANY 175 CURTNER AVENUE SAN JOSE, CALIFORNI A 95125 UNDER PURCHASE ORDER NO. 205-XH160 PREPARED BY CONTINUUM DYNAMICS, INC.
P.O. B0X 3073 PRINCETON, NEW JERSEY 08540 APPROVED BY
(
/tt,
'fr ALAN J. BILANIN PRINCIPAL INVESTIGATOR June, 1982
i TABLE OF CdNTENTS.
l Section Pa'ge 4
Summary i
i
-1 Introduction ^
1 2
Estimation of-FSI Induced Pool 3
1 Accelerations j
3 Formulation 7
4 Selected Results 10 1
4
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4 0
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4 d
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a
---e e-e w y --
--gwe--
,,-,----.-w,,,we,v-e-.-
.--,,w--
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.,-. _,. --.-i
. wiw
--=,----+w<-
,v-,
4
SUMMARY
In the NRC Acceptance Criteria #or the Mark I program, drag on submerged structures resulting from fluid structural interaction (FSI) "shall be included for any structural segment for which a local fluid acceleration is less than twice the torus boundary acceleration.
This may be accomplished by adding boundary accelera-tion to the local fluid accelerations."
This methodology introduces extreme conservatism in the estimation of FSI induced drag loads.
For this reason, a less conservative methodology is developed herein.
The alternate methodology computes the actual acceleration field across a submerged structure resulting from FSI.
It is shosm that this procedure, when implemented, can significantly reduce the loads which must be sustained by a submerged structure during containment transients.
i
INTRODUCTION The approach used by architect engineers in analyzing the torus shell for LOCA condensation loads has been to develop the finite element structural model of the containment steel and fluid suppression pool.
This model is driven by applying Fourier transformed pressure time histories on the containment walls and predicting the displacement of the torus shell as a function of frequency.
From this analysis strains (and hence stresses) for the deformed structure can be computed and the containment itself can be qualified for condensation loads.
A by-product of this analysis is the detailed displacement and acceleration field of the torus shell.
When this acceleration field is known a priori, it is straightforward to compute the pool fluid acceleration field compatible with the shell acceleration field.
Having this field specified permits an accurate evaluation of the acceleration field about a submerged structure located in the pool.
It is possible to compute this acceleration field and generate a file for each Mark I containment which can be accessed by an architect engineer when evaluating the FSI induced accel-eration drag load on submerged structures within that containment.
This methodology, especially for structures located away from the shell boundary, is expected to give appreciably reduced loads when compared with NRC acceptance methodology which requires the FSI induced acceleration drag load to be taken equal to the loading resulting from predicted shell acceleration.
i
O The following technical memorandum is organized as follows.
In Chapter 2 an estimate of the conservatism which may be elim-inated when using the above prescribed methodology is made.
In Chapter 3 formulation for analyzing a sector of a Mark I torus is prescribed and in Chapter 4 results are presented for analysis of the induced submerged structure loads for the Enrico Fermi plant.
N I
i r
i 2
2.
ESTIMATION OF FSI INDUCED POOL ACCELERATIONS Consider a cross section of the torus sketched in Figure 1.
The shell boundary is undergoing harmonic oscillation at circular frequency with the displacement w
iet ri = il sin n(p-0) e (1) where n
is an integer and n+1 is the number of displacement nodes in the azimuthal direction on the wetted shell.
Assuming an incompressible inviscid fluid (this approximation is consistent with the previous analysis of the torus and pool) the pressure field in the pool is related to the fluid acceleration field by Bu# =
1 I P-(2) at o ar Bu (3)
=-
at where ur ' "9 and p are the radial velocity, azimuthal velocity and pressure respectively.
Utilizing continuity it may be shown that the pressure field satisfies E
11 + 1 BP
+
=0 (4)
Br B0 whose solution, subject to the displacement boundary condition e = { and f can be shown to be (1) at r=R and p=0 at sinn(f-0)e n
2a r
iwt p = pu n Rn-1 n
3
i i
1 i
l (p=6 i
s f
/
I y
I
/
I
/
t 6
R i
/
\\
7
/
\\
\\
/
\\
/
\\
/
\\,
I
/
~%~.
/
/
~
s A
/w
' g = g s.in n (T-6 e.iwt O
i l
l Figure 1.
Cross section of a Mark I torus with shell displacement n
4
The corresponding fluid acceleration field is given-by.
2()n-1 sinn(j-0)e"U Bu
.l r
,_g 6
.(6) n-l 2
iet e,ug cosn({-0)e g) whose magnitude is given by
)n-1 lal (8)
=
2
/76w It is apparent from the above that the fluid acceleration field in the pool drops off away from the shell boundary at a rate which is strongly dependent on the complexity of the shell dis-placement.
As expected, the more convoluted the shell displace-ment field, the more rapid the drop off of the FSI induced acceleration field in the pool.
Figure 2 shows the magnitude of the FSI induced acceleration field in the pool as a function of the number of shell displacement nodes, n + 1.
It is anticipated that an exact calculation of the FSI induced pool acceleration field will result in a substantial reduction in the FSI induced submerged structure's load over that computed by the method suggested in the i
NRC Mark I Acceptance Criteria.
0 4
5
I l
l shell displacement nodes = 2 l
T 8
.6 lal E hu2 3
.4 14 6
.2 o
O
.2
.4
.6
.8 1
r/ R Figure 2.
Distribution of FSI induced fluid acceleration magnitude in a two-dimensional cylindrical pool 6
s x
3.
FORMULATION
$5rus shell accelerations normal to the shell during conden-sation oscillation are now determined by a finite-element analysis of the Mark I plant-unique facility.
The effect of these accelera-tions induces a pressure field and, hence, an acceleration field in the fluid which would not be present if the shell were rigid.
This FSI induced acceleration field in the pool may be determined by solving Laplace's equatton for the pressure with appropriate.boun-dary conditions including specified shell normal accelerations.
This pressure may further be differentiated in the three directions to determine the (complex) acceleration vector.
With the results stored in a data file, the interpolated local acceleration vector anywhere within the pool may be obtained for further evaluation of submerged structure loads.
s The shell acceleration data was supplied to Continuum Dynamics, Inc. following the coordinate system established in Figure 3.
Here is measured positive from the center of the torus, 6
is measured r
from pool bottom dead center, and z
is measured positive.from midbay to the mitered joint.
Resultant positive accelerations follow this J
same left-handed coordinate system.
The data was transmitted as (complex)' accelerations frequency. component by frequency component.
The pool pressure is solved using Laplace's equation
~.
g + 1 32 + 7 as'5phap=0 Bo 1
r ar 2
2 3z
'1 finite-differenced onto a uniform grid through a transformation that represents the computational domain as 5nd-half of a right cylinder.
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7
TOP VIEW P.idbay F.
% A
\\
Mitered joint r
z
\\
A B
SECTION A-A T
- 9 Figure 3:
?.sel Coordinate System Convention 8
The pressure is assumed' equal to zero on the surface of the water, and the normal pressure gradient at midbay and along the mitered j
joint are assumed zero from symmetry arguments.
The boundary I
condition along the torus shell requires the pressure gradient to be consistent with the specified normal acceleration field, hence D
= - piwu (9) 3r r
J r=R j
where O
is in general a complex quantity.
r 1
1 5
0 l
i l
4.
SELECTED RESULTS As an aid toward illustrating the predicted FSI induced acceleration field, contours of constant acceleration magnitude have been plotted at planes shown in Figure 4.
The planes are denoted 1, 3 and 5 and are located at midbay, halfway between midbay and the mitered joint, and at the mitered joint.
In Figures 5 through 8 contours of constant acceleration magnitude are shown for the frequencies 18.94, 25.71, 31.80 and 35.79 Hz.
2 The units of acceleration in these figures is ft/sec, and is noted on each figure along with the number of the plane cut and the frequency.
The acceleration is a complex number = ar + iat where a
and a
are functions of the r, 0 and z directions.
r t
10
- 4.08'
" T 4.08' +
b
' Torus radius = 15.28'
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x
[
Midbay
\\
Mitered Joint
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\\
3 5
s Ns s
% f N
/ N
\\
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N 7.11' O
7.11' Figure 4 :
Locat. ions of planen on which contours of constant acceleration magnitude are displayed (Enrico Fermi).
MJTECH4 2 FIED PLArE: 1 0.e is.9773e HZ VIEIRILE: 7 se.eee rPss
.... Se.ese FPss
- 40. 00e rPss 30.eee rPss 2e.ese rPss 10.000 FPsS l
s~%
./
[
.._._; l A
y
- i. l
./ ~'
- ~.~..
..-)
Ili~~.
'~-
I
~
.f..
f e
Io Figure Sa.
Contours of constant acceleration magnitude for frequency = 18.94 Hz, plane 1.
12
PtJTECH4 2 rI e PJtC: 3 5.5945 18.9372 HZ V8EIABLE: 7 e.eae ress 3e.aae rPss m.ase rPSS 10.000 FPSS 1
l 1
j l
. :l p.
\\
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'w.
.i
-~
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Figure 5b.
Plane 3 13
O MJTrow 2 FI e PM: 5 11.1991 19.937M HZ VARIAILE: 7 te.eee rPSS 1
.../
/../.../
~.~...,,'s-s. 'N..
. %,,, %... _., /
Figure 5 c.
Plane 5 14
4 1
ttntoe 2 FIxto PLRE:
1 e.e 25.7e74e Hz V5RIAR.E:.7 j
25.000 ress
- 22. M FPss
- 15. m rPss 1e.000 rPss l
l
/
.E
./
./
./
/
~
\\
l
\\
l i x
-s i
s s
s s
s
~
/
s-i Figure 6a.
Contours of constant acceleration magnitude for frequency = 25.71 Hz, plane 1.
15
t NLirtou Z Fle PLRE: 3 5.5945 25.7Er74e Hz VfRIAILE: 7 22.eee ress 25.0e0 rPss le.eee ress l
I
./
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-1
.I
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./
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....._..~......
j
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-s
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Figure 6b.
Plane 3
/
16
MJrtou Z FI O PM: 5 11.1991 25.7e74e Hz VEIAILE: 7 l
10.000 %
5.EEE FPss l
l
\\
.\\.
3 l
\\*\\
.I N
'N
.I
\\-s
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- ~.~..j
._ ~._.
Figure 6c.
Plane 5 17
e o
MJTECH4 1
2 rI O l
PJPC: 1 0.0 31.1B499 HZ WRIAILE: 7 20.eee rPs5 16.000 FPSs 12.eee rPSS e.eee rpss 4.eee FPSS a
./'i
%.\\.
./
./
/
./
./
/
I
.~.,.
j l
-s ~ ~.
/
\\.
L.
r t
g
/
\\.
(.I s
-\\
l s
/
t j
s'
-g e
s N
\\.
i
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i\\
~
Figure 7a.
Contours of constant acceleration magnitude for frequency = 31.80 Hz, plane 1.
18
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Plane 5 23
NRC Ouestion #8 Provide a complete description of the bases for the local to bulk pool temperature differences which are presented in Section 1-5.1 of the PUAR.
The AC (Section 2.13.8.2) stipulate that this parameter should be supported either by existing Monticello pool temperature data or inplant tests.
If the first of these options is. employed, the applicant must demonstrate the applicability of the Monti-cello data base by providing a detailed comparison of the respective quencher and suppression pool gemotries.
- Also, since credit for RHR cffectiveness in reducing the local to bulk temperature difference is being taken by the appli-cant, comparison of the suction and discharge geometries of the respective RHR systems should also be provided.
If the Monticello data base is used in conjunction with any analytical modeling to estimate plant unique values of local to bulk temperature differences, a complete description of the analyses should be supplied together with a demonstration of the credibility of the model in terms of its ability to accurately predict experimental suppression pool temperature responses to extended SRV discharges.
Response
GE had analyzed seven postulated long-term SRV events in Fermi-2 to demonstrate the plant's conformance with the local pool temperature limit as defined by the NRC (c.f.,
Reference 15 of the Fermi-2 PUAR).
The assumptions and results of this analysis are presented in Section 1-5.1 of the PUAR.
The analysis is based on properly modeling each of the seven events using two GE proprietary computer codes to evaluate local and bulk pool temperatures as a function of time.
The first code is a coupled RPV and suppression pool thermo-dynamics model which calculates the transient response of the
Response
(Continued) suppression pool during long-term events which add heat to the pool.
This model performs fluid mass and energy balances in the reactor primary system and the suppression pool and calculates the reactor vessel water level, pressure, and the long-term response of the suppression pool bulk temerature.
The various modes of operation of all important auxiliary systems, such as the SRVs, main steam isolation valves (MSIVs),
Emergency Core Cooling System (ECCS), Residual Heat Removal (RHR)
System, and feedwater are modeled.
To simulate a specified reactor cooldown rate or depressurization rate, a rate of change of temperature or pressure may be imposed on the reactor vessel.
In addition, the model also simulates system set points (automatic and manaul), and specified operator actions.
The calculated maximum suppression pool bulk temperatures of each event are tabulated in Table 1-5.1-1 of the PUAR.
The second computer code is a local pool temperature model which calculates the water temperature in the vicinity of the quencher during SRV discharge events which add heat to the pool.
This code was developed under the Mark I Program expressly to model Mark I plants equipped with T-Ouencher discharge device.
The Fermi-2 T-Quencher is applicable to the computer code.
The model is calibrated to the Monticello test results.
Response
(Continued)
Pool temperature distributions predicted by the model have been compared with the Monticello T-Quencher Test results and the Monticello T-Quencher Thermal Mixing Test results.
Results of the comparison indicate that the model predicts the local quencher temperature during SRV actuation.
Results from the first model, such as the mass and energy added to and removed from the pool during each transient (i.e., RHR and SRV flows) are input into the second model along with pool geometry, submerged structures geometry, and initial pool conditions.
The overall local temperature analysis consists of two major, coupled components:
a momentum balance to solve for the bulk pool velocity, and a two-dimensional energy model which determines the temperature distribution in the pool by superimposing the circulation of pool water induced by the SRV discharge on the bulk motion of the pool.
The energy model is of sufficient generality to accomodate multiple SRV actuations for random patterns of T-Quencher discharge at selected points in time.
The energy model is applied locally at uniformaly distributed nodes throughout the pool. One axial node is assigned to each half bay for each of eight horizontal layers.
- Thus, a total of 16 nodes per bay are used to describe the temperature distribution in the pool.
Application of the models to these
. _ _ _ - - ~ _.
i
Response
(Continued) podes results in a coupled set of algebraic equations which are solved by successive substitution at each time step.
A simple iterative scheme is employed to ensure conservation of energy.
1 The local temperatures of interest in this analysis are cal-i j
culated by averaging the temperature of the nodes directly above and below the T-Quencher in the downstream portion of the bay.
The local temperatures tabulated'in Table 1-5.1-1 of the PUAR correspond to the bay with the highest temperature throughout each event calculated in this manner.
l The remaining portion of this response pertains to'the oral request to address the basis of the Fermi-2 Local Pool Temp-erature Limit curve as given in Figure 1-5.1-1 of the PUAR.
i The curve (Figure 1-5.1-1 of the PUAR)is based on NUREG-0783 (c.f., Reference 15 of the Fermi-2 PUAR) which states:
1 1.
For all plant transients involving SRV operations during which the steam flux through the quencher i
2 j
perforations exceeds 94 lbm/ft -sec, the suppression pool local temperature shall not exceed 200 F.
[
2.
For all plant transients involving SRV operations during which the steam flux through the quencher 2
i perforations is less than 42 lbm/ft -sec, the
r
Response
(Continued) suppression pool local temperature shall be at least 20 F subcooled.
3.
For all plant transierts involving SRV operations during which the steam flux through the quencher 2
perforations exceeds 42'lbm/ft -sec, but is less 2
than 94 lbm/ft -sec, the suppression pool' local temperature is obtained by linearly interpolating the local temperatures established under afore-mentioned items 1 and 2.
Fermi-2 T-quenchers have a submergence of 10 feet of water, corresponding to 18.9 psia.
The saturation temperature at 18.9 psia is 224.8 F.
Thus, for limit 2,.a 20 F subcooling translates into a suppression pool local temperature limit of 204.8 F.
Since the steam mass flux through the quencher perforations is directly dependent on reactor vessel pressure, mass fluxes 2
2 of 42 lbm/ft -sec and 94 lbm/ft -sec correspond to reactor vessel pressures of 273 psia and 615 psia, respectively.
The maximum local pool temperature of 202 F calculated for case 3A (small-break accident (SBA) accident mode assuming one RHR loop available) occurs at a time when the quencher mass fluxes are far below 42 lbm/ft -sec, which defines the l
Response
(Continued) region where the NRC limit is 204.8 F.
Therefore the maximum 1 coal pool temperature for this case lies below the NRC limit.
As shown in Table 1-5.1-1 of the Fermi-2 PUAR, the maximum local pool temperatures of all other cases also remained below the NRC limit throughout the transient.
Considering the degraded assumptions employed for each case, and the conservatism of the NRC limit, the results are con-sidered acceptable, and unstable steam condensation would not be expected.
l f
1 I
l
)
l l
i
f NRC Question #9 The description of the Suppression Pool Temperature Monitoring System (SPTMS) which is provided in the PUAR is inadequate.
Additional information is needed to provide a clear demonstration that the FERMI 2 SPTMS design is in accordance with the requirements of AC section 2.13.8.3.
Response
The Fermi 2 Suppression Pool Temperature Monitoring System (SPTMS) design is discussed in the Fermi 2 PUAR Section 1-5.2.
In the design of the SPTMS, particular attention was given to the placement of the temperature sensors to ensure that the system would provide a conservative measure of bulk pool temperature and early operator notification of energy discharges into the pool.
The considerations provided in the design included functional redundancy (dual element thermo couples), potential pool circulation patterns, the location of the RilR discharges, and identification of energy discharges (S RV, IIPCI turbine exhaust and RCIC turbine exhaust).
Addi-tional information to demonstrate that the SPTMS design is in accordance with the requirements of NUREG-0661, Appendix A, Article 2.13.8.3 has been provided in Table 1 and Figures 1 and 2 of this response.
TABLE 1 Comparison of the FERMI 2 Suppression Pool Temperature Monitoring System with NRC Acceptance Criteria NRC Acceptance Criteria Fermi 2 Suppression Pool NUREG-0661 Appendix A Temperature Monitoring Article 2.13.8.3
System Design
af Each licensee shall demonstrate a) The Fermi 2 Suppression Pool that there is a sufficient number Temperature Monitoring System and distribution of pool tempera-(SPTMS) utilizes twelve (12) ture sensors to provide a reason-dual element thermocouples able measure of the bulk tempera-installed in the suppression ture.
Alternatively, redundant pool water space.
In addition, pool temperature monitors may be there are four (4) dual element located at each quencher, either thermocouples installed in the on the quencher support or on the suppression pool air space.
torus shell, to provide a measure The distribution of the water of local pool temperature for each space thermocouples relative to quencher device.
In such cases, Safety Relief Valve Discharge the Technical Specification limits (SRVD) quencher positions is for local pool temperature shall shown in Figure #1.
Eight (8) be derived from the calculated of water space thermocouples bulk pool temperature and the have been installed on the bulk to local pool temperature torus shell at elevation 556'-1".
difference transient.
The other four (4) thermo-couples are installed at eleva-tion 551'-4".
Figure #2 provides a section elevation of the torus and shows the relative orienta-tion of the quencher and the water space thermocouples.
f
TABLE 1 (Cont'd)
Figure #1 shows that the place-ment of the thermocouples essentially provides an even distribution of temperature sensors.
A thermocouple is located in the vicinity of a pair of quencher arms.
The placement of the eight thermo-couples in the upper region of the pool will ensure measure-ment of the hotter water that is essentially pumped to the pool surface due to the re-circulation flow pattern in the pool established during quencher discharge.
These temperature elements have also been appropriately placed in positions downstream of the RHR,
discharges.
Therefore, the Fermi 2 SPTMS design will provide a conservative measure of the suppression pool bulk temper-ature.
l l
t i
TABLE 1 (Cont'd) b) Sensors shall be installed b) The elevation of the thermo-sufficiently below the minimum couple placements relative to water level, as specified in the the suppression pool water level plant Technical Specifications, is shown in Figure 2.
The to assure that the sensor pro-normal operating suppression perly monitors pool temperature, water level is at elevation 557'-0".
The low-low suppres-sion pool water level (minimum water level) is at elevation 556'-10".
The minimum sub-mergence of the SPTMS thermo-couples would be nine (9) inches.
Therefore, the temperature sen-sors are installed sufficiently below the minimum water level to provide proper temperature monitoring.
TABLE 1 (Cont'd) t c) Pool temperature shall be indi-c) The Fermi 2 SPTMS design cated and recorded in the control provides the suppression pool room.
Where the suppression pool temperature indication and temperature limits are based on recording in the main control bulk pool temperature, operating room.
The indication and procedures or analyzing equip-recording devices are located ment shall be used to minimize on the panel providing the SRV the actions required by the actuation controls and position operator to determine the bulk indication.
The puncl display pool temperature.
Operating is arranged to allow quick procedures and alarm set points operator identification of shall consider the relative suppression pool energy inputs, accuracy of the measurement reading of pool temperature system.
values, and determination of the bulk pool temperature.
The suppression pool bulk' temp-erature will be calculated based on the eight (8) temperature, sensor readings available in the upper region of the pool water space.
The recirculation flow pattern established during quencher discharge moves the warmer water toward the pool surface.
Therefore, utilizing the temperature values measured by the eight thermocouples will ensure a conservatively cal-culated bulk pool temperature.
An operating procedure will provide details and necessary steps such that minimum oper-ator action will be required to determine the, pool bulk temperature.
i
\\'
\\
TABLE-1 (Cont'd)
~
s d)
Instrument set points for alarm d)
The Fermi 2 technical speci-shall be established, such that fications provides that the the plant will operate withiN' plant will be operated'tnder the suppression pool temperature the appropriate suppression
. limits discussed above.
pool temperature limit's.
A copy of the applicable. draft standard technical specifica-N i
tion under development between the NRC staff and Detroit T
Edison is attached.
In g
,, addition, an alarm in the main control room is annun ciated when any one,of_ the, A
thermocoupl'es at' elevation' 556'-1" measure a' temperature of'105 F.
The 105 F alarm set point will alert the s
operator very early during hlanttransientconditions-of energy discharges into the pool and consequently will 6nsure that the suppression pool will be maintained within
,o, 3
allowable suppression pool temperature limits.
~.,
N
-f.
~
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m
T TABLE 1 (Cont'd) e) All sensors shall be designed to e) The suppression pool temperature seismic Category 1, quality Group sensors.(thermocouples) are B, and energized from onsite emer-seismically qualified.
The gency power supplies.
sensors are a passive element and do not require any power supply.
The sensors are mounted on seismically qualified channels and supports, and the signal cables are routed in seismically qualified and supported trays and conduits to the main. control room recorders.
There are three multi-pen (12 pens) Strip-chart Recorders in the main control room and they are powered from onsite emergency bus power supplies.
These recorders are seismically qualified.
i l
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r SUPPRESSION N
I CHAMBER
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27F 90 56'-3" N
TE TE E
TE g
g RHR DIV. I
's
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RHR DIV. II DISCHARGE DISCHARGE TE TE SUPPRESSION SRV DISCHARG3 CHAMBER T-QUENCH CENTERLINE TE l180 PLAN VIEW hDUAL ELEMENT THERMOCOUPLES IN THE WATER SPACE AT.
hDUAL ELEMENT THERMOCOUPLES IN THE W hDUAL ELEMENT THERMOCOUPLES IN THE AIR SPACE FIGURE #1 DISTRIBUTION OF SUPPRESSION POOL THERMOCOUPLES
- f. SUPPRESSION CHAMBER I
TE 7,
VENT EL. 56B'-6' Y#
LINE s
h' Mt /
iif
-~(
SUPPRESSION E
k/8.9w 5LT557'-O" NORMAL CHAMBER
=
EL. 556'-I-gER EL. 556'-l" EL TE EL. 55I'-4*
TE I,,
Q%,_548'-6 8 iQUENCHER
'DISHARGE DEVICE
,X VERTICAL QUENCHER SUPPORT BEAM hDUAL ELEMENT THERMOCOUPLES. IN THE WATER. SPACE AT.
hDUAL ELEMENT THERM,0 COUPLES IN THE WATER SPACE hDUAL ELEMENT THERMOCOUPLES IN THE AIR SPACE FIGURE.#2 PARTIAL SUPPRESSION. CHAMBER. SECTION RELATIVE ELEVATION OF SUPPRESSION POOL TEMPERATURE SENSORS
l T.:.3 PAGE OPEN PENDUG RECElPT OF
.ha.4
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- iU
- 1Riu;Il0N FROM THE APPUCAST i
)
CONTAltfr'ENT SYSTDis 3/4.6.2 D* PRESSURIZATION SYSTEMS SUPPRESSION CHAM 3ERf UiWilIFR6II61 TION f OR OPiiRATRii~
M.2.1 The-tsehwrer-ehoN-ee--GPEftABt.C.;i =
g a.
Tha', pool water:
3 3
1.
Voluce between (87,600) ft and(89,600)ft, equi %1enttoa i
level between (22' 0") and (24'0"), and a d
Maximum overage tacperature of 95'F during OPERATIONAL CONDITION l
N 2.
1 or 2, except that the naxt::ua average temperature may be permitted to increase to:
a) 105'F during testing which adds heat to the suppression l
b) 110*F with THERMAL POWER less than or equal to 1% of RATED l
charber.
THERMAL POVER.
c) 120*F with the main steam line isolation valves closed l
folicwing a scram.
A total leakage between the suppression charber and drywell of less b.
than the equivalent leakage through a 1 inch diameter orifice at a differential pressure of 1 psig.
- APPLICABILITY: OPERATIOKAL CONDITIONS 1, 2 and 3.
gyyp.
With the suppression chamber water level outside the above limits, a.'
restore the water level to within the limits within 1 hour1.157407e-5 days <br />2.777778e-4 hours <br />1.653439e-6 weeks <br />3.805e-7 months <br /> or be in at least HOT SHOTDOWN within the next 12 hours1.388889e-4 days <br />0.00333 hours <br />1.984127e-5 weeks <br />4.566e-6 months <br /> and in COLD SHUTDOWN i
',, within the following 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br />.
.\\
.In OPERATIONAL CONDITION 1 or 2 with the suppression chamber average
< b."
water teoperature greater than 95'F, restore the average temperature to less than or equal to 95'F within 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> or be in at least HOT SHUTDOWN within the next 12 hours1.388889e-4 days <br />0.00333 hours <br />1.984127e-5 weeks <br />4.566e-6 months <br /> and in COLD SHUTDOW within the following 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br />, except, as permitted above:
1:
With the' suppression chamber average water temperature greater l
1.
than 105"F during testing which adds heat to the suppression charber, stop all testing which adds heat to the suppression chacber and restore the average ter.perature to less than 95*F l
within 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> or be in at least HOT SHUTDOW within the next 12 hours1.388889e-4 days <br />0.00333 hours <br />1.984127e-5 weeks <br />4.566e-6 months <br /> and in COLD SHUTDOW within the following 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br />.
With the suppression charber average water temperature greater 2.
than:
90*F for more than 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> and THERMAL POWER greater than a) 1% of RATED THERMAL FOWER, or J
b) 110'F, place the reactor mode switch in the Shutdown position and j
operate at least one residual heat removal loop in)'fe suppres-
- sion pool cooling mode.
r With the suppression chamber average water temperature greater l
3.'
than 120*F, depressurize the reactor pressure vessel to less than 200 psig within 12 hours1.388889e-4 days <br />0.00333 hours <br />1.984127e-5 weeks <br />4.566e-6 months <br />.
"See Specification 3.5.3 for ECCS requirements.
3/4 G-12 MAY 2 41982 FERMI - IJHIT 2
u CONTAINMENT SYSTEMS LIMITING CONDITION FOR OPERATION (Continued)
ACTION:
(Continued) 3.
With the suppression chamber average water temperature greater 4
jthan120*F,depressurizethereactorpressurevesseltoless2
'than 200 psig within 12 hours1.388889e-4 days <br />0.00333 hours <br />1.984127e-5 weeks <br />4.566e-6 months <br />.
p'* c.
With one suppression chamber water level instrumentation channel ti inoperable and/or with one suppression pool water temperature instrumentation channel inoperable, restore the inoperable chan-nel(s) to OPERABLE status within 7 days or verify suppression chamber water level and/or temperature to be within the limits at least once per 12 hours1.388889e-4 days <br />0.00333 hours <br />1.984127e-5 weeks <br />4.566e-6 months <br />.
d.
With both suppression chamber water level instrumentation channels inoperable and/or with more than one suppression p'ool water temperature instrumentation channel inoperable, restore at least one inoperable water icvel channel and seven temperature instrumentation channels to OPERABLE status within 8 hours9.259259e-5 days <br />0.00222 hours <br />1.322751e-5 weeks <br />3.044e-6 months <br /> or be in at least HOT SHUTDOWN within the next 12 hours1.388889e-4 days <br />0.00333 hours <br />1.984127e-5 weeks <br />4.566e-6 months <br /> and in COLD SHUTDOWN within the following 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br />.
With the drywell-to-suppression chamber bypass leakage in excess of e.
the limit, restore the bypass leakage to within the limit prior to increasing reactor coolant temperature above 200*F.
SURVEILLANCE REQUIREMENTS 4.6.2.1 The suppression chamber shall be demonstrated OPERABLE:
By verifying the suppression chamber water volume to be within the a.
limits at least once per 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br />.
b.
At least once per 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> in OPERATIONAL CONDITION 1 or 2 by verifying the suppression chamber average water temperature to be less than or equal to 95*F, except:
1.
At least once per 5 minutes during testing which adds heat to the suppression chamber, by verifying the suppression chamber average water temperature less than or equal to 105 F.
l 2.
At least once per hour when suppression chamber average cater temperature is greater than or equal to 95*F, by verifying:
a)
Suppression chamber average water temperature to be less than or equal to 110 F, and I
b)
THERMAL POWER to be less than or equal to 1% of RATED l
-d THERMAL POWER after suppression chamber average water 3
temperature has exceeded 95*F for more than 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br />.
3.
At least once per 30 minutes following a scram with suppression chamber average water temperature greater than or equal to 95*F, by verifying suppression chamber average water temperature less than or equal to 120*F.
WN 171982 FERMI - UNIT 2 3/4 6-13 a_
p-_
I UACE 3 PEN PEUiu Id2Pi[i hh. A -*,-
.iirc....l.TlGi:. ROM THE api'L:C h, I
)
CON"AIhMENT SYSTEMS SURVEILLANCE REQUIREMENTS (Continued) c.
By an external visual examination of the suppression chamber after l
safety / relief valve operation with the suppression chamber average water temperature greater than or equal to 160 F and reactor coolant system pressure greater than 200 psig.
d.
By verifying two suppression chamber water level instrumentation channels and eight suppression pool water temperature instrumentation channels OPERABLE by perfomance of.a:
1.
CHANNEL CliECK at 1 cast once per 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br />, 2.
CHANNEL FUNCTIONAL TEST at least once per 31 days, and 3.
CHANNEL CALIBRATION at least once per 18 months, with the water level and temperature alarm setpoint for:
1.
High water level 1 (
),
2.
Low water Icvel > (
), and 3.
High water temperature 1 (105)*F.
(
At least once per 18 months by conducting a drywell-to-suppression l
e.
chamber bypass leak test at an initial differential pressure of 1 psi and verifying that the differential pressure does not decrease by more than 0.25 inches of water per minute for a period of 10 minutes.
If any drywell-to-suppression chamber bypass Icak test fails to meet g.
the specified limit, the test schedule for subsequent tests shall be reviewed and approved by the Comission.
If two consecutive tests fail to meet the specified linit, a test shall be performed at least every 9 ronths until two consecutive tests cect the specified limit, at which time the 18 nonth test schedule may be resumed.
l
)
FERMI - UNIT 2 3/4 6-14 W 2 41982 l
. _ _ _,_., _ _. -- _ _,.,.. _