ML20082Q805

TMI-1 Core Thermal-Hydraulic Methodology Using VIPRE-01 Computer Code

ML20082Q805
Person / Time
Site:	Crane
Issue date:	03/10/1995
From:	Byoun T, Irani A, Luoma J GENERAL PUBLIC UTILITIES CORP.
To:
Shared Package
ML20082Q803	List: ML20082Q800 ML20082Q805
References
TR-087, TR-087-R00, TR-87, TR-87-R, NUDOCS 9505010097
Download: ML20082Q805 (80)

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TMi-1 CORE THERMAL-HYDRAUUC METHODOLOGY USING THE VIPRE-01 COMPUTER CODE j

Topical Report 047 (Rev. 0)

BA No.135425 l

AUTHORS:

(a Nn,n rd l

A. A. IRANI ENGINEER, SAFETY ANALYSIS AND PLANT CONTROL h r-f T. Y. BYdtlN V

]

ENGINEER, TMI FUEL PROJECTS j

DATE: March 10,1995 t./PROVALS:

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%] A h et MAMGER, TMl FUEL PROJECTS (J.D. LUOMA)

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S DIRECTOR, NUCLEAR Al'ALYSIS & FUEL (G.R. BOND) l GPU Nuclear One Upper Pond Road Persippany, New Jersey 07054 I

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TR 087 Rev. 0 i

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ABSTRACT ru

'Ihis report presents the methods for performing core thermal-hydraulic analysis of the TMI 1 Nuclear Power Station.

A description of the VIPRE-01 model and general code features are discussed. The adequacy of the model and the associated analysis methodology are demonstrated by comparison of representative analytical results to vendor calculations. The BWC critical heat flux (CHF) correlation is also qualified in the VIPRE-01 model based on the CHF experimental data. The overall good agreement in these comparisons demonstrates GPUN's ability to perform core thermal-hydraulic operational and licensing analysis of TMI 1 using VIPRE 01.

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TR 087 Rev.O Page 3 l

TABLE OF CONTENTS 7

1.0 INTRODUCTION

f 8

2.0 BRIEF DESCRIPTION OF TMI-1 CORE................................

l 10 3.0 BRIEF DESCRH'flON OF VIPRE.01....................................

l 11 t

4.0 TMI-1 VIPRE-01 CORE MODEL...

I 11 4.1 M ode l Layout................................................

12 4.2 Axia l N od in g................................................

12 43 Axial Power Distribution.......................................

12 I

4.4 Radial Power Distribution.....................................

13 1

4.5 Spacer Grid Form 14ss Coe!Ticients..............................

13 l

4.6 Inlet Flow Distribution......................................

13 4.7 Conducting Fuel Rods.....

14 4.8 Active Fuel length..................................

15 4.9 Hot Channel Factors......

15 4.9.1 Power Peaking Factor (Fo)..........................

15 4.9.2 Local Heat Flux Factor (Fg).........................

15 i

1 4.93 Flow Area Reduction Factor (F,)........................

24 5.0 M ODEL Q U ALIFICATION............................................

24 L

5.1 Qualification of VIPRE-01/BWC CHF Correlation...................

53.1 Brief Description of CHF Test Data and BWC Correlation.... 25 S.I.2 VIPRE-01/BWC Predictions Compared with Measured Data.. 25 I

5.13 Determination of Design DNBR Limit B~d ~ 95/95 26 Protection Criterion..................................

I 5.1.4 Design DNBR (DDNBR) Limit Based on VIPRE-01/BWC 27 l

Co mbin a tion........................................

28 5.2 Initial Con ditions............................................

29 5.2.1 Initial System Pressure................................

29 5.2.2 Initial Inlet Temperature..............................

l 29 5.23 Initial Core Flow....................................

I 30 5.2.4 Initial Core Power...................................

30

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53 Steady State Benchmarks..........................,............

30 5.4 TraAsient Benchmark........'..............

44 6.0 MODEL SENSITIVITY l

44 6.1 Model Nodalization Sensitivity......

45 6.2 Axial Noding Sensitivity........................................

45 63 VIPRE 01 Correlations Sensitivity.......

45 63.1 Friction Pressure Loss......

i 48 63.2 Turbulent Mixing....................................

49 633 Two-Phase Flow Correlations................

63.4 Heat Transfer Correlations............................. 50 51 6.4 Conduction Model Sensitivity...............

7.0 TMI-1 THERMAIAIYDRAULIC ANALYSES USING VIPRE-01............... 62 62 7.1

'Ihermal-Hydraulic Design Criterion.

l TR 087 Rev. 0 Page 4 63 7.2 Generic Maximum Allowable Peaking (MAP) Limit Curves 65 73 Reactor Protection System (RPS) Safety Limits 65 l

73.1 Core Pressure Temperature Envelope....................

73.2 Axial Power Imbalance Protective Limits.................. 66 5

67 733 Flux / Flow Limits....................................

68 7.4 Core Operating Limits.........................................

81 8.0 CO N CLU SI O N S....................................................

82 9.0 REFEREN CES.....................................................

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TR 087 Rev. 0 1

Page 5

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LIST OF TABLES Eagg Tahle No.

k Table 2.1 Three Mile Island Unit 1, Cycle 9 Fuel Assembly 9

Design Information...........................................

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16 Table 4.1 Axial Node Is.ngth in VIPRE-01 Model............................

f Reference Design Axial Power Shape for 1.65 Cosine with Tails......... 17 Table 4.2 Table 43 VIPRE 01 Reference Design Power Distribution and Rod Layout........ 19

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Table 5.1 Applicable Range of System Conditions for the f

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VIPRE-01/BWC Combination...................................

Table 5.2 Design DNBR Limits for Various Confidence Levels and f

Population Protection 33 Table 53 VIPRE.01 MDNBR Predictions Compared with Reference Results 34 (Steady State)...............................................

Table 5.4 VIPRE-01 MDNBR Predictions Compared with Reference Results for the 4.to.3 Pump Coastdown.................................. 35 Table 6.1 Operating Conditions for Sensitivity Studies........................ 52 Table 6.2 VIPRE-01 DNBR Results of Model Nodalization Senaitivity Study....... 53 Table 63 VIPRE-01 DNBR Results of the Axial Noding Sensitivity Study......... 54 Table 6.4 Turbulent Momentum Factor Sensitivity Study...................... 55 Table 6.5 Turbulent Mixing Coefficient Sensitivity Study.......... :...

56 Table 6.6 Flow Correlation and Two Phase Friction Multiplier 57 Sensitivity Study..............................................

Table 6.7 Nucleate Boiling Heat Transfer Correlation Sensitivity Study........... 58 Table 6.8 Sensitivity to Number of Conducting Rods.......................... 59 Table 7.1 Maximum Thermal-Hydraulic Design Conditions for TMI l Cycle 9...... 69 l

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E TR 087 Rev. O g

Page 6 3

I LIST OF FIGURES Ficure No.

Eagq Figure 4.1 VIPRE-01 13 Channel Model (Base Model)........................ 21 Figure 4.2 Reference Design Axial Power Profile (1.65 Cosine with Tails).......... 22 Figure 43 Spacer Grid Model in VIPRE-01................................. 23 Figure 5.1 Measured CHF vs. VIPRE-01/BWC Predicted CHF.................. 36 Figure 5.2 Histogram of Measured.to Predicted CHF Ratio Compared with Population Density............................................ 37 Figure 53 VIPRE-01/BWC Predicted CHF vs. Measured CHF as a Function of System Pressure.................................... 38 Figure 5.4 VIPRE-01/BWC Predicted CHF vs. Measured CHF as a Function of Inlet Enthalpy.....................................

39 Figure 5.5 VIPRE-01/BWC Predicted CHF vs. Measured CHF as a l

Function of Coolant Mass Flux.................................. 40 y

Figure 5.6 VIPRE-01/BWC Predicted CHF vs. Measured CHF as a Function of Coolant Local Quality.............................. 41 g

Figure 5.7 VIPRE-01/BWC Design Limit Minimum DNB Ratio as 3

Functions of Population Protection and Confidence Levels............. 42 Figure 5.8 Core Average Pressure Drop vs. Axial Position 43 Figure 6.1 VIPRE-0130 Channel Model (Detailed Model)..................... 60 Figure 6.2 VIPRE-01 12 Channel Model (Simplified Model).................... 61 Figure 7.1 Core Pressure-Temperature Envelope............................. 70 Figure 7.2a Typical Axial Power Imbalance Protective Limits................

71 Figure 7.2b Protection System Setpoints for Axial Power Imbalance 72 Figure 73 Typical Axial Power Imbalance Limits............................. 73 Figure 7.4 Typical Control Rod Insertion Limits.............................. 74 Figure 7.5 A Typical Set of MAP Limits.................................... 75 Figure 7.6a Typical Axial Power Shapes for VIPRE-01 MAP Limit Analyses (Fixed Peak Location (x/l=0.4))..................... 76 Figure 7.6b Typical Axial Power Shapes for VIPRE-01 MAP Lintit Analyses (Fixed Axial Peaking Factor of L5)...... :............ 77 Figure 7.7 Determination of Flux / Flow Ratio................................ 78 Figure 7.8 DNBR Results for the 4 to-3 Pump Coastdown with Flux / Flow Trip........................................... 79 Figure 7.9 DNBR Results for the 4-to-3 Pump Coastdown l

without Flux / Flow Trip........................................ 80 m

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t TR 087 I

Rev. O Page 7 i'

1.0 INTRODUCTION

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GPU Nuclear (GPUN) has developed the capability to perform core thermal hydraulic analysis of nree Mile Island Unit 1 (TMI 1) Nuclear Power Station, ne principal analysis

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tool is the computer mde, VIPRE 01, MOD-2 (VIPRE-01 from here on), which is a thermal hydraulic code for calculating departure from nucleate boiling ratios (Reference 1.1). He NRC has reviewed VIPRE-01 and issued a Safety Evaluation Report (SER) which

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allows the. code to be referenced in a licensing submittal (Reference 1.2).

L A " base" eighth core symmetry VIPRE-01 model of TMI 1 was developed for this purpose.

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Re geometric representation of the core is illustrated and di-M along with the models and empirical correlations used to determine friction pressure losses, coolant mixing and

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subcooled voids. Sensitivity studies were performed to demonstrate that the base model was conservatively developed and the model was also independently verified. The adequacy of

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the model and GPUN's ability to apply the VIPRE-01 code for performing licensing calculations was demonstrated by comparing model predictions with vendor results.

b nis report is organized in the following manner: Section 2 is a brief description of the TMI 1 Cycle 9 core and Section 3 is an overview of the VIPRE-01 computer code. Section 4 provides details of the TMI 1 VIPRE 01 model and Section 5 qualifies the VIPRE-01 model by benchmarking against the critical heat flux (CHF) test data and vendor predictions. Section 6 is a justification of the nodalization and correlations selected through sensitivity studies. He application of the VIPRE-01 code to the thermal-hydraulic design and setpoint detenninations is given in Section 7. He report conclusions and references are provided in Sections 8 and 9, respectively.

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E-TR 087 Rev. O Page 8 I

2.0 BRIEF DESCRIPTION OF TMI 1 CORE I

TMI 1 is a 2568 MWth pressurized water reactor manufactured by Babcock & Wilcox (B&W). The reactor core consists of 177 fuel assemblies each of which is a 15 x 15 array containing 208 fuel rods,16 control rod guide tubes and one incore instrument guide tube.

Eight non mixing vane spacer grids provide lateral stiffness and fuel rod positioning. Table 21 shows typical dimensions and characteristics of the Cycle 9 TMI 1 fuel assembly design.

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F TR 087 Rev. O PaSe9 L.

Table 2.1. 'Ihree Mlle Island Unit 1, Cycle 9 Fuel Assembly Design Information iL h

Fuel assembly design Mk B8 15 x 15 Fuel assembly design, lattice type i

208 Fuel rods per assembly Spacer grids per assembly 8 (6 per active fuellength)

Spacer grid material Inconel 718 & Zircaloy4

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Fuel assembly overall length, in.

165.6875 i

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Fuel assembly pitch, in.

8.587 Control rod guide tube OD, in.

0.530 Instrument tubes per assembly 1

Instrument tube OD, in.

0.554 j

i Fuel Ibs!

1 i

Fuel rod pitch, in.

0.568 Cladding material Zircaloy-4 l

Cladding OD, in.

0.430 Cladding thickness, in.

0.0265 Active fuel length, in.

141.80 1

1 Fuel Pellets Material UO, Nominal density, % TD 95 Pellet diameter, in.

0.3686 b

I; TR 087 g.

Rev. O gl Page 10 I

3.0 BRIEF DESCRIPTION OF VIPRE-01 VIPRE-01 (Reference 1.1) is an open channel, homogeneous equilibrium, thermal hydraulic code which features diversion crossflow and turbulent mixing to calculate the departure from mmleate be %g ratios (DNBRs). The code accepts input data which defines the geometric, hydraulic and thermal characteristics of the core, and permits the user to select correlations E5 and solution methodologies.

Generally, core representation is made by inputting parameters defining and describing the number of channels within the model and their individual channel characteristics, such as flow area, wetted and heated perimeters, adjacent channel data, and centroidal distances between adjacent channels. Hydraulics of the code are defined by crossflow resistances determined from gap dimensions through which the channels communicate, spacer grid locations and form loss coefficients, mixing coefficients, two-phase flow correlations, friction pressure losses, and inlet flow distributions. Thermal modeling of the reactor core is a function of the core radial and axial power distribution, core power, operating conditions, hot channel factors, heat transfer correlations and correlation limits. VIPRE-01 was designed to perform steady-state and transient thermal hydraulic analyses of nuclear reactor cores for normal operating conditions and several accident conditions. 'Ihe VIPRE-01 code has been reviewed by the NRC and was found to be acceptable for referencing in licensing applications with the limitations addressed in Reference 1.2.

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l TR 087 Rev. 0 L

Page 11 FL 4.0 TMI 1 VIPRE-01 CORE MODEL F

L 4.1 Model layout f~u The VIPRE-01 model for the TMI 1 core consists of eighth-core symmetry as

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shown on Figure 4.1. De single pass model consists of a " hot" assembly modeled as the center assembly or channel and the balance of the eighth-core modeled as P

a lumped channel. His is conservative in that it minimizes interchange by the hot L

channel with the adjacent channels. He hot assembly is the assembly in which the minimum DNBR (MDNBR) can be expected to occur. The hot assembly is r

L divided into subchannels with boundaries formed by fuel rods and guide tubes within the assembly. De TMI 1 VIPRE-01 model consists of 12 subchannels in the hot assembly and lumping the remaining assemblies into one large channel, channel 13, as shown on Figure 4.1.

The location of each channel is defined by numbering all the channels, inputting r

connecting channel numbers, and defining the distance between centroids of adjacent channels. De centroidal distance in a normal square array, is the c' annel a

pitch. The centroidal distance determines the length over which the crossflow exists and defines the lateral pressure gradient in the crossflow momentum equation. He centroidal distance for a channel cut by a line of symmetry is the same as the centroidal distance for the complete channel. For the lumped channels, the centroidal distance is increased from its individual channel value in proportion to the number of rod rows between channel centroids. Likewise the centroidal distances between lumped assemblies is increased in proportion to the rows of assemblies between the lumped channel centroids.

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E TR 087 Rev. O Page 12 I

Crossflow resistances are calculated by nputting connecting channel information i

and crossflow gap widths. The product of the gap width and the axial node length defines the lateral flow area between channels. The gap widths are easily calculated given the rod pitches and diameters, ne gap width fuc a fuel assembly or any lumped channel is the sum of the channel gaps through which the two assemblies communicate.

4.2 Axial Noding Given the axial power shape and specified heated rod length, VIPRE 01 determines the axial power factor for each axial node. The node length determines how well the code approximates the axial power shape, the shorter the node length, the better the approximation of the curve.

The TMI-1 VIPRE 01 model uses a detailed varying axial node length as shown in Table 41 with one inch node length applied to the rod at elevations where the MDNBR is expected to occur.

43 Axial Power Distribution Predicted and actual axial power shapes vary for cycle specific reloads and transients since they are functions of control rod positions, xenon transients, etc.

He reference design axial flux shape is a 1.65 cosine with tails given in Figure 4.2 and. Table 4.2.

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I 4.4 Radial Power Distribution ne power distribution within the hot assembly is referred to as the local peaking distribution where each fuel rod peaking factor is equivalent to the rod absolute l

power divided by the hot assembly average power. The hot fuel rod exhibits the maximum local peak within the hot assembly with a value of 1.0615 (Table 43).

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TR 087 Rev. O Page 13 1-I The reference design power distribution in the hot channel, as shown in Table 43, was modeled into VIPRE-01 code using a reference ' design pin power peak,

- F[y of 1.714 and an assembly power peakmg factor of 1.6147. He value of F[g = 1.714 is the same reference design pin peak used in the Cycle 9 Reload Report (Reference 4.1).

Table 43 also shows the rod to-channel connection input or rod layout, identifying the channels with which a rod can exchange heat, and the fraction of the rod that faces the channel.

4J5 Spacer Grid Fons Imss Coemcients j

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Form loss coefficients are used to account for the unrecoverable pressure losses caused by the abrupt variation in flow area and turbulence at a spacer grid. He i

Mark B8 fuel assemblies have six intermediate zircaloy spacer grids and two inconel end grids. Spacer grid form loss coefficients are developed from full size l-fuel assembly flow tests performed by the vendor. He value of the grid form loss coefficients are given in Reference 4.2. He location of the lower / upper end j

4 fittings and spacer grids as input into VIPRE-01 is pictorially represented on Figure 43.

4.6 Inlet Flow Distribution VIPRE-01 allows the user to specify the core inlet flow maldistribution. He TMI-1 core thermal-hydraulic analyses' include a 5% reduction in inlet flow to the hot assembly to produce slightly conservative results compared with a uniform inlet flow distribution. His is consistent with the assumptions of the FSAR.

k 4.7 Conducting Fuel Rods ne TMI 1 model uses the VIPRE-01 conduction model for the four rods which comprise the hot channel. This accounts for the time delay of the thermal power reaching the coolant through conduction and convection after reactor trip. He

5, TR 087 Rev. O Page 14 I

rest of the fuel rods are modeled as " dummy" rods with the power applied directly to the coolant. He nuclear fuel rod geometry data is given in Table 2-1 and consists of fuel pellet diameter, rod outside diameter and clad thickness. The power profile in the pellet was modeled as uniform and a constant gap conductance of 800 BTU /hr ft' 'F was used which is consistent with the fuel vendor values used for BOC conditions in LYNXT (Reference 43).

i The heat generated in the fuel is 973 percent of the total nuclear heat. He j

remaining 2.7 percent is the gamma decay energy from fission products.

4.8 Active Fuel length I'

he active fuellength used is the undensified cold nominal fuel stack height. The 1

selection of this parameter was based on the physical behavior of the fuel pellet stack within the fuel rod. Irradiation effects comprise both densification and swelling phenomena. The densification effects are more predominant at low g

exposure levels, while the swelling effects are more predominant at higher exposure 5

levels. Fuel stack densification decreases the active fuel length and increases the surface heat flux. Fuel swelling, which occurs once the fuel pores are filled with fission / backfill gases, tends to increase the active fuel length. In addition to the irradiation effects, the active fuellength is affected by thermal expansion. For 95%

TD fuel with a typical densification characteristic, the thermal expansion effects are greater than the irradiation effects as shown below:

1 Cold nominal stack height 141.8 in.

Hot nominal stack height '

143.2 in.

Minimum hot densified stack height 142.2 in.

Herefore, the hot rod fuel stack, while being irradiated, will have a length greater than its cold nominal stack height. It is then conservative to consider the cold nominal stack height in DNBR calculations.

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3 TR 087 W

Rev. O Page 15 4.9 Hot Channel Factors ne following hot channel factors are applied to the hot channel in the VIPRE-01 I

modet 4.9.1 Power Peaking Factor (Fo)

He power peaking factor is equal to the maximum deviation expected in pin power resulting from manufacturing deviations. Rese variations have been obtained from the measured or specified tolerances and combined statistically to give a power factor on the hot rod. For 99 percent population protection with 99 percent confidence, this factor, Fo, is 1.011 (Reference 4.1).

I 4.9.2 Local Heat Flux Factor (Fo')

I ne local heat flux factor incorporates variations in pellet density, pellet cross-sectional area, weight per unit length, local enrichment and local outer clad diameter. It is only used in the computation of the surface heat flux of the hot pin when calculating the DNBR for the hot subchannel. For similar conditions as described above i.e.,99/99, Fo*

is 1.014 (Reference 4.1). This factor is applied directly to the DNBR l

calculated by VIPRE 01 as follows:

DNBR = DNBRv,

/Fo" l

4.9.3'.

Flow Area Reduction Factor (F,)

A flow area reduction factor is determined for the as-built fuel assembly by taking channel flow area measurements and statistically determining an equivalent hot channel flow area reduction factor. For i

99 percent population protection with 99 percent confidence, the F, factor is 0.97 (Reference 4.4).

E se TR 087 g

Rev. 0 E

Page 16 ll I,

Table 4.1 Axial Node length in VIPRE 01 Model I)

Elevation Node Size 0 - 6 in 3 in 6 - 60 in 10 in 60 - 78 in 3in 78 - 86 in 2in 86 - 96 in 1 in 96 - 104 in 2in 104 - 165.625 in 6.1625 in I

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(l TR 087 Rev. O Page 17 Table 4.2 Reference Design Axial Power Shape for 1.65 Cosine with Tails X(inch)

Shape 0.0 38286 2.836 34606 5.672 33464 8.508 34533 11344 3 7504 14.18

.42083 17.016

.47995 19.852

.54978 22.688

.62789 25.524

.712 2836

.8 31.1 %

.88994 34.032

.98003 36.868 1.0686 39.704 1.1543 42.54 1.2358 45376 13119 48.212 1.3817 1.4443

., 51.048 53.884 1.4992 56.72 1.5459 59.556 1.5839 62392 1.6133 l

65.228 1.6339 68.064 1.6461 70.9 1.65 73.736 1.6461

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TR 087 3

Rev. O g

Page 18 Table 4.2 (Cont.)

Reference Design Axial Power Shape for 1.65 Cosine with Tails j

X (lach)

SHAPE 76.572 1.6339 79.408 1.6133 g

82.244 1.5839 5

85.08 1.5459 87.916 1.4992 90.752 1.4443 93.588 13817

%.424 13119 99.26 1.2358 102.1 1.1543 104.93 1.0686 107.77

.98003 110.6

.88994 113.44

.8 116.28

.712 119.11

.62789 121.95

.54978 124.78

.47995 127.62

.42083 130.46 37504 133.29 34533 136.13 33464 138.%

34606 141.8 38286 i

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E TR 087 g

Rev, 0 g

Page 20 Table 4.3 (Continued)

Note 1:

Rod #1 combines 2 rods having peaking of 1.02 and 1.0166 to give a local peaking of 0.5 (1.02

+ 1.0166) = 1.0183.

Note 2 Rod #7 combines 2 rods having peaking of 0.9950 and 0.9884 to give a local peaking of 0.5 (0.995 + 0.9884) = 0.9917 Note 3:

Rod #16 combines 7 rods having peakings 0.9717 + 0.9659 + 0.9642 + 1.0083 + 1.02 + 0.9975 + 0.9776 = 6.9251 Average = 6.9251/7 = 0.9893 Note 4:

I Rod #17 combines 8 rods having peakings 0.9762 + 0.9634 + 0.9618 + 0.9684 + 0.9776 + 0.9809 + 0.9726 + 0.9667

= 7.768 Average = 7.768/8 = 0.971 l

Note 5-Rod # 18 combines 22 equivalent assemblies'= 22 x 208 = 4576 Rods I

Note 6 A power peaking factor, Fo = 1.011 is applied to the four rods comprising the hot channel.

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FIGURE 4.1 VIPRE-0113 CHANNEL MODEL (BASE MODEL)

R 0

D = 0.564 Page 21 GAP = 0.076" '

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W l4 ROD PITCH = 0.566*

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= ROD 1.D.

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J e HOT ASSEM8LY:

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b (CHANNELS 1 TO 12 A80VE)

FUEL ASSEM8LY

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l 13 l

-g-ASSEMBLY PITCH = 6.567" 7'Z -%

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I Figure 4.2 Reference Design Axial Power Profile (1.65 Cosine with Tails) l 2

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Distance Along Heated Length (X/L) l I

TR 087 Rev.O Page 23 I

I FIGURE 4.3 SPACER GRID MODEL IN VIPRE-01

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- UPPER END FITTING--->

165.6875" 3

- --UPPER END GRID

> 156.849"

}

> 135.1563" 16$.6875" INTERMEDIATE 114.0625" SPACER GRID (6)

I 92.9688" J

\\

> 71.875" i

i f

> 50.7813" i

29.6875" D

- -LOWER END GRID 5.85"

- -LOWER END FITTINGM 2.0" Y

0.0" b

1

I_

TR 087 g

Rev. O g

Page 24 I

5.0 MODEL QUALIFICATION I

ne adequacy of the TMI 1 VIPRE-01 model and GPUN's ability to apply the VIPRE-01 code for performing licensing calculations can be demonstrated by comparing model predictions with measurements. This section justifies the use of the current design DNBR limit of 1.18 using the BWC Critical Heat Flux (CHF) correlation (Reference 5.1) on the VIPRE-01 modet his qualification of the VIPRE-01/BWC was performed against CHF test data (Reference 5.1). The other DNBR results available for comparison were mainly steady state MDNBR values at different power levels obtained from Cycle 8 (Reference 4.2) and Cycle 9 (Reference 4.1) reload reports. Details of the calculations and assumptions, other than MDNBR values are not available. Unfortunately, the vendor predictions in the i

FSAR were performed for the initial core many years ago with a different CHF correlation, and a comparison to those results would not be meaningful due to the different methods and critical heat flux correlation used at that time.

I 5.1 Qualification of VIPRE-01/BWC CHF Cornlation l

I i

ne BWC CHF correlation was originally developed for 17x17 Mark C fuel and later justified for 15x15 Zircaloy spacer grid Mark-BZ fuel by using the LYNX 2 computer code (Reference 5.2). He crossflow computer code LYNXT was developed with the BWC correlation application to the licensing analyses (Reference 43). Duke Power Company (DPC) demonstrated the use of the BWC correlation on the VIPRE-01 program which was approved by NRC (References 53 and 5.4).

l I

ne BWC correlation with VIPRE-01 will be used for TMI 1 thermal hydraulic l

analyses including all the DNB analyses. The design DNBR limit will be 1.18, the i

same value as used by the fuel vendor and DPC.

I I

I

TR 087 Rev. 0 Page 25 Since the BWC correlation is to be used with VIPRE-01, it is necessary to demonstrate that the design DNBR limit of 1.18 used. in the VIPRE-01/BWC combination can predict its data base of DNB occurrence with at least 95% of the population protected with a 95% mand-ace levet ne following subsections provide the justification for the use of the BWC correlation on the VIPRE-01 code by analyzing the Zircaloy grid CHF test data given in Reference 5.1:

5.1.1 Brief Description of CHF Test Data and BWC Correlation The BWC CHF tests utilized bundles with a 5x5 rod array,12 feet long heated section with non-uniform axial flux shapes (Reference 5.5).

hree kinds of test geometries were used- (1) fuel assembly geometry near a guide tube thimble, (2) normal matrix geometry, and (3) geometry at the intersection of four assemblies. He total number of data points is 211. He ranges of test system conditions such as pressure, mass velocity, and quality are given in Table 5.1.

Equations for the BWC CHF correlation based on above test conditions are given in Reference 5.1.

5.1.2 VIPRE 01/BWC Predictions Compared with Measured Data The VIPRE-01/BWC predictions (Reference 5.6) are compared to the test data in Figures 5.1 to 5.6. Figure 5.1 shows, the measured CHF i

versus the VIPRE 01 predicted CHF for all 211 data points demonstrating that the overall prediction of the VIPRE-01/BWC combination is correct. In Figure 5.2, the histograms of measured-to-predicted CHF ratios (M/P) are compared with the population density L

based on normal distribution. He histograms demonstrate that the data distribution is near normal He ratio of measured-to-predicted CHF is plotted as functions of pressure (Figure 5.3), inlet enthalpy r-

E TR 087 g

Rev.0 3

Page 26 (Figure 5.4), coolant mass flux (Figure 5.5), and local quality at the l

CHF location (Figure 5.6). nese figures demonstrate that the CHF dependence on each operating parameter is properly modeled. These figures show that there is no significant bias in the VIPRE-01/BWC predictions with the test system conditions over the ranges given in Table 5.1.

5.13 Determination of Design DNBR Limit Based on 95/95 Protection Criterion ne design DNBR limit is the lowest DNBR that can be calculated on the limiting fuel pins in the reactor while maintaining a 95% confidence that 95% of the limiting pins are not in film boiling.

Based on one-sided tolerance theory from Owen (Reference 5.7), a E

lower tolerance value of predicted CHF can be defined for a given 3

corlidence and population protection:

I qEr = q;(M/P Kg,,,

• a).

Eq.5.1 Lower tolerance limit of calculated CHF qEr

=

I calculated CHF from the correlation q:

=

mean va'lue of measured to-predicted ratios M/P

=

I one sided tolerance factor based on N degrees of Kg,,,

=

freedom, y confidence level, and portion of population l

1 protected (P).

standard deviation of M/P a

=

I l

Il

[~

TR 087 Rev. O Page 27 Now equating the maximum allowable design heat flux (qb) to the

{

lower limit CHF (q"r), the design DNBR limit can be determined:

e ir - edo - e; G/r - r,.,,,..>.

Eq. 5.2 f

Defining the Design DNBR (DDNBR) as q'/qh

" (#/P - K,.,,,= o)

Eq. 53 De confidence factor, K,.,,r can be obtained from tabulations of many text books on statistics.

5.1.4 Design DNBR (DDNBR) Limit Based on VIPRE-01/BWC Combination he Design DNBR (DDNBR) limits using VIPRE-01/BWC combination (Reference 5.6) are given in Table 5.2 and Figure 5.7 as functions of both population protection and confidence levels. As can be seen in Table 5.2, the DDNBR derived from the VIPRE-01/BWC combination is 1.1705 based on the 95/95 protection criterion.

he mean value of the measured-to-predicted (M/P) is 0.98206 with -

standard deviation, a, of 0.069696. He 95/95 confidence factor Ka ii,,,,

based on 211 data points is 1.8327 (Table 5.2) and the corresponding Design DNBR (DDNBR) limit is (from Eq. 53):

E, TR 087 Rev.O Page 28 1'O DDNBR =

(#/P - K,, y,,

• c )

Il1 1

= (0.98206 - 1.8327

• 0.069696)

= 1.1705 Il Table 5.2 shows that the DDNBR of the 95% population protection with 99% confidence is 1.1787. This indicates that the current design value of 1.18 in Technical Specifications is equivalent to the 95/99 protection value (see Table 5.2 and Figure 5.7). This means that the VIPRE 01 code enhances the confidence level from 95% to 99% with design value of 1.18.

i The applicable ranges of variables for the BWC correlation are given in Table 5.1.

5.2 Initial Conditions VIPRE-01 requires initial conditions input for pressure, temperature, flow and power. For accident conditions, the initial conditions are obtained by adding or subtracting. as appropriate, maximum steady-state errors to or from rated values.

'Ihe. errors are chosen in the direction which minimizes core thermal margin as disc 6ssed below:

I I;

I I

h TR 087 l

Rev.0 l

I Page 29

,u 5.2.1 Initial System Pressure De normal operating system pressure is 2200 psia with a measurement

{

uncertainty of 65 psi (Reference 4.1). De VIPRE-01 input for pressure which will result in the lowest DNBR is 2200-65 = 2135 psia.

p L-5.2.2 InitialInlet Temperature ry ne nominal inlet temperature is 555.7"F with a measurement uncertainty of 22*F (Reference 4.1).

He VIPRE-01 input for temperature which will result in the lowest DNBR is 555.7 +

2 = 557.7'F.

f 5.23 Initial Core Flow he Dow is input into VIPRE-01 as an average inlet mass flow. Core flow is equal to the total reactor coolant system Dow less the bypass flow (the Sow which does not contact the effective heat transfer surface area). De bypass Sow paths are the (1) core shroud, (2) core barrel

{

annulus, (3) control rod guide tubes and instrument tubes, and (4) all interfaces separating the inlet and outlet regions of the reactor vessel.

{

ne actual core bypass Dow is 7.75% (Reference 4.1), however, the VIPRE 01 model uses a conservative value of 8.8% for Cycle 9.

k In addition, a total reactor vessel inlet Dow rate of 139.7 Mlbm/hr (Reference 4.2) is used for analysis, which is 3% less than the measured Gow of 144 Mlbm/hr. Considering the effective km brr,fer Gow area is 49.65 ft', the VIPRE 01 input mass flux in ivifom/hr-id [s l

calculated below:

1oosriow M ,*y,***)

- 2.sss x1hathr-re s

i 5l TR 087 g ;i Rev. O Page 30 g

Il 5.2.4 Initial Core Power j

ne power is input in KW/ft per rod (including gamma heat) which is calculated as:

gogg g,, 2568 x 10 Av x 12 in/fe 3

5, gggffe 208 x 177 x 141.8 in I

where 141.8 in is the fuel heated length,208 is the number of rods per assembly,177 if the number of assemblies in the core and 2568 is the power in MW..

I 53 Steady State Benchmarks I

The reference predictions of steady state DNBR's for various power levels are provided in References 4.1 and 4.2. De comparisons with VIPRE-01 predictions are shown on Tab'e 53. He Case l inlet temperature was calculated as shown in Section 5.2.2 and a 5% reduction in inlet flow to the hot assembly was applied.

The results show close comparisons with VIPRE-01 predictions being 0.56%,1.9%,

2.4% and 43% higher than the reference results for Cases 1, 2, 3 and 4 g

respectively.

Figure 5.8 shows comparisons between VIPRE 01 and the. reference results for core average pressure drop versus axial positions for 100% power and 100% flow.

The agreement between the two results is good.

I, i

5.4 Transient Benchmark i

He limiting loss-of flow transient is a one-pump coastdown from four pump operation. He flow decrease results in the reactor being tripped at 53 seconds from a flux / flow trip signal.

I l

TR 087 Rev. O i

Page 31 ne RCS flow fraction, trip delay time and fraction of power after trip are shown in Table 5.4. Since the reactor is tripped by the flux / flow trip setpoint of 1.08, the initial power input to VIPRE-01 is 108% full pcwer and held constant until reactor trip. As can be seen from Table 5.4, the minimum DNBR obtained from VIPRE-01 is 1.637 which is 1.7% higher than the referena prediction of 1.61 (Reference 5.8).

i i

\\

(

R.

TR 087 Rev. O Page 32 I

Table 5.1. Applicable Range of System Conditions for the VIPRD01/BWC Combination I

Operational Applicable Range of Parameters Parameters l

Pressure (psia) 1600 to 2600 Mass Velocity 0.43 to 3.8 2

(Mlbm/hr-ft )

Quality

-0.20 to +0.26 I

I I

I I

I I

I I

I' l

(.:

TR 087 Rev. O L

Page 33 L

Table 5.2. Design DNBR Ilmits For Various Confidence Imels

[

and Population Protection Population Confidence Protection Level Confidence DDNBRM l

Level %

Factor (BWC) 90 90 1.4079 1.1313 l

90 95 1.4454 1.1347 90 99 1.5187 1.1413 95 90 1.7895 1.1664

(

95 95 1.8327 1.1705

(

95 99 1.9174 1.1787 99 90 2.5094 1.2389 99 95 2.5643 1.2448

{

99 99 2.6726 1.2566 f

M DDNBR = Design DNBR limit based on different population protection and confidence levels l

i l

i i

E TR 087 Rev. 0 Page 34 I

Table 53: VIPRE 01 MDNBR Predictions Compared with Reference Results (Steady State)

I Case Power Pressure Temperature Mass Flux VIPRE Reference R

(osla)

(*F)

(Mlbm/hr-ft )

Results Results 2

1 112 2135 557.7 2.566 1.78 1.77(84 (100%)

(0.56%)m 2

102 2135 557.7 2.566 2.05 2.01m (100%)

(1.9%)

I 3

100 2135 557.7 2.566 2.11 2.06m (100%)

(2.4%)

4 91 2135 552.7 1.9168 1.975 1.89m (74.7%)

(43%)

)

NOTE:

(1) From Reference 4.2 (2) From Reference 4.1 (3) 0.56% = (1.78 - 1.77)/1.77*100 I

I I

I I

I I

p TR 087 Rev. O Page.'5 L.

I L

Table 5.4: VIPRE41 MDNBR Pmdictions Compared with Reference Results for 4-to 3 Pump Coa 6tdown IL Time Flow Power MDNBR

[.

faggl

(% Initial)

(% FP) 0.0 100 108 1.886 7

1.0 97.5 108 1.846

{

i 2.0 94 3 108 1.801 e

3.0 91.2 108 1.758 4.0 89.4 108 1.711 5.0 88.0 108 1.677 53 87.5 108 1.647 5.4 87.4 108 1.637(*)

5.5 87.2 107.5 1.639 b.

5.6 87.1 105.8 1.640 5.7 87.0 103.1 1.650

(

5.8 86.8 98.8 1.660 6.0 86.6 84.2 1.730

[

(*) Reference Result = 1.61 (From Reference 5.8)

{

[

l c

)

[

[

.A

I TR 087 g

Rev. O Page 36 m

FIGURE 5.1 MEASURED CHF VS VIPRE-01/BWC PREDICTED CHF 1.2 I

1.0

[x I

e0.8 x"

g x

[x "xx E'

Z x

5<

s 5yx Rx*

x x

XW x

x g 0.e spf x

i l

b 0.4 G*

=

xy g

x xk D.2

~f g'

x i

Il O.0 0

0.2 0.4 0.6 0.8 1

l PREDICTED CHF IN MBTUIHR.FT2 I

(-

l rn on Rev.0 we l

Figure 5.2 r

L-Histogram of Measured-to-Predicted CHF Ratio Compared with Population Density l

r t

80

(

~

i 70 -

7 L

ee

('

m -

~

Normal

/ oieritxxion

{

E 50

/

'5 CL 5

\\

{

5 0 40

• o

~

41 36 i

E

(

i Q 30

\\

20 10 11

~

7\\v a

0.6 0.7 0.8 0.9 1

1.1 1.2 1.3 1.4 Ratio of Measured-to-Predicted CHF

E TR 087 Rev. O Page 38

=

I I

FIGURE 5.3 VIPRE-01/BWC PREDICTED CHF VS. MEASURED CHF AS A FUNCTION OF SYSTEM PRESSURE 2.0 I

1.5 g

E I

s m

n x

11 L,

e 6

I o 1.0 j

x 5m O

O E

0.5 I

0.0 g

1,000 1,500 2,000 2,500 3,000 m

PRESSURE IN PSIA I

I I

L TR 087 I

R2v. O P g3 39 fa

?

L r

L FIGURE 5.4 VIPRE-01/BWC PREDICTED CHF VS MEASURED CHF AS A FUNCTION OF INLET ENTHALPY 2.0

,u F

L e

I o 1.5 5i

[

R u.

j l

N kN b

X >:

x "E

y W"

~ " 3x

[

l"

=y x

[

s lE O

O 0.5

{

s 0.0 200

• 300 400 500 600 700 l

f lNLET ENTHALPY IN BTU /LBM

[

l

[i

[

p

I TR 087 g

Rev. O Page 40 m

I FIGURE 5.5 VIPRE-01/BWC PREDICTED CHF VS. MEASURED CHF AS A FUNCTION OF COOLANT MASS FLUX 2.0 I

l 1.5 8

I w

n.

I O

i a

x w

. k o 1.0 v

m.

1 x

lE O

o P

g 0.5 l

I 0.0 O.0 1.0 2.0 3.0 4.0 MASS FLUX - MLB/HR.FT2 I

I P

-e

TR 087 Rev. 0 Page 41 FIGURE 5.6 VIPRE 01/BWC PREDICTED CHF VS MEASURED CHF AS A FUNCTION OF COOLANT LOCAL QUALITY 2.0 D

1. 1.5 O

O u

N 4 %

• + i i t +.:.

• t+

+

+

++

1.0

+p.

g + t++ ++ +

3

+

+ +

+

+

e

+

+

+-

5m b

Ob I

.5 0

i 0.0

-0.20

-0.10 0.00 0.10 020 0.30 QUALITY AT CHF LOCATION r

E1 TR 067 Rev.0 Figure 5.7 VIPRE-01/BWC Design Limit Minimum DNB Ratio as Functions of Population Protection and Confidence Levels l,

g) 99 -

i El

.~

l Eg 98 -

i VIPRE-01/BWC f,

3 g7 Predicted if 0)

Design DNBR

.t o

( = 1.1705) f' wL l 1 U

~

./

CO

/

f 3

3 Q.

95

/ '

O n.

O

/

't l

$M l

5 l

m.,

g

/

! ucensed o

/

Value

$ 93

! ( = 1.18) 90% Confidence D.

l l

i' 95% Confidence 92 t

/

i i

99% Confidence B

91

/

i i

I I

90 1.1 1.15 1.2 1.25 1.3 95/95 Design DNBR g

TR 067 Rev. 0 PeGe 43 FIGURE 5.8 i

CORE AVERAGE PRESSURE DROP VS. AXIAL POSITION 20 4

4 0

15 l

i

[

l VIPRE PREDICTION 3

a0 10 E

a a

E D

,o'W f

i.mecP-c. i Os 0

A'D '

~

o

/

i 00 0

30 t,0 90 120 150 180 AXIAL POSITION (FUEL ASSEMBLY)IN INCHES

5l TR 087 g

Rev. 0 g

Page 44 6.0 MODEL SENSITIVITY I

ne TMI 1 VIPRE-01 model described in Section 4.0 was developed using conservative assumptions for axial power distribution, radial power distribution, and inlet flow distribution. Additional hot channel factors for enthalpy rise and flow area reduction were applied. His section addresses the choice of VIPRE-01 correlations selected, and justifies the nodalization by performing sensitivity studies. He studies were conducted at two different conditions as shown in Table 6.1 to cover the range of anticipated model applications for licensing calculations. Case 1 corresponds to a low flow operating condition such as when only three pumps are available, while Case 2 corresponds to a high power condition such as occurs for N.I. calibration error transients. As described in Section 5.2, measurement uncertainties on pressure ( 65 psi) and temperature (+2'F) were also applied to the normal operating conditions to yield the most conservilive DNBR results.

6.1 Model Nodalization Sensitivity The nodalization chosen for the model as described in Section 4.1, was actually determined by performing a series of sensitivity stodies, starting with a very detailed model as shown in Figure 6.1. This detailed model consists ofindividually modeling each of the subchannels in the hot assembly, and lumping the rest of the 1/8 core into two channels. ': bis detailed model was progressively reduced, maintaining normal channels for the hot subchannel and its neighboring channels, but combining the remaining subchannels gradually. This graduallumping resulted in a'rriving at the base model configuration, which yielded negligible differences in MDNBR from the detailed model. A further reduction in the model to the configuration shown in Figure 6.2 resulted in a 0.5% difference in DNBR in the nonconservative direction as shown on Table 6.2 for the two operating conditions i

discussed above.

Thus the " base" model was established, and contains sufficient detail without being overly complex and without loss of accuracy.

I

TR 087 Rev. O Page 45 i

{

6.2 Axial Noding Sensitivity Volume 4 of the VIPRE 01 manual (Reference 1.1) states as a general rule that nodes on the order of 2 or 3 inches long are recommended in the region where MDNBR is likely to occur. Calculations involving node sizes smaller than 2 to 3 inches require more computer processing time without gaining significant increase

(

in the accuracy of results. 'Ihe base model uses a node length size of 12 inches at elevations where the MDNBR is expected to occur; i.e., from 78 to 104 inches of the fuel assembly. A sensitivity study was performed using a 3 inch node size in this region (from 78 to 104 inches) and resulted in a 0.1% difference in MDNBR as shown in Tabie 6.3. Since the effect on DNBR is small, but using a j

small axial node length would provide better accuracy in detailed analyses for j

I relative power and pressure, the VIPRE-01 base deck will maintain the detailed noding scheme described in Section 4.2.

63 VIPRE 01 Correlattaan Sensitivity Empirical correlations are used in the VIPRE-01 code to model turbulent mixing and the effects of two-phase flow on friction pressure losses, non equilibrium-J subcooled boiling, and the relationship between the quality and void fraction. The

{

correlations which have been selected for use in the TMI 1 thermal hydraulic analyses are dLc==d in the subsections which follow.

6.3.1 Friction Pressure Loss l

l Pressure losses due to frictional drag are calculated for flow in both the I

axial and lateral directions. In the axial direction the friction pressure loss is calculated by I

I E

L 1

.___i

5 TR 087 g

Rev. O gi Page 46

$? = f G* v dZ 2ga Da I

where E

f

= friction factor determined from an empirical correlation defined by user input G

= Mass flux, Ibm /sec-ft' 8

v

= specific volume for momentum, ft /lbm g,

= force-to-mass units conversion factor,32.2 lbm ft/lbf sec' D,

= hydraulic diameter based on wetted perimeter, ft.

Based on the recommendation in Reference 1.1, Vol. 4 of the VIPRE-01 manual, the default Blasius smooth tube friction factor expression f = 032 RE" + 0.0 will be used to calculate the friction pressure loss for turbulent flow.

Based on sensitivity' study results (discussed in Section 633), the friction pressure loss for two-phase Dow will be calculated using the EPRI two-phase friction multiplier, which gives slightly conservative results.

In the lateral direction the pressure loss is treated as a form drag loss that is calculated by I

TV. 087 Rev. 0 Page 47 L

=

g, IWIW V r

ap 2 Sage where f.

L

( = loss coefficient in the pp between adjacent channels j

r

= crossflow through a pp, Ibm /sec-ft w

= specific volume for momentum, it'/lbm y

l S

= pp width, ft g,

= force-to-mass units conversion factor, 2

U 32.2 lbf/sec*

i When rod arrays are modeled as lump channels the effective crossflow f

resistance is the sum of the resistance of the rod rows between the lumped channel centroids. The lateral loss coefficient becomes

%=N%

where N is the number of rod rows between lumped channels and %

is the nominal drag coefficient for a single pp. Crossflow resistance coefficients are not precisely known, but sensitivity study results dhamd in Volume 4 of Reference 1.1 show that for applications where the axial flow is predominant relative to' crossflow, crossflow resistance has an insignificant effect on mass flux and DNBR. A

_____-_______.___._._m_--

.E_

TR 087 Rev.O g

Page 48 N.

subchannel drag coefficient, Ko, of 0.5 will be used with the coefficient for lumped channels calculated internally by the code based on the input centroid distances between lumped channels and the standard subchannel fuel rod pitch.

63.2 Turbulent Mixing The VIPRE-01 transverse momentum equation includes terms to calculate the exchange of momentum between adjacent channels due to turbulent mixing.

Two parameters must be input to include turbulent mixing: a factor for turbulent momentum (FTM) and a turbulent mixing coefficient (p).

The FTM defines how efficiently the turbulent crossflow mixes momentum. FTM can be input on a scale from 0.0 to 1.0, where 0.0 indicates that the crossflow mixes enthalpy only, and 1.0 indicates that it mixes enthalpy and momentum with the same strength. In actuality, some proportion of enthalpy and momentum mixing does take place; therefore, turbulent momentum factors of 0.8 and 1.0 are probably more representative of actual crossflow effects. Sensitivity studies discussed in Volume 4 of Reference 1.1 show that changes in the fraction of momentum mixing have negligible impact on the flow field; l

therefore, FTM = 0.8 is recommended.

Sensitivity studies using the " base" model were pezformed for the Case i

1 and 2 operating conditions given in Table 6.1. The runs were made l

using FTM = 0.0, 0.8 and 1.0.

The results of the analyses are presented in Table 6.4. Since the results show that MDNBRs for an E

FTM = 0.8 is only 0.1% higher than for FTM = 1.0, and since FTM =

5 O.8 more realistically assumes some momentum mixing, an FTM = 0.8 will be used in the TMI 1 model.

I

.w---,--.----,.---_____..___

TR 087 Rev. O Page 49 Turbulent crossflow between adjacent channels is calculated by 50 l

where w' is the turbulent flow per axial length, p is the turbulent -

crossflow mixing coefficient, S is the gap width, and G is the average mass flux of the adjacent channels. Results of a sensitivity study on the effects of the p mixing coefficient are documented in Table 6.5. As is

]

to be expected a value of 0.0, signifying no mixing gives the most 1

conservative results. Volume 5 of Reference 1.1, states that a value of 0.01 to 0.02 gives good comparisons to experiments. The TMI 1 FSAR (Reference 4.4) states a mixing coefficient of 0.02 is sufficiently conservative for design evaluation.

E 633 Two Phase Flow Correlations Two correlations are used in VIPRE 01 to make two phase flow predictions. 'Ihe first correlation is referred to as the subcooled void correlation. It uses a quality model to calculate the flowing vapor mass fraction including the effects of subcooled boiling. Once the flowing

{

vapor mass fraction is calculated, the bulk void correlation is applied to calculate the void fraction including any effects due to slip

[

(Reference 1.1, Volume 1).

i Sensitivity studies were performed using two diff'erent combinations of subcooled void and bulk void correlations to evaluate their effects on I

the hot channel local coolant conditions and MDNBR.

~

Subcooled Void BulLVid

[

Levy Zuber Findlay EPRI EPRI I-

l E

TR 087 Rev. O g

Page 50 E

The hot channel MDNBRs are given in Table 6.6 for the Case 1 and 2 operating conditions. As Table 6.6 shows, the combination of the Levy subcooled void correlation and the Zuber Findlay bulk void correlation yields slightly conservative results. Section 33 of Volume 4 of the VIPRE-01 manual, Reference 1.1, presents the results of g

VIPRE-01 predictions of the Martin void fraction tests at high pressure B

(1565 and 1991 psia). Of the two-phase flow correlations evaluated, the Levy /Zuber Findlay combinations compared most favorably with the test results. The Levy subcooled void correlation and the Zuber-Findlay correlation will be used for TMI 1 thermal-hydraulic analyses.

63.4 Heat Transfer Correlations Heat transfer correlations are used by the VIPRE-01 code when the conduction model is specified. The code contains a set of correlations for each of the four major segments of the boiling curve: single phase forced convection, subcooled boiling, saturated nucleate boiling and film boiling.

The default single phase forced convection correlation, the Dittus-Boelter correlation with the leading coefficient compatible with the EPRI void model is used in the TMI 1 VIPRE-01 model To quantify the effects of different nucleate boiling correlations on MDNBR, a sensitivity study was performed during a four to three pump coastdown transient. The :-sults given in Table 6.7 show that the choice of I

nucleate boiling correlations make very little difference in the MDNBR.

As is to be expected, the correlations show very close comparison until after the reactor is tripped, when slight deviations occur. However, the g

Thom subcooled and saturated nucleate boiling correlations yielded a 5

conservative MDNBR and will be used in the TMI 1 model For DNB analysis, the BWC correlation is selected, which is consistent with the type of fuelin the core.

Il

TR 087 h

Rev.O

)

Page 51 6.4 Conduction Model kasitivity I

In order to demonstrate the adequacy of applying the conduction model to only i

)

four fuel rods, a four to three pump coast down trar.sient was run with all the fuel j

[

rods as conducting rods. As shown on Table 6.8, the minimum DNBR which I~

occurs shortly after reactor trip, is not affected and the use of four conducting rods

)

is adequate to capture the lag between the heat flux and neutron power after scram, for MDNBR purposes.

i 4

l

E, TR 087 Rev. O Page 52 I

I Table 6.1: Operating Conditions for Sensitivity Studies Inlet Can Power Ekm Pressure Temperature

(%)

(%)

(Psia)

('F)

I 1

91 74.7 2135 552.7 2

125 100 2135 539.7 I

I I

I l

I l

I l

I i

I I:

l

W'.

4-TR 087 Rev. 0 Page 53 r

W

{

Table 6.2: VIPRE 01 DNBR Results of Model Nodall= tion Sensitivity Study F

Caat MDNBR Detailed Model")

Base Modela)

Simplified ModeP L

1 2.015 2.012 2.023 2

1.723 1.722 1.729 r

L b

m See Figure 6.1 of VIPRE-0130 Channel Model (Detailed Model) m See Figure 4.1 of VIPRE-01 13 Channel Model (Base Model) m See Figure 6.2 of VIPRE-01 12 Channel Model (Simplified Model) i 1

(

(

(

E' as TR 037 Rev. O gl Page 54 g

I Table 63: VIPRFAI DNBR Results of the Axlal Noding Sensitivity Study I1 MDNBR Node Size Case 1 Elevation Case 2 Elevation 3" node from 0" to 120" 5" node from 120" to 160" 2.008 96-99" 1.719 93 %"

Base Model 2.012

% 98" 1.722 93-94" I

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TR 087 g.

Rev.O Page 55 i

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e Table 6A: Tudmient Momentum Factor Sensitivity Study i

F EDd MDNBR

]

CASEI CASE 2

!E 0.0 2.027 1.730 O.8 2.012 1.722 p'

L.,

1.0 2.01 1.721 L

s l

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TR 087 Rev. O Page 56 Il i

I Table 6.5: Turbant Mixing Coefficient Sensitivity Study I

8-Coerf.

MDNBR CASE 1 CASEJ J

l 0.0 1.874 1.624 l

0.01 1.982 1.7 0.02 2.012 1.722 l

0.03 2.032 1.736 I

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TR 087 Rev. O Page 57 I

Table 6.6: Flow Correlation and Two Phase Friction Multiplier Sensitivity Study I

I i

Subcooled Bulk Two Phase MDNBR l

Void ygid Friction Multiolier Case 1 Case 2 i

L I

F EPRI EPRI EPRI 2.026 1.727 L

EPRI EPRI HOMO 2.026 1.727 EPRI EPRI BEAT 2.04 1.735 LEVY ZUBR EPRI 2.012 1.722

{

~

L_

LEVY ZUBR HOMO 2.016 1.723 LEVY ZUBR BEAT 2.012 1.731 FL I

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__-_______________________.________________._-_________m_

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E TR 087 g

Rev. O g

Page 58 Il Table 6.7: Nucleate Bouing Heat Transfer Comlation Sensitivity Study I

TIME MDNBR (SEC)

THOM/THOM THSPNHSP CHEN/CHEN I

0.0 1.912 1.912 1.912 1.0 im 1.873 1.874 2.0 1.826 1.827 1.830 3.0 1.783 1.783 1.787 4.0 1.735 1.736 1.739 5.0 1.701 1.704 5.3

..i7 1.671 1.675 5.4 1.666 1.667 1.671

• 5.5 1.662 1.663 1.667 5.6 1.663 1.663 1.666 5.7 1.669 1.667 1.669 5.8 1.683 1.679 1.679 6.0 1.754 1.744 1.737 l

• Power starts decreasing as a result of reactor trip I

I I

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r

TR 087 Rev. O Page 59 Table 6.8: Sensitivity to Number of Conducting Rods MDNBR All Rods l

Ilme (Sec)

Base Model Conducting 0.0 1.912 1.912 1.0 1.872 1.872 2.0 1.826 1.827 3.0 1.783 1.784 4.0 1.735 1.736 5.0 1.7 1.701 5.3 1.67 1.671 5.4 1.666 1.667

• 5.5 1.662 1.664 5.6 1.663 1.663 5.7 1.669 1.666 5.8 1.683 1.674 6.0 1.754 1.719

• Power starts decreasing as a result of reactor trip L

i

aI FIGURE 6.1 VIPRE-0130 CHANNEL MODEL (DETAILED MODEL)

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7.0 TMI-1 TIIERMAIA1YDRAULIC ANALYSES USING VIPRE-01 A thermal-hydraulic analysis of the TMI 1 reactor core is necessary to define the core thermal margin and acceptable operating limits. This section describes how the VIPRE-01 code will be applied for future thermal-hydraulic analyses during the reload design process.

7.1 Thermal-Hydraulle Design Criterion ne maximum thermal-hydraulic design conditions for TMI-1 Cycle 9 are given in Table 7.1. The thermal-hydraulic design criterion is that the hot fuel rod in the core shall not experience a departure from nuclea:e boiling (DNB) during both steady state operation and anticipated transients. His DNB safety criterion is numerically represented by a design DNBR (DDNBR) limit value of 1.18 with the BWC CHF correlation, which ensures 95% population protection with 95%

confidence as discussed in Section 5.1 of this report.

I Based on the above DNBR safety criterion, the VIPRE 01 crossflow model will be applied to derive the core protection limits and core operating limits. He core protection limits consist of the pressure temperature envelope (Figure 7.1), the axial power imbalance protective limits (Figure 7.2a), and the flux / flow limit (Figure 7.2b). These limits are used to determine the reactor protection system (RPS) trip setpoints, which would trip the reactor prior to exceeding the thermal l

limits. He core operating limits (or limiting conditions f'or operatic n - LCO) consist of axial power imbalance limits (Figure 73).nd control rod insertion limits (Figure 7.4).

i I

Il g-i

1 TR 087 Rev. O Page 63 A new analysis is performed for a reload core whenever there is a significant change in the fuel design, a change in thermal-hydraulic conditions, or a change in the regulatory criteria. The VIPRE 01 DNBR analysis for the various reactor l

transients given in the TMI 1 FSAR, Chapter 14 will be performed with forcing functions (power, pressure, and temperature as a function of time) from the RETRAN code (Reference 7.1).

7.2 Generic Maximum Allowable Peaking (MAP) Limit Curves DNBR analyses for transient events in the TMI 1 FSAR and for the determination of RPS safety limits are performed using a reference design power peaking factor of 1.714 with a center peaked axial power shape given in Figure 4.2. However, the actual power operation could produce not only a center peaked shape as given in Figure 4.2, but also various skewed types of axial power shapes depending upon the given on-rating parameters. For example, the axial power shape could become bottom-peaked with a certain degree of control rod insertion, or a top-peaked shape when a xenon mismatch condition occurs during a load swing mode.

Maximum allowable peaking (MAP) limits ensure that the reference design peaking factor with the center-peaked power shape in Figure 4.2 bounds the various axial power shapes and corresponding power peaking factors throughout a fuel cycle operation. In other words, MAP limits are determined to represent DNBR performance equivalent to the design power distribution used for both RPS trip setpoint analyses and limiting transients in the FSAR. A typical set of MAP limit' curve is shown in Figure 7.5, which are a family of curves of the maximum allowable peaking points at which the minimum DNBR is equal to the target DNBR limit.

MAP limits are used as input to the determination of both RPS trip setpoints and core operating limits (or LCO). Depending upon how MAP limits are applied, they are called either RPS MAP or LCO MAP limits. 'Ihe RPS MAP limits are applied in determining the axial power imbalance protective limits given in Figure

E-TR 087 Rev. O g

Page 64 3

72, while the LCO MAP limits are used for the axial power imbalance limits (Figure 73) and control rod insertion limits (Figure 7.4). Therefore, two sets of MAP limit curves are generated with two different analysis criteria.

He RPS MAP limit analysis is performed by using the VIPRE-01 hot channel model given in Figure 4.1 at the reference design condition for power (112%),

coolant flow, and system pressure. He target DNBR limit is determined as the worst of DNBR results analyzed along the pressure temperature limit state points in Figure 7.1 applying the reference design axial power profile given in Figure 42.

In general, the extremities of the P T protection envelope (high temperature and low pressure point) in Figure 7.1 provide the worst DNBR. Once the target DNBR is determined, VIPRE-01 hot channel analyses are performed based on various axial power shapes given in Figures 7.6a and 7.6b. Figure 7.6a shows how the peaking factors are varied for a fixed axial peak location, while Figure 7.6b shows the variation of the axial peak locations for a fixed axial peaking factor. For a given axial power shape, the MAP limit is determined by incretsing the fuel pin l

peaking factor in the hot channel until the target DNBR limit is reached. This pin peaking factor multiplied by corresponding axial peaking factor becomes a total MAP limit for a specified axial peak and its location.

The target DNBR limit for the LCO MAP limits are determined as the minimum DNBR for the limiting loss-of-coolant flow transient, which is given in Figure 7.7.

LCO MAP limit curves are developed in the same manner as the RPS MAP limits.

If a predicted peaking factor from an analysis is greater than,the appropriate MAP limit, the minimum DNBR will be calculated by incorporating both the predicted radial power distribution and axial power shape directly into the VIPRE-01 code.

He MAP margin evaluation for the setpoint analysis is further described below in Section 73.2.

i i

I.

f P

TR 087 Q

Rev. 0 Page 65 l

y f

d I

r 73 Reactor Pradacelan System (RPS) Safety Lhnits L,

he following subsections discuss how the VIPRE-01 code is applied in y

k determining the DNBR-related safety limits such as the core P T envelope, power imbalance protective limits and the flux / flow limit.

73.1 Core Pressure Temperature Envelope ne core P-T envelope is shown in Figure 7.1 and includes the core protection safety limits and the core P T RPS trip setpoints. The core I

protection safety limit represents the thermal hydraulic conditions at which the minimum design DNBR (= 1.18) or greater is predicted with the reference design peaking factor of 1.714 and at the maximum over-

[

power of 112%. It limits reactor coolant outlet temperature and outlet pressure.

The determination of core protection safety limits requires a series of VIPRE 01 hot channel analyses by varying coolant Dow, inlet temperature, and system pressure. He DNB analysis for each particular pump condition is performed at the maximum design overpower condition. The design overpower for 4 pump operation is 112%. De core protection safety limit for each pump condition is -

{

determined at a pressure temperature statepoint at which the minimum DNBR reaches the design limit of 1.18.

[-

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E us TR 087 Rev. O Page 66 73.2 Axial Power Imbalance Protective Limits ne axial power imbalance protective limits and corresponding reactor trip setpoints are shown in Figures 7.2a and 7.2b. These figures contain two typ s of protective limits, one is the axial power imbalance limit and the other is flux / flow limit (horizontal lines for each pump condition in Figures 7.2a and 7.2b). He purpose of these limits and setpoints is to provide core protection during transients involving a flow reduction and during abnormal conditions involving excessive power I

ne safety criteria for the detennination of the imbalance limits are:

(1) center fuel melt (CFM) limit and (2) DNBR criterion. The DNBR criterion is numerically represented by the RPS MAP limits as described in Section 7.2.

The maneuvering analysis generates three dimensional power distributions and imbalances for various operating conditions such as control rod positions, fuel burnup, xenon mismatch, and power levels.

The VIPRE-01 generated RPS MAP limits are compared with i

calculated power distribution data from maneuvering analysis as a function of power imbalance. The RPS MAP margins, a(MAP), are determined as-4(MAP) = (MAP lirnit - 3D peaking) / MAP limit nese RPS MAP margins are plotted as a function of power imbalance gl at each maneuvering analysis statepoint throughout a fuel cycle m'

operation. Then, the imbalance limit is determined as an imbalance point where a zero margin occurs. If a negative margin occurs, DNBR I.

I

E TR 087 I

Rev. O i

Page 67 analysis is performed with the predicted values of peaking and I

corresponding axial power shapes directly inputted to the VIPRE-01 d.

i 733 Flux / Flow Limits l

De main purpose of the flux / flow trip (=1.08 in Figure 7.2b) is to l

provide the DNBR protection during the loss of coolant Dow (LOCF) transients (pump coastdown events). It also functions as an overpower j

trip when the plant is in a partial pump operation as shown in Figure 7.2b for both 3 and 2 pump conditions.

L The limiting LOCF transient for TMI 1 is a one-pump coastdown from F

four-pump operation. His is because the redundant power / pump L_

status monitor immediately trips the reactor if power is lost to two or more pumps.

VIPRE-01 transient analysis based on a 1.08 flur/ flow setpoint is discussed in Section 5.4 and also shown in Figure 7.7. The VIPRE-01 analysis assumes the initial power of the 4 to 3 pump coastdown as 108% (102% + 2% heat balance error + 4% neutron measurement error = 108%). He reference design radial peaking of 1.714 is used as well as the axial power shape of 1.65 cosine with tails as shown in Figure 4.2.

DNBR becomes smaller as coolant flow is reduced during the pump

[

coastdown. When the minimum DNBR reaches the design DNBR limit at a certain time into the pump coastdown, the ratio of the power to

[

the flow is determined to be the Dux/ flow limit after incorporating the instrumentation delay time and uncertainties as shown in Figure 7.7.

[

L M

E TR 087 Rev. O Page 68 with the flux / flow trip setpoint of 1.08, as shown in Figure 7.8, the Cycle 9 minimum DNBR decreases to 1.637 from an initial value of 1.886. Comparing the minimum DNBR result with the design DNBR limit of 1.18, the trip setpoint of 1.08 produces a safety margin of 38.%

(= 1.6291.18)/1.18)). In fact, Figure 7.9 shows that the minimum DNBR never reaches the design DNBR limit of 1.18 even without the flux / flow trip being activated (minimum DNBR=1.282). This means that the TMI-1 flux / flow setpoint of 1.08 is quite conservative, mainly because the limiting LOCF event is the 4 to-3 pump coastdown.

7.4 Care Operating Limits ne core operating limits (or limiting conditions for operation LCO) mainly consist of axial power imbalance limits (APIL) in Figure 73 and control rod insertion limits (CRIL) in Figure 7.4. The safety criteria for these alarm limits are: (1)

LCO MAP limits (DNBR criterion), (2) LOCA linear heat generation limits, (3) g shutdown margin, and (4) ejected rod werth limits.

5 The VIPRE-01-generated LCO MAP limits described in Sectior. 7.2 are compared with the predicted power distributions from the maneuvering analyses he LCO MAP margins are calculated by applying analysis uncertainties and other peaking a gnentation factors such as the quadrant tilt factor and transient xenon factors.

Then alarm limits are determined by using the same approach as given in Section 73.2.

I I

I I

I; I!

L F

TR 087 Rev. 0 Page 69 L

Table 7.1. Maximum Thermal-Hydraulle Design Conditions for TMI 1 Cycle 9 7

L Cvele 9 2568 Design power level, MWt (a) l 2200 System pressure, psia 374880 F

Reactor coolant flow, gpm l

8.8 Core bypass flow, %(a)

Crossflow L-DNBR modeling 1.714 Reference design radial-local power peaking factor r

L 1.65 cosine Reference design axial flux shape r

Hot channel factors 1.011 Enthalpy rise 1.014 Heat flux 0.97 l

Flow area 141.8 Active fuel length, in. (b) 2 174 Avg heat flux at 100% power,10' Btu /h ft 492 Max heat flux at 100% power,10$ Btu /h-ft' BWC CHF correlation 1.18 CHF correlation DNB limit Minimum DNBR 1.77 at 112% power'-

2.01 at 102% power f

(a)

Used in the analysis.

(b)

Cold nominal stack height.

E TR 087 eels l

Figure 7.1 Core Pressure-Temperature Envelope l

2,500 Core P-T Tr:p Setpoints l

,b I

2,300 I

^c)

'iT) g S:

u 2,100 vs 8

High Te mp, Low Pressure g

Statepoint l

\\

l O 1,900 x

a

/ \\

o 3

m Core Protection 3

Safety U mits I!

1,700 jI!

I 1,500 g

540 560 580 600 620 640 660 g

Reactor Outlet Temperature (Deg-F)

I Il l,

~

Ta ou J

Rev.O Figure 7.2a Typical Axial Power Imbalance Protective Limits L

Thermal Power Level, %

L

--120 F

L 4 PUMP L

OPERATION

-- 100 E

u 3 PUMP r

L OPERATION

-- 80

[

^

-- 60 2 PUMP OPERATION L

-_ 40 f

[

-- 20

[

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-80

-60 40

-20 0

20 40 60 80 Axial Power Imbalance, %

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El

=1 TR 067 gi Rev.0 Figure 7.2b Protection System Setpoints g;

For Axial Power Imbalance Thermal Power Level, %

l

--120 I

E i 4 PUMP

--100 I

i OPERATION l

Flux / Flow Setpoints i

~~ 80 l 3 PUMP j

! OPERATION i

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-- 60 i

i i

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20 40 60 80 Axial Power imbalance, %

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TR067 Rev.O Figure 7.3 Typical Axial Power Imbalance Limits 110 RESTRICTED REGION 100 90 PERMISSIBLE 80

-REGION :

l b3 E

50 0

t-8 cc 20 0

-50

-40

-30

-20

-10 0

10 20 30 40 50 Axial Power Imbalance

El TR 067 oge 74 Figure 7.4 Typical Control Rod Insertion Limits I

I 110 100 NOT ALLOWED 90 REGION 80 g

70 k

60 RESTRICTED REGION u

O 50 CC l

40 PERMISSIBLE 30 REGION 20 I

0 0

50 100 150 200 250 300 indicated Rod index, % Withdrawn g,

l i

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Page 75

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FIGURE 7.5 A TYPICAL SET OF MAP LIMITS 3.5 1.9 r

L r

3 L

u)

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a 0

1.5 p

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I 25

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1.5 0

0.2 0.4 0.6 0.8 i

AXtAL LOCATION ALONG HEATED LENGTH (X/L) 1

R t

1"!

g Figure 7.6a Typical Axial Power Shapes l

for VIPRE-01 MAP Limit Analyses

[ Fixed Peak Location (x/l = 0.4)]

l 2

1.9 1.7 1.6 1.5 1.4 1.3 1.2 g

1.1 E

Lt.

• g 1

g

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.8 0

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0.6 0.4 O.2 L

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0.2 0.4 0.6 0.8 1

Distance Along Heated Length (X/L) l I

l

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TR 057 ge 77 Figure 7.6b l

Typical Axial Power Shapes for VIPRE-01 MAP Limit Analyses

[ Fixed Axial Peak Value of 1.5]

)

I 1.8 -

1.6 0.2 0.4 0.6 0.8 1.4 -

l 8

g 1.2 U-jl 32 1

s Q.

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0.6 O.4 O.2 I

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O 0.2 0.4 0.6 0.8 1

-l Distance Along Heated Length (X/L)

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=l TR 087 Rev. O Page T8 FIGURE 7.7. DETERMINATION OF FLUX / FLOW RATIO 1.00 I

REATOR POWER = 108% CONSTANT TRIP POWER

/

/

COOLANT FLOW 8 0.90 IN FRACTION Po DNER = 1.18 AT THIS Poll T E

E b

TRIP FLOW i

,O 0.85 K

TRIP P LIMIT

)

(

TRIP

/

TRIP DELAY TIME A

I' 0.80 I

F/F TRIP MUST BE INITIATED AT THIS TIME I

i 0,75 0

1 2

3 4

5 6

7 8

9 to TIME AFTER PUMP TRIP IN SECONDS I

a

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l TR 067 Rev.0 Pape 79 FIGURE 7.8 DNBR RESULTS FOR THE 4-TO-3 PUMP COASTDOWN WITH FLUX / FLOW TRIP 7

l 2.00 3

l l DN8R RESULTS l

/

1.75

(

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[

l I

l h1*50 DNBR = 1.637 AMNST DNBR LNIT OF 1.18

[

2

(

a.

5 iEO 1.25 FLUX / FLOW TRIP y

3 t= 5.3 see POWER LEVEL f,

100% @ t = 0

.1 g

E e 1.00 <

E

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COOLANT FLOW:

(

FRACTION OF

(

0.75 DESIGN FLOW

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1 2

3 4

5 6

7 8

(

TIME AFTER PUMP TRIP IN SECONDS E

_________.._______________.______.____________.__________o

O TR 067 Rev. 0 Page 80 FIGURE 7.9 DNBR RESULTS FOR THE 4-TO 3 PUMP COASTDOWN WITHOUT FLUX / FLOW TRIP 2.00 I

1.75 DNBR RESULTS 1*50 DNBR = 1.282 AMNST w

DNBR LIMIT OF 1.18 Y

n.

b V

iE 0 1.25 THERMAL POWER y

= 106% FP i

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= ~ =f 0.75 0

l Ii 0.50 3

0 10 20 M

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TIME AFTER PUMP TRIP IN SECONDS j

=

l I

TR 087

(

Rev. 0

[

Page 81 l.

~

I

8.0 CONCLUSION

S 1

nis report presents the methods for performing core thermal-hydraulic analysis for Dree Mile Island Unit 1 Nuclear Power Station. A description of the VIPRE-01 i

model and general code features have been discussed, ne methodology and l

adequacy of the model for licensing applications has been demonstrated by comparison of representative analytical results to both vendor calculations and test I

data. Sensitivity studies further justify the overall model and code options, and l

assure that these are selected so as to predict a conservative response. His

[

demonstrates GPUN's ability to perform core thermal hydraulic licensing analysis of TMI 1, using VIPRE 01.

(

(

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[

(

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TR 087 Rev. O Page 82

9.0 REFERENCES

1.1 VIPRE-01

"A Thermal Hydraulic Code for Reactor Cores," Volumes 1-4, EPRI-NP 2511-CCM A, Rev. 3, August 1989.

W 1.2 Letter from A. C. Thadani (NRC) to Y. Y. Yung (UG RA)," Acceptance for Referencing of the Modified Licensing Topical Report, VIPRE-01: A Thermal Hydraulic Analysis Code for Reactor Cores," EPRI NP-2511-CCM, Rev. 3, October 30,1993.

4.1 BAW 2134, TMI 1 Cycle 9 Reload Report," May 1991.

ga 4.2 BAW 211P, TMI 1 Cycle 8 Final Design Report," May 1990.

4.3 BAW 0156, "LYNXT; Core Transient Thermal-Hydraulic Program," B&W, February 1984.

4.4 TMI-1 Final Safety Analysis Report, Updated Version March 1994.

5.1 BAW 10143P-A, "BWC Correlation of Critical Heat Flux," B&W, April 1985.

I 5.2 BAW-0130, " LYNX 2; Subchannel Thermal Hydraulic Analysis Program,"

B&W, February 1984.

5.3 DPC NE 2003-A, " Duke Power Compan." Oconee Nuclear Station, Core l

T H Methodology using VIPRE-01," October 1989.

I 5.4 NRC Docket Nos.: 50-269, 270, & -287, " Safety Evaluation Report on DPC NE-2003," July 19,1989.

5.5 BAW-10143 A,"BWC Correlation of Critical Heat Flux," B&W, April 1985

.B

m I

I TR 087 Rev. 0 Page 83 5.6 GPUN TDR 930 " Qualification of BWC CHF Correlation on VIPRE-01 Code," August 1988.

l 5.7 Owen, D.B., " Factors for One sided Tolerance Limits and for Variables Sampling Plane," SCR 607, March 1%3.

I 5.8 BAW-2015,"TM11 Cycle 7 Reload Report, March 1988, and GPUN SE l

)

No. TI-135400-005," Cycle 7 Reload Safety Evaluation Report," December 1989 I

7.1 GPUN Topical Report No. TR-078 Rev. O, "TMI 1 Transient Analyses Using the RETRAN Computer Code," January 6,1995 I

I I

iI l

i l